axiom-databases 20170501-3 / usr / share / axiom-20170501 / algebra / interp.daase

(5967261 . 3683892817)       
((|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) 62) (((|Boolean|) $) NIL)) (|sort!| (($ (|Mapping| (|Boolean|) |#2| |#2|) $) 17) (($ $) NIL)) (|setelt| ((|#2| $ (|Integer|) |#2|) NIL) ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) 34)) (|reverse!| (($ $) 58)) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) 40) ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) 38) ((|#2| (|Mapping| |#2| |#2| |#2|) $) 37)) (|position| (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) 22) (((|Integer|) |#2| $) NIL) (((|Integer|) |#2| $ (|Integer|)) 70)) (|parts| (((|List| |#2|) $) 13)) (|merge| (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) 47) (($ $ $) NIL)) (|map!| (($ (|Mapping| |#2| |#2|) $) 29)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL) (($ (|Mapping| |#2| |#2| |#2|) $ $) 44)) (|insert| (($ |#2| $ (|Integer|)) NIL) (($ $ $ (|Integer|)) 49)) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) 24)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 21)) (|elt| ((|#2| $ (|Integer|) |#2|) NIL) ((|#2| $ (|Integer|)) NIL) (($ $ (|UniversalSegment| (|Integer|))) 48)) (|delete| (($ $ (|Integer|)) 55) (($ $ (|UniversalSegment| (|Integer|))) 54)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) 26) (((|NonNegativeInteger|) |#2| $) NIL)) (|copyInto!| (($ $ $ (|Integer|)) 51)) (|copy| (($ $) 50)) (|construct| (($ (|List| |#2|)) 52)) (|concat| (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 63) (($ (|List| $)) 61)) (|coerce| (((|OutputForm|) $) 69)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 20)) (= (((|Boolean|) $ $) 64)) (< (((|Boolean|) $ $) 72))) 
(((|OneDimensionalArrayAggregate&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE = ((|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE |sort!| (|#1| |#1|)) (SIGNATURE |sort!| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1|)) (SIGNATURE |reverse!| (|#1| |#1|)) (SIGNATURE |copyInto!| (|#1| |#1| |#1| (|Integer|))) (SIGNATURE |sorted?| ((|Boolean|) |#1|)) (SIGNATURE |merge| (|#1| |#1| |#1|)) (SIGNATURE |position| ((|Integer|) |#2| |#1| (|Integer|))) (SIGNATURE |position| ((|Integer|) |#2| |#1|)) (SIGNATURE |position| ((|Integer|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |sorted?| ((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) |#1|)) (SIGNATURE |merge| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1| |#1|)) (SIGNATURE |setelt| (|#2| |#1| (|UniversalSegment| (|Integer|)) |#2|)) (SIGNATURE |insert| (|#1| |#1| |#1| (|Integer|))) (SIGNATURE |insert| (|#1| |#2| |#1| (|Integer|))) (SIGNATURE |delete| (|#1| |#1| (|UniversalSegment| (|Integer|)))) (SIGNATURE |delete| (|#1| |#1| (|Integer|))) (SIGNATURE |elt| (|#1| |#1| (|UniversalSegment| (|Integer|)))) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2| |#2|) |#1| |#1|)) (SIGNATURE |concat| (|#1| (|List| |#1|))) (SIGNATURE |concat| (|#1| |#1| |#1|)) (SIGNATURE |concat| (|#1| |#2| |#1|)) (SIGNATURE |concat| (|#1| |#1| |#2|)) (SIGNATURE |construct| (|#1| (|List| |#2|))) (SIGNATURE |find| ((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2| |#2|)) (SIGNATURE |elt| (|#2| |#1| (|Integer|))) (SIGNATURE |elt| (|#2| |#1| (|Integer|) |#2|)) (SIGNATURE |setelt| (|#2| |#1| (|Integer|) |#2|)) (SIGNATURE |count| ((|NonNegativeInteger|) |#2| |#1|)) (SIGNATURE |parts| ((|List| |#2|) |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |map!| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |copy| (|#1| |#1|))) (|OneDimensionalArrayAggregate| |#2|) (|Type|)) (T |OneDimensionalArrayAggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE = ((|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE |sort!| (|#1| |#1|)) (SIGNATURE |sort!| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1|)) (SIGNATURE |reverse!| (|#1| |#1|)) (SIGNATURE |copyInto!| (|#1| |#1| |#1| (|Integer|))) (SIGNATURE |sorted?| ((|Boolean|) |#1|)) (SIGNATURE |merge| (|#1| |#1| |#1|)) (SIGNATURE |position| ((|Integer|) |#2| |#1| (|Integer|))) (SIGNATURE |position| ((|Integer|) |#2| |#1|)) (SIGNATURE |position| ((|Integer|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |sorted?| ((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) |#1|)) (SIGNATURE |merge| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1| |#1|)) (SIGNATURE |setelt| (|#2| |#1| (|UniversalSegment| (|Integer|)) |#2|)) (SIGNATURE |insert| (|#1| |#1| |#1| (|Integer|))) (SIGNATURE |insert| (|#1| |#2| |#1| (|Integer|))) (SIGNATURE |delete| (|#1| |#1| (|UniversalSegment| (|Integer|)))) (SIGNATURE |delete| (|#1| |#1| (|Integer|))) (SIGNATURE |elt| (|#1| |#1| (|UniversalSegment| (|Integer|)))) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2| |#2|) |#1| |#1|)) (SIGNATURE |concat| (|#1| (|List| |#1|))) (SIGNATURE |concat| (|#1| |#1| |#1|)) (SIGNATURE |concat| (|#1| |#2| |#1|)) (SIGNATURE |concat| (|#1| |#1| |#2|)) (SIGNATURE |construct| (|#1| (|List| |#2|))) (SIGNATURE |find| ((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2| |#2|)) (SIGNATURE |elt| (|#2| |#1| (|Integer|))) (SIGNATURE |elt| (|#2| |#1| (|Integer|) |#2|)) (SIGNATURE |setelt| (|#2| |#1| (|Integer|) |#2|)) (SIGNATURE |count| ((|NonNegativeInteger|) |#2| |#1|)) (SIGNATURE |parts| ((|List| |#2|) |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |map!| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |copy| (|#1| |#1|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) 91) (((|Boolean|) $) 85 (|has| |#1| (|OrderedSet|)))) (|sort!| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) 82 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $) 81 (AND (|has| |#1| (|OrderedSet|)) (|has| $ (ATTRIBUTE |shallowlyMutable|))))) (|sort| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) 92) (($ $) 86 (|has| |#1| (|OrderedSet|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setelt| ((|#1| $ (|Integer|) |#1|) 49 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) 53 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 70 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) 7 T CONST)) (|reverse!| (($ $) 83 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) 93)) (|removeDuplicates| (($ $) 73 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove| (($ |#1| $) 72 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#1|) $) 69 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 71 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 68 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 67 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| ((|#1| $ (|Integer|) |#1|) 50 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#1| $ (|Integer|)) 48)) (|position| (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) 90) (((|Integer|) |#1| $) 89 (|has| |#1| (|SetCategory|))) (((|Integer|) |#1| $ (|Integer|)) 88 (|has| |#1| (|SetCategory|)))) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|new| (($ (|NonNegativeInteger|) |#1|) 64)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|minIndex| (((|Integer|) $) 40 (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) 80 (|has| |#1| (|OrderedSet|)))) (|merge| (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) 94) (($ $ $) 87 (|has| |#1| (|OrderedSet|)))) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|maxIndex| (((|Integer|) $) 41 (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) 79 (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35) (($ (|Mapping| |#1| |#1| |#1|) $ $) 59)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|insert| (($ |#1| $ (|Integer|)) 55) (($ $ $ (|Integer|)) 54)) (|indices| (((|List| (|Integer|)) $) 43)) (|index?| (((|Boolean|) (|Integer|) $) 44)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|first| ((|#1| $) 39 (|has| (|Integer|) (|OrderedSet|)))) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) 66)) (|fill!| (($ $ |#1|) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|entry?| (((|Boolean|) |#1| $) 42 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|entries| (((|List| |#1|) $) 45)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| ((|#1| $ (|Integer|) |#1|) 47) ((|#1| $ (|Integer|)) 46) (($ $ (|UniversalSegment| (|Integer|))) 58)) (|delete| (($ $ (|Integer|)) 57) (($ $ (|UniversalSegment| (|Integer|))) 56)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copyInto!| (($ $ $ (|Integer|)) 84 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) 13)) (|convert| (((|InputForm|) $) 74 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 65)) (|concat| (($ $ |#1|) 63) (($ |#1| $) 62) (($ $ $) 61) (($ (|List| $)) 60)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (>= (((|Boolean|) $ $) 77 (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) 76 (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (<= (((|Boolean|) $ $) 78 (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) 75 (|has| |#1| (|OrderedSet|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|OneDimensionalArrayAggregate| |#1|) (|Category|) (|Type|)) (T |OneDimensionalArrayAggregate|)) 
NIL 
(|Join| (|FiniteLinearAggregate| |t#1|) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| (|Integer|) |#1|) . T) ((|EltableAggregate| (|Integer|) |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteLinearAggregate| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| (|Integer|) |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|LinearAggregate| |#1|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|SetCategory|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|Type|) . T)) 
((|subtractIfCan| (((|Union| $ "failed") $ $) 12)) (- (($ $) NIL) (($ $ $) 9)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) 16) (($ (|Integer|) $) 21))) 
(((|AbelianGroup&| |#1|) (CATEGORY |domain| (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|)) (SIGNATURE |subtractIfCan| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|AbelianGroup|)) (T |AbelianGroup&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|)) (SIGNATURE |subtractIfCan| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19))) 
(((|AbelianGroup|) (|Category|)) (T |AbelianGroup|)) 
((- (*1 *1 *1) (|ofCategory| *1 (|AbelianGroup|))) (- (*1 *1 *1 *1) (|ofCategory| *1 (|AbelianGroup|))) (* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|AbelianGroup|)) (|isDomain| *2 (|Integer|))))) 
(|Join| (|CancellationAbelianMonoid|) (CATEGORY |domain| (SIGNATURE - ($ $)) (SIGNATURE - ($ $ $)) (SIGNATURE * ($ (|Integer|) $)))) 
(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((|zero?| (((|Boolean|) $) 10)) (|sample| (($) 15)) (* (($ (|PositiveInteger|) $) 14) (($ (|NonNegativeInteger|) $) 18))) 
(((|AbelianMonoid&| |#1|) (CATEGORY |domain| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE |zero?| ((|Boolean|) |#1|)) (SIGNATURE |sample| (|#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|AbelianMonoid|)) (T |AbelianMonoid&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE |zero?| ((|Boolean|) |#1|)) (SIGNATURE |sample| (|#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|sample| (($) 16 T CONST)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (+ (($ $ $) 13)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14))) 
(((|AbelianMonoid|) (|Category|)) (T |AbelianMonoid|)) 
((|Zero| (*1 *1) (|ofCategory| *1 (|AbelianMonoid|))) (|sample| (*1 *1) (|ofCategory| *1 (|AbelianMonoid|))) (|zero?| (*1 *2 *1) (AND (|ofCategory| *1 (|AbelianMonoid|)) (|isDomain| *2 (|Boolean|)))) (* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|AbelianMonoid|)) (|isDomain| *2 (|NonNegativeInteger|))))) 
(|Join| (|AbelianSemiGroup|) (CATEGORY |domain| (SIGNATURE (|Zero|) ($) |constant|) (SIGNATURE |sample| ($) |constant|) (SIGNATURE |zero?| ((|Boolean|) $)) (SIGNATURE * ($ (|NonNegativeInteger|) $)))) 
(((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((* (($ (|PositiveInteger|) $) 10))) 
(((|AbelianSemiGroup&| |#1|) (CATEGORY |domain| (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|AbelianSemiGroup|)) (T |AbelianSemiGroup&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (= (((|Boolean|) $ $) 6)) (+ (($ $ $) 13)) (* (($ (|PositiveInteger|) $) 12))) 
(((|AbelianSemiGroup|) (|Category|)) (T |AbelianSemiGroup|)) 
((+ (*1 *1 *1 *1) (|ofCategory| *1 (|AbelianSemiGroup|))) (* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|AbelianSemiGroup|)) (|isDomain| *2 (|PositiveInteger|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE + ($ $ $)) (SIGNATURE * ($ (|PositiveInteger|) $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((|zerosOf| (((|List| $) (|Polynomial| $)) 29) (((|List| $) (|SparseUnivariatePolynomial| $)) 16) (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 20)) (|zeroOf| (($ (|Polynomial| $)) 27) (($ (|SparseUnivariatePolynomial| $)) 11) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 54)) (|rootsOf| (((|List| $) (|Polynomial| $)) 30) (((|List| $) (|SparseUnivariatePolynomial| $)) 18) (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 19)) (|rootOf| (($ (|Polynomial| $)) 28) (($ (|SparseUnivariatePolynomial| $)) 13) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) NIL))) 
(((|AlgebraicallyClosedField&| |#1|) (CATEGORY |domain| (SIGNATURE |zerosOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|) (|Symbol|))) (SIGNATURE |zerosOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |zerosOf| ((|List| |#1|) (|Polynomial| |#1|))) (SIGNATURE |zeroOf| (|#1| (|SparseUnivariatePolynomial| |#1|) (|Symbol|))) (SIGNATURE |zeroOf| (|#1| (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |zeroOf| (|#1| (|Polynomial| |#1|))) (SIGNATURE |rootsOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|) (|Symbol|))) (SIGNATURE |rootsOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |rootsOf| ((|List| |#1|) (|Polynomial| |#1|))) (SIGNATURE |rootOf| (|#1| (|SparseUnivariatePolynomial| |#1|) (|Symbol|))) (SIGNATURE |rootOf| (|#1| (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |rootOf| (|#1| (|Polynomial| |#1|)))) (|AlgebraicallyClosedField|)) (T |AlgebraicallyClosedField&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |zerosOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|) (|Symbol|))) (SIGNATURE |zerosOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |zerosOf| ((|List| |#1|) (|Polynomial| |#1|))) (SIGNATURE |zeroOf| (|#1| (|SparseUnivariatePolynomial| |#1|) (|Symbol|))) (SIGNATURE |zeroOf| (|#1| (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |zeroOf| (|#1| (|Polynomial| |#1|))) (SIGNATURE |rootsOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|) (|Symbol|))) (SIGNATURE |rootsOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |rootsOf| ((|List| |#1|) (|Polynomial| |#1|))) (SIGNATURE |rootOf| (|#1| (|SparseUnivariatePolynomial| |#1|) (|Symbol|))) (SIGNATURE |rootOf| (|#1| (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |rootOf| (|#1| (|Polynomial| |#1|)))) 
((~= (((|Boolean|) $ $) 7)) (|zerosOf| (((|List| $) (|Polynomial| $)) 78) (((|List| $) (|SparseUnivariatePolynomial| $)) 77) (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 76)) (|zeroOf| (($ (|Polynomial| $)) 81) (($ (|SparseUnivariatePolynomial| $)) 80) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 79)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 73)) (|squareFree| (((|Factored| $) $) 72)) (|sqrt| (($ $) 90)) (|sizeLess?| (((|Boolean|) $ $) 58)) (|sample| (($) 16 T CONST)) (|rootsOf| (((|List| $) (|Polynomial| $)) 84) (((|List| $) (|SparseUnivariatePolynomial| $)) 83) (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 82)) (|rootOf| (($ (|Polynomial| $)) 87) (($ (|SparseUnivariatePolynomial| $)) 86) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 85)) (|rem| (($ $ $) 54)) (|recip| (((|Union| $ "failed") $) 33)) (|quo| (($ $ $) 55)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 50)) (|prime?| (((|Boolean|) $) 71)) (|one?| (((|Boolean|) $) 30)) (|nthRoot| (($ $ (|Integer|)) 89)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 51)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 70)) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|factor| (((|Factored| $) $) 74)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 53) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 52)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 49)) (|euclideanSize| (((|NonNegativeInteger|) $) 57)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 56)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42) (($ (|Fraction| (|Integer|))) 65)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 69)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (/ (($ $ $) 64)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 68) (($ $ (|Fraction| (|Integer|))) 88)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ (|Fraction| (|Integer|))) 67) (($ (|Fraction| (|Integer|)) $) 66))) 
(((|AlgebraicallyClosedField|) (|Category|)) (T |AlgebraicallyClosedField|)) 
((|rootOf| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|rootOf| (*1 *1 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|rootOf| (*1 *1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|isDomain| *3 (|Symbol|)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|rootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)) (|isDomain| *2 (|List| *1)))) (|rootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)) (|isDomain| *2 (|List| *1)))) (|rootsOf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *1 (|AlgebraicallyClosedField|)) (|isDomain| *2 (|List| *1)))) (|zeroOf| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|zeroOf| (*1 *1 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|zeroOf| (*1 *1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|isDomain| *3 (|Symbol|)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|zerosOf| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)) (|isDomain| *2 (|List| *1)))) (|zerosOf| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)) (|isDomain| *2 (|List| *1)))) (|zerosOf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *1 (|AlgebraicallyClosedField|)) (|isDomain| *2 (|List| *1))))) 
(|Join| (|Field|) (|RadicalCategory|) (CATEGORY |domain| (SIGNATURE |rootOf| ($ (|Polynomial| $))) (SIGNATURE |rootOf| ($ (|SparseUnivariatePolynomial| $))) (SIGNATURE |rootOf| ($ (|SparseUnivariatePolynomial| $) (|Symbol|))) (SIGNATURE |rootsOf| ((|List| $) (|Polynomial| $))) (SIGNATURE |rootsOf| ((|List| $) (|SparseUnivariatePolynomial| $))) (SIGNATURE |rootsOf| ((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|))) (SIGNATURE |zeroOf| ($ (|Polynomial| $))) (SIGNATURE |zeroOf| ($ (|SparseUnivariatePolynomial| $))) (SIGNATURE |zeroOf| ($ (|SparseUnivariatePolynomial| $) (|Symbol|))) (SIGNATURE |zerosOf| ((|List| $) (|Polynomial| $))) (SIGNATURE |zerosOf| ((|List| $) (|SparseUnivariatePolynomial| $))) (SIGNATURE |zerosOf| ((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| (|Fraction| (|Integer|))) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| (|Fraction| (|Integer|))) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T) ((|RightModule| (|Fraction| (|Integer|))) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|UniqueFactorizationDomain|) . T)) 
((|zerosOf| (((|List| $) (|Polynomial| $)) NIL) (((|List| $) (|SparseUnivariatePolynomial| $)) NIL) (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 50) (((|List| $) $) 19) (((|List| $) $ (|Symbol|)) 41)) (|zeroOf| (($ (|Polynomial| $)) NIL) (($ (|SparseUnivariatePolynomial| $)) NIL) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 52) (($ $) 17) (($ $ (|Symbol|)) 37)) (|rootsOf| (((|List| $) (|Polynomial| $)) NIL) (((|List| $) (|SparseUnivariatePolynomial| $)) NIL) (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 48) (((|List| $) $) 15) (((|List| $) $ (|Symbol|)) 43)) (|rootOf| (($ (|Polynomial| $)) NIL) (($ (|SparseUnivariatePolynomial| $)) NIL) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) NIL) (($ $) 12) (($ $ (|Symbol|)) 39))) 
(((|AlgebraicallyClosedFunctionSpace&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |zerosOf| ((|List| |#1|) |#1| (|Symbol|))) (SIGNATURE |zeroOf| (|#1| |#1| (|Symbol|))) (SIGNATURE |zerosOf| ((|List| |#1|) |#1|)) (SIGNATURE |zeroOf| (|#1| |#1|)) (SIGNATURE |rootsOf| ((|List| |#1|) |#1| (|Symbol|))) (SIGNATURE |rootOf| (|#1| |#1| (|Symbol|))) (SIGNATURE |rootsOf| ((|List| |#1|) |#1|)) (SIGNATURE |rootOf| (|#1| |#1|)) (SIGNATURE |zerosOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|) (|Symbol|))) (SIGNATURE |zerosOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |zerosOf| ((|List| |#1|) (|Polynomial| |#1|))) (SIGNATURE |zeroOf| (|#1| (|SparseUnivariatePolynomial| |#1|) (|Symbol|))) (SIGNATURE |zeroOf| (|#1| (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |zeroOf| (|#1| (|Polynomial| |#1|))) (SIGNATURE |rootsOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|) (|Symbol|))) (SIGNATURE |rootsOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |rootsOf| ((|List| |#1|) (|Polynomial| |#1|))) (SIGNATURE |rootOf| (|#1| (|SparseUnivariatePolynomial| |#1|) (|Symbol|))) (SIGNATURE |rootOf| (|#1| (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |rootOf| (|#1| (|Polynomial| |#1|)))) (|AlgebraicallyClosedFunctionSpace| |#2|) (|Join| (|OrderedSet|) (|IntegralDomain|))) (T |AlgebraicallyClosedFunctionSpace&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |zerosOf| ((|List| |#1|) |#1| (|Symbol|))) (SIGNATURE |zeroOf| (|#1| |#1| (|Symbol|))) (SIGNATURE |zerosOf| ((|List| |#1|) |#1|)) (SIGNATURE |zeroOf| (|#1| |#1|)) (SIGNATURE |rootsOf| ((|List| |#1|) |#1| (|Symbol|))) (SIGNATURE |rootOf| (|#1| |#1| (|Symbol|))) (SIGNATURE |rootsOf| ((|List| |#1|) |#1|)) (SIGNATURE |rootOf| (|#1| |#1|)) (SIGNATURE |zerosOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|) (|Symbol|))) (SIGNATURE |zerosOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |zerosOf| ((|List| |#1|) (|Polynomial| |#1|))) (SIGNATURE |zeroOf| (|#1| (|SparseUnivariatePolynomial| |#1|) (|Symbol|))) (SIGNATURE |zeroOf| (|#1| (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |zeroOf| (|#1| (|Polynomial| |#1|))) (SIGNATURE |rootsOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|) (|Symbol|))) (SIGNATURE |rootsOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |rootsOf| ((|List| |#1|) (|Polynomial| |#1|))) (SIGNATURE |rootOf| (|#1| (|SparseUnivariatePolynomial| |#1|) (|Symbol|))) (SIGNATURE |rootOf| (|#1| (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |rootOf| (|#1| (|Polynomial| |#1|)))) 
((~= (((|Boolean|) $ $) 7)) (|zerosOf| (((|List| $) (|Polynomial| $)) 78) (((|List| $) (|SparseUnivariatePolynomial| $)) 77) (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 76) (((|List| $) $) 122) (((|List| $) $ (|Symbol|)) 120)) (|zeroOf| (($ (|Polynomial| $)) 81) (($ (|SparseUnivariatePolynomial| $)) 80) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 79) (($ $) 123) (($ $ (|Symbol|)) 121)) (|zero?| (((|Boolean|) $) 15)) (|variables| (((|List| (|Symbol|)) $) 197)) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) 229 (|has| |#1| (|IntegralDomain|)))) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|tower| (((|List| (|Kernel| $)) $) 160)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) 150) (($ $ (|List| (|Equation| $))) 149) (($ $ (|Equation| $)) 148)) (|squareFreePart| (($ $) 73)) (|squareFree| (((|Factored| $) $) 72)) (|sqrt| (($ $) 90)) (|sizeLess?| (((|Boolean|) $ $) 58)) (|sample| (($) 16 T CONST)) (|rootsOf| (((|List| $) (|Polynomial| $)) 84) (((|List| $) (|SparseUnivariatePolynomial| $)) 83) (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 82) (((|List| $) $) 126) (((|List| $) $ (|Symbol|)) 124)) (|rootOf| (($ (|Polynomial| $)) 87) (($ (|SparseUnivariatePolynomial| $)) 86) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 85) (($ $) 127) (($ $ (|Symbol|)) 125)) (|retractIfCan| (((|Union| (|Polynomial| |#1|) "failed") $) 247 (|has| |#1| (|Ring|))) (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") $) 231 (|has| |#1| (|IntegralDomain|))) (((|Union| |#1| "failed") $) 193) (((|Union| (|Integer|) "failed") $) 191 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Symbol|) "failed") $) 184) (((|Union| (|Kernel| $) "failed") $) 135) (((|Union| (|Fraction| (|Integer|)) "failed") $) 119 (OR (AND (|has| |#1| (|RetractableTo| (|Integer|))) (|has| |#1| (|IntegralDomain|))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))))) (|retract| (((|Polynomial| |#1|) $) 248 (|has| |#1| (|Ring|))) (((|Fraction| (|Polynomial| |#1|)) $) 232 (|has| |#1| (|IntegralDomain|))) ((|#1| $) 194) (((|Integer|) $) 190 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Symbol|) $) 185) (((|Kernel| $) $) 136) (((|Fraction| (|Integer|)) $) 118 (OR (AND (|has| |#1| (|RetractableTo| (|Integer|))) (|has| |#1| (|IntegralDomain|))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))))) (|rem| (($ $ $) 54)) (|reducedSystem| (((|Matrix| |#1|) (|Matrix| $)) 237 (|has| |#1| (|Ring|))) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) 236 (|has| |#1| (|Ring|))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) 117 (OR (|and| (|has| |#1| (|Ring|)) (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (|and| (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|))))) (((|Matrix| (|Integer|)) (|Matrix| $)) 116 (OR (|and| (|has| |#1| (|Ring|)) (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (|and| (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|)))))) (|recip| (((|Union| $ "failed") $) 33)) (|quo| (($ $ $) 55)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 50)) (|prime?| (((|Boolean|) $) 71)) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) 189 (|has| |#1| (|PatternMatchable| (|Float|)))) (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) 188 (|has| |#1| (|PatternMatchable| (|Integer|))))) (|paren| (($ (|List| $)) 154) (($ $) 153)) (|operators| (((|List| (|BasicOperator|)) $) 161)) (|operator| (((|BasicOperator|) (|BasicOperator|)) 162)) (|one?| (((|Boolean|) $) 30)) (|odd?| (((|Boolean|) $) 182 (|has| $ (|RetractableTo| (|Integer|))))) (|numerator| (($ $) 214 (|has| |#1| (|Ring|)))) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) 213 (|has| |#1| (|Ring|)))) (|nthRoot| (($ $ (|Integer|)) 89)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 51)) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) 179 (|has| $ (|Ring|)))) (|min| (($ $ $) 133)) (|max| (($ $ $) 132)) (|map| (($ (|Mapping| $ $) (|Kernel| $)) 168)) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) 158)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|kernels| (((|List| (|Kernel| $)) $) 159)) (|kernel| (($ (|BasicOperator|) (|List| $)) 167) (($ (|BasicOperator|) $) 166)) (|isTimes| (((|Union| (|List| $) "failed") $) 208 (|has| |#1| (|SemiGroup|)))) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) 217 (|has| |#1| (|Ring|)))) (|isPlus| (((|Union| (|List| $) "failed") $) 210 (|has| |#1| (|AbelianSemiGroup|)))) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) 211 (|has| |#1| (|AbelianSemiGroup|)))) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) 216 (|has| |#1| (|Ring|))) (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) 215 (|has| |#1| (|Ring|))) (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) 209 (|has| |#1| (|SemiGroup|)))) (|is?| (((|Boolean|) $ (|Symbol|)) 165) (((|Boolean|) $ (|BasicOperator|)) 164)) (|inv| (($ $) 70)) (|height| (((|NonNegativeInteger|) $) 157)) (|hash| (((|SingleInteger|) $) 10)) (|ground?| (((|Boolean|) $) 195)) (|ground| ((|#1| $) 196)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|freeOf?| 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(|Symbol|)) 206 (|has| |#1| (|ConvertibleTo| (|InputForm|)))) (($ $) 205 (|has| |#1| (|ConvertibleTo| (|InputForm|)))) (($ $ (|List| (|Symbol|))) 204 (|has| |#1| (|ConvertibleTo| (|InputForm|)))) (($ $ (|Symbol|)) 203 (|has| |#1| (|ConvertibleTo| (|InputForm|)))) (($ $ (|BasicOperator|) (|Mapping| $ $)) 178) (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) 177) (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) 176) (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) 175) (($ $ (|Symbol|) (|Mapping| $ $)) 174) (($ $ (|Symbol|) (|Mapping| $ (|List| $))) 173) (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) 172) (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) 171) (($ $ (|List| $) (|List| $)) 142) (($ $ $ $) 141) (($ $ (|Equation| $)) 140) (($ $ (|List| (|Equation| $))) 139) (($ $ (|List| (|Kernel| $)) (|List| $)) 138) (($ $ (|Kernel| $) $) 137)) (|euclideanSize| (((|NonNegativeInteger|) $) 57)) (|elt| (($ (|BasicOperator|) (|List| $)) 147) (($ 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(|ConvertibleTo| (|Pattern| (|Integer|)))))) (|conjugate| (($ $ $) 250 (|has| |#1| (|Group|)))) (|commutator| (($ $ $) 249 (|has| |#1| (|Group|)))) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42) (($ (|Fraction| (|Integer|))) 65) (($ (|Polynomial| |#1|)) 246 (|has| |#1| (|Ring|))) (($ (|Fraction| (|Polynomial| |#1|))) 230 (|has| |#1| (|IntegralDomain|))) (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) 228 (|has| |#1| (|IntegralDomain|))) (($ (|Polynomial| (|Fraction| |#1|))) 227 (|has| |#1| (|IntegralDomain|))) (($ (|Fraction| |#1|)) 226 (|has| |#1| (|IntegralDomain|))) (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) 212 (|has| |#1| (|Ring|))) (($ |#1|) 192) (($ (|Symbol|)) 183) (($ (|Kernel| $)) 134)) (|charthRoot| (((|Union| $ "failed") $) 235 (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|box| (($ (|List| $)) 152) (($ $) 151)) (|belong?| (((|Boolean|) (|BasicOperator|)) 163)) (|associates?| (((|Boolean|) $ $) 38)) (|applyQuote| (($ (|Symbol|) (|List| $)) 202) (($ (|Symbol|) $ $ $ $) 201) (($ (|Symbol|) $ $ $) 200) (($ (|Symbol|) $ $) 199) (($ (|Symbol|) $) 198)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 69)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $ (|Symbol|)) 241 (|has| |#1| (|Ring|))) (($ $ (|List| (|Symbol|))) 240 (|has| |#1| (|Ring|))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 239 (|has| |#1| (|Ring|))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 238 (|has| |#1| (|Ring|)))) (>= (((|Boolean|) $ $) 130)) (> (((|Boolean|) $ $) 129)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 131)) (< (((|Boolean|) $ $) 128)) (/ (($ $ $) 64) (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) 225 (|has| |#1| (|IntegralDomain|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 68) (($ $ (|Fraction| (|Integer|))) 88)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ (|Fraction| (|Integer|))) 67) (($ (|Fraction| (|Integer|)) $) 66) (($ $ |#1|) 234 (|has| |#1| (|CommutativeRing|))) (($ |#1| $) 233 (|has| |#1| (|CommutativeRing|))))) 
(((|AlgebraicallyClosedFunctionSpace| |#1|) (|Category|) (|Join| (|OrderedSet|) (|IntegralDomain|))) (T |AlgebraicallyClosedFunctionSpace|)) 
((|rootOf| (*1 *1 *1) (AND (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *2)) (|ofCategory| *2 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|rootsOf| (*1 *2 *1) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *3)))) (|rootOf| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|rootsOf| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *4)))) (|zeroOf| (*1 *1 *1) (AND (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *2)) (|ofCategory| *2 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|zerosOf| (*1 *2 *1) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *3)))) (|zeroOf| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|zerosOf| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *4))))) 
(|Join| (|AlgebraicallyClosedField|) (|FunctionSpace| |t#1|) (CATEGORY |domain| (SIGNATURE |rootOf| ($ $)) (SIGNATURE |rootsOf| ((|List| $) $)) (SIGNATURE |rootOf| ($ $ (|Symbol|))) (SIGNATURE |rootsOf| ((|List| $) $ (|Symbol|))) (SIGNATURE |zeroOf| ($ $)) (SIGNATURE |zerosOf| ((|List| $) $)) (SIGNATURE |zeroOf| ($ $ (|Symbol|))) (SIGNATURE |zerosOf| ((|List| $) $ (|Symbol|))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) . T) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) . T) ((|AlgebraicallyClosedField|) . T) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) . T) ((|BiModule| |#1| |#1|) |has| |#1| (|CommutativeRing|)) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|ConvertibleTo| (|Pattern| (|Float|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) ((|ConvertibleTo| (|Pattern| (|Integer|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Evalable| $) . T) ((|ExpressionSpace|) . T) ((|Field|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) |has| |#1| (|Ring|)) ((|FullyPatternMatchable| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|FunctionSpace| |#1|) . T) ((|GcdDomain|) . T) ((|Group|) |has| |#1| (|Group|)) ((|InnerEvalable| (|Kernel| $) $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) . T) ((|LeftModule| (|Fraction| (|Integer|))) . T) ((|LeftModule| |#1|) |has| |#1| (|CommutativeRing|)) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|LinearlyExplicitRingOver| (|Integer|)) AND (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|))) ((|LinearlyExplicitRingOver| |#1|) |has| |#1| (|Ring|)) ((|Module| (|Fraction| (|Integer|))) . T) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedSet|) . T) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|Ring|)) ((|PatternMatchable| (|Float|)) |has| |#1| (|PatternMatchable| (|Float|))) ((|PatternMatchable| (|Integer|)) |has| |#1| (|PatternMatchable| (|Integer|))) ((|Patternable| |#1|) . T) ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T) ((|RetractableTo| (|Fraction| (|Integer|))) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (AND (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|RetractableTo| (|Integer|))))) ((|RetractableTo| (|Fraction| (|Polynomial| |#1|))) |has| |#1| (|IntegralDomain|)) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| (|Kernel| $)) . T) ((|RetractableTo| (|Polynomial| |#1|)) |has| |#1| (|Ring|)) ((|RetractableTo| (|Symbol|)) . T) ((|RetractableTo| |#1|) . T) ((|RightModule| (|Fraction| (|Integer|))) . T) ((|RightModule| |#1|) |has| |#1| (|CommutativeRing|)) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) 
((|yRange| (((|Segment| (|DoubleFloat|)) $) NIL)) (|xRange| (((|Segment| (|DoubleFloat|)) $) NIL)) (|refine| (($ $ (|DoubleFloat|)) 122)) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) 84)) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) 134)) (|coerce| (((|OutputForm|) $) 146))) 
(((|PlaneAlgebraicCurvePlot|) (|Join| (|PlottablePlaneCurveCategory|) (CATEGORY |domain| (SIGNATURE |makeSketch| ($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|))))) (SIGNATURE |refine| ($ $ (|DoubleFloat|)))))) (T |PlaneAlgebraicCurvePlot|)) 
((|makeSketch| (*1 *1 *2 *3 *3 *4 *4) (AND (|isDomain| *2 (|Polynomial| (|Integer|))) (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|Segment| (|Fraction| (|Integer|)))) (|isDomain| *1 (|PlaneAlgebraicCurvePlot|)))) (|refine| (*1 *1 *1 *2) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|PlaneAlgebraicCurvePlot|))))) 
(|Join| (|PlottablePlaneCurveCategory|) (CATEGORY |domain| (SIGNATURE |makeSketch| ($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|))))) (SIGNATURE |refine| ($ $ (|DoubleFloat|))))) 
((|affineSingularPoints| (((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) |#3|) 38)) (|affineRationalPoints| (((|List| |#5|) |#3| (|PositiveInteger|)) 33)) (|affineAlgSet| (((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) (|List| |#3|)) 40))) 
(((|AffineAlgebraicSetComputeWithGroebnerBasis| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |affineAlgSet| ((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) (|List| |#3|))) (SIGNATURE |affineSingularPoints| ((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) |#3|)) (SIGNATURE |affineRationalPoints| ((|List| |#5|) |#3| (|PositiveInteger|)))) (|Field|) (|List| (|Symbol|)) (|PolynomialCategory| |#1| |#4| (|OrderedVariableList| |#2|)) (|DirectProductCategory| (|#| |#2|) (|NonNegativeInteger|)) (|ProjectiveSpaceCategory| |#1|)) (T |AffineAlgebraicSetComputeWithGroebnerBasis|)) 
((|affineRationalPoints| (*1 *2 *3 *4) (AND (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|DirectProductCategory| (|#| *6) (|NonNegativeInteger|))) (|isDomain| *2 (|List| *8)) (|isDomain| *1 (|AffineAlgebraicSetComputeWithGroebnerBasis| *5 *6 *3 *7 *8)) (|ofCategory| *3 (|PolynomialCategory| *5 *7 (|OrderedVariableList| *6))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *5)))) (|affineSingularPoints| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|isDomain| *2 (|Union| (|List| *7) "failed" "Infinite" (|Integer|))) (|isDomain| *1 (|AffineAlgebraicSetComputeWithGroebnerBasis| *4 *5 *3 *6 *7)) (|ofCategory| *3 (|PolynomialCategory| *4 *6 (|OrderedVariableList| *5))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *4)))) (|affineAlgSet| (*1 *2 *3) (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|isDomain| *2 (|Union| (|List| *8) "failed" "Infinite" (|Integer|))) (|isDomain| *1 (|AffineAlgebraicSetComputeWithGroebnerBasis| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |affineAlgSet| ((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) (|List| |#3|))) (SIGNATURE |affineSingularPoints| ((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) |#3|)) (SIGNATURE |affineRationalPoints| ((|List| |#5|) |#3| (|PositiveInteger|)))) 
((|polyRing2UPUP| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) |#3|) 35)) (|allPairsAmong| (((|List| (|List| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)))) 54)) (|affineSingularPoints| (((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) 56) (((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) |#3|) 57)) (|affineRationalPoints| (((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) |#3| (|PositiveInteger|)) 51)) (|affineAlgSetLocal| (((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) (|List| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)))) 70)) (|affineAlgSet| (((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) (|List| |#3|)) 50))) 
(((|AffineAlgebraicSetComputeWithResultant| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |affineSingularPoints| ((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) |#3|)) (SIGNATURE |affineSingularPoints| ((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)))) (SIGNATURE |affineAlgSetLocal| ((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) (|List| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))))) (SIGNATURE |affineAlgSet| ((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) (|List| |#3|))) (SIGNATURE |polyRing2UPUP| ((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) |#3|)) (SIGNATURE |allPairsAmong| ((|List| (|List| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))))) (SIGNATURE |affineRationalPoints| ((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) |#3| (|PositiveInteger|)))) (|Field|) (|List| (|Symbol|)) (|PolynomialCategory| |#1| |#4| (|OrderedVariableList| |#2|)) (|DirectProductCategory| (|#| |#2|) (|NonNegativeInteger|)) (|ProjectiveSpaceCategory| |#1|)) (T |AffineAlgebraicSetComputeWithResultant|)) 
((|affineRationalPoints| (*1 *2 *3 *4) (AND (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|DirectProductCategory| (|#| *6) (|NonNegativeInteger|))) (|isDomain| *2 (|Union| (|List| *8) "failed" "Infinite" (|Integer|))) (|isDomain| *1 (|AffineAlgebraicSetComputeWithResultant| *5 *6 *3 *7 *8)) (|ofCategory| *3 (|PolynomialCategory| *5 *7 (|OrderedVariableList| *6))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *5)))) (|allPairsAmong| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|isDomain| *2 (|List| (|List| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4))))) (|isDomain| *1 (|AffineAlgebraicSetComputeWithResultant| *4 *5 *6 *7 *8)) (|isDomain| *3 (|List| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4)))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)))) (|polyRing2UPUP| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|isDomain| *2 (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4))) (|isDomain| *1 (|AffineAlgebraicSetComputeWithResultant| *4 *5 *3 *6 *7)) (|ofCategory| *3 (|PolynomialCategory| *4 *6 (|OrderedVariableList| *5))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *4)))) (|affineAlgSet| (*1 *2 *3) (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|isDomain| *2 (|Union| (|List| *8) "failed" "Infinite" (|Integer|))) (|isDomain| *1 (|AffineAlgebraicSetComputeWithResultant| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)))) (|affineAlgSetLocal| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4)))) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|isDomain| *2 (|Union| (|List| *8) "failed" "Infinite" (|Integer|))) (|isDomain| *1 (|AffineAlgebraicSetComputeWithResultant| *4 *5 *6 *7 *8)) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)))) (|affineSingularPoints| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4))) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|isDomain| *2 (|Union| (|List| *8) "failed" "Infinite" (|Integer|))) (|isDomain| *1 (|AffineAlgebraicSetComputeWithResultant| *4 *5 *6 *7 *8)) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)))) (|affineSingularPoints| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|isDomain| *2 (|Union| (|List| *7) "failed" "Infinite" (|Integer|))) (|isDomain| *1 (|AffineAlgebraicSetComputeWithResultant| *4 *5 *3 *6 *7)) (|ofCategory| *3 (|PolynomialCategory| *4 *6 (|OrderedVariableList| *5))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |affineSingularPoints| ((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) |#3|)) (SIGNATURE |affineSingularPoints| ((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)))) (SIGNATURE |affineAlgSetLocal| ((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) (|List| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))))) (SIGNATURE |affineAlgSet| ((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) (|List| |#3|))) (SIGNATURE |polyRing2UPUP| ((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) |#3|)) (SIGNATURE |allPairsAmong| ((|List| (|List| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))))) (SIGNATURE |affineRationalPoints| ((|Union| (|List| |#5|) "failed" "Infinite" (|Integer|)) |#3| (|PositiveInteger|)))) 
((~= (((|Boolean|) $ $) NIL)) (|setelt| ((|#1| $ (|Integer|) |#1|) NIL)) (|removeConjugate| (((|List| $) (|List| $) (|NonNegativeInteger|)) NIL) (((|List| $) (|List| $)) NIL)) (|rational?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL) (((|Boolean|) $) NIL)) (|pointValue| (((|List| |#1|) $) NIL)) (|origin| (($) NIL)) (|orbit| (((|List| $) $) NIL) (((|List| $) $ (|NonNegativeInteger|)) NIL)) (|list| (((|List| |#1|) $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|elt| ((|#1| $ (|Integer|)) NIL)) (|degree| (((|PositiveInteger|) $) NIL)) (|definingField| ((|#1| $) NIL)) (|conjugate| (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (((|List| |#1|) $) NIL) (($ (|List| |#1|)) NIL)) (|affinePoint| (($ (|List| |#1|)) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|AffinePlane| |#1|) (|AffineSpaceCategory| |#1|) (|Field|)) (T |AffinePlane|)) 
NIL 
(|AffineSpaceCategory| |#1|) 
((~= (((|Boolean|) $ $) NIL)) (|setelt| (((|PseudoAlgebraicClosureOfFiniteField| |#1|) $ (|Integer|) (|PseudoAlgebraicClosureOfFiniteField| |#1|)) NIL)) (|removeConjugate| (((|List| $) (|List| $) (|NonNegativeInteger|)) NIL) (((|List| $) (|List| $)) NIL)) (|rational?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL) (((|Boolean|) $) NIL)) (|pointValue| (((|List| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) $) NIL)) (|origin| (($) NIL)) (|orbit| (((|List| $) $) NIL) (((|List| $) $ (|NonNegativeInteger|)) NIL)) (|list| (((|List| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|elt| (((|PseudoAlgebraicClosureOfFiniteField| |#1|) $ (|Integer|)) NIL)) (|degree| (((|PositiveInteger|) $) NIL)) (|definingField| (((|PseudoAlgebraicClosureOfFiniteField| |#1|) $) NIL)) (|conjugate| (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (((|List| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) $) NIL) (($ (|List| (|PseudoAlgebraicClosureOfFiniteField| |#1|))) NIL)) (|affinePoint| (($ (|List| (|PseudoAlgebraicClosureOfFiniteField| |#1|))) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|) (|AffineSpaceCategory| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) (|FiniteFieldCategory|)) (T |AffinePlaneOverPseudoAlgebraicClosureOfFiniteField|)) 
NIL 
(|AffineSpaceCategory| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) 
((~= (((|Boolean|) $ $) NIL)) (|setelt| ((|#2| $ (|Integer|) |#2|) NIL)) (|removeConjugate| (((|List| $) (|List| $) (|NonNegativeInteger|)) 39) (((|List| $) (|List| $)) 40)) (|rational?| (((|Boolean|) $ (|NonNegativeInteger|)) 36) (((|Boolean|) $) 38)) (|pointValue| (((|List| |#2|) $) 31)) (|origin| (($) 12)) (|orbit| (((|List| $) $) 48) (((|List| $) $ (|NonNegativeInteger|)) 45)) (|list| (((|List| |#2|) $) 30)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|elt| ((|#2| $ (|Integer|)) NIL)) (|degree| (((|PositiveInteger|) $) 20)) (|definingField| ((|#2| $) 26)) (|conjugate| (($ $ (|NonNegativeInteger|)) 33) (($ $) 47)) (|coerce| (((|OutputForm|) $) 23) (((|List| |#2|) $) 28) (($ (|List| |#2|)) 51)) (|affinePoint| (($ (|List| |#2|)) 29)) (= (((|Boolean|) $ $) 35))) 
(((|AffineSpace| |#1| |#2|) (|AffineSpaceCategory| |#2|) (|NonNegativeInteger|) (|Field|)) (T |AffineSpace|)) 
NIL 
(|AffineSpaceCategory| |#2|) 
((|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) 42)) (|operator| (((|BasicOperator|) (|BasicOperator|)) 54)) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) 129 (|has| |#1| (|RetractableTo| (|Integer|))))) (|iroot| ((|#2| |#1| (|Integer|)) 108 (|has| |#1| (|RetractableTo| (|Integer|))))) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) 30)) (|droot| (((|OutputForm|) (|List| |#2|)) 84)) (|definingPolynomial| ((|#2| |#2|) 125 (|has| |#1| (|RetractableTo| (|Integer|))))) (|belong?| (((|Boolean|) (|BasicOperator|)) 18)) (** ((|#2| |#2| (|Fraction| (|Integer|))) 89 (|has| |#1| (|RetractableTo| (|Integer|)))))) 
(((|AlgebraicFunction| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rootOf| (|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|))) (SIGNATURE |operator| ((|BasicOperator|) (|BasicOperator|))) (SIGNATURE |belong?| ((|Boolean|) (|BasicOperator|))) (SIGNATURE |inrootof| (|#2| (|SparseUnivariatePolynomial| |#2|) |#2|)) (SIGNATURE |droot| ((|OutputForm|) (|List| |#2|))) (IF (|has| |#1| (|RetractableTo| (|Integer|))) (PROGN (SIGNATURE ** (|#2| |#2| (|Fraction| (|Integer|)))) (SIGNATURE |minPoly| ((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|))) (SIGNATURE |definingPolynomial| (|#2| |#2|)) (SIGNATURE |iroot| (|#2| |#1| (|Integer|)))) |noBranch|)) (|Join| (|OrderedSet|) (|IntegralDomain|)) (|FunctionSpace| |#1|)) (T |AlgebraicFunction|)) 
((|iroot| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Integer|)) (|ofCategory| *2 (|FunctionSpace| *3)) (|isDomain| *1 (|AlgebraicFunction| *3 *2)) (|ofCategory| *3 (|RetractableTo| *4)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|definingPolynomial| (*1 *2 *2) (AND (|ofCategory| *3 (|RetractableTo| (|Integer|))) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|AlgebraicFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|minPoly| (*1 *2 *3) (AND (|isDomain| *3 (|Kernel| *5)) (|ofCategory| *5 (|FunctionSpace| *4)) (|ofCategory| *4 (|RetractableTo| (|Integer|))) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *2 (|SparseUnivariatePolynomial| *5)) (|isDomain| *1 (|AlgebraicFunction| *4 *5)))) (** (*1 *2 *2 *3) (AND (|isDomain| *3 (|Fraction| (|Integer|))) (|ofCategory| *4 (|RetractableTo| (|Integer|))) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|AlgebraicFunction| *4 *2)) (|ofCategory| *2 (|FunctionSpace| *4)))) (|droot| (*1 *2 *3) (AND (|isDomain| *3 (|List| *5)) (|ofCategory| *5 (|FunctionSpace| *4)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|AlgebraicFunction| *4 *5)))) (|inrootof| (*1 *2 *3 *2) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *2)) (|ofCategory| *2 (|FunctionSpace| *4)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|AlgebraicFunction| *4 *2)))) (|belong?| (*1 *2 *3) (AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|AlgebraicFunction| *4 *5)) (|ofCategory| *5 (|FunctionSpace| *4)))) (|operator| (*1 *2 *2) (AND (|isDomain| *2 (|BasicOperator|)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|AlgebraicFunction| *3 *4)) (|ofCategory| *4 (|FunctionSpace| *3)))) (|rootOf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *2)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *2 (|FunctionSpace| *5)) (|isDomain| *1 (|AlgebraicFunction| *5 *2)) (|ofCategory| *5 (|Join| (|OrderedSet|) (|IntegralDomain|)))))) 
(CATEGORY |package| (SIGNATURE |rootOf| (|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|))) (SIGNATURE |operator| ((|BasicOperator|) (|BasicOperator|))) (SIGNATURE |belong?| ((|Boolean|) (|BasicOperator|))) (SIGNATURE |inrootof| (|#2| (|SparseUnivariatePolynomial| |#2|) |#2|)) (SIGNATURE |droot| ((|OutputForm|) (|List| |#2|))) (IF (|has| |#1| (|RetractableTo| (|Integer|))) (PROGN (SIGNATURE ** (|#2| |#2| (|Fraction| (|Integer|)))) (SIGNATURE |minPoly| ((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|))) (SIGNATURE |definingPolynomial| (|#2| |#2|)) (SIGNATURE |iroot| (|#2| |#1| (|Integer|)))) |noBranch|)) 
((~= (((|Boolean|) $ $) 7)) (|setelt| ((|#1| $ (|Integer|) |#1|) 14)) (|removeConjugate| (((|List| $) (|List| $) (|NonNegativeInteger|)) 20) (((|List| $) (|List| $)) 19)) (|rational?| (((|Boolean|) $ (|NonNegativeInteger|)) 18) (((|Boolean|) $) 17)) (|pointValue| (((|List| |#1|) $) 13)) (|origin| (($) 29)) (|orbit| (((|List| $) $) 24) (((|List| $) $ (|NonNegativeInteger|)) 23)) (|list| (((|List| |#1|) $) 16)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|elt| ((|#1| $ (|Integer|)) 15)) (|degree| (((|PositiveInteger|) $) 12)) (|definingField| ((|#1| $) 27)) (|conjugate| (($ $ (|NonNegativeInteger|)) 22) (($ $) 21)) (|coerce| (((|OutputForm|) $) 11) (((|List| |#1|) $) 26) (($ (|List| |#1|)) 25)) (|affinePoint| (($ (|List| |#1|)) 28)) (= (((|Boolean|) $ $) 6))) 
(((|AffineSpaceCategory| |#1|) (|Category|) (|Field|)) (T |AffineSpaceCategory|)) 
((|origin| (*1 *1) (AND (|ofCategory| *1 (|AffineSpaceCategory| *2)) (|ofCategory| *2 (|Field|)))) (|affinePoint| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *1 (|AffineSpaceCategory| *3)))) (|definingField| (*1 *2 *1) (AND (|ofCategory| *1 (|AffineSpaceCategory| *2)) (|ofCategory| *2 (|Field|)))) (|coerce| (*1 *2 *1) (AND (|ofCategory| *1 (|AffineSpaceCategory| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|List| *3)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *1 (|AffineSpaceCategory| *3)))) (|orbit| (*1 *2 *1) (AND (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|AffineSpaceCategory| *3)))) (|orbit| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|AffineSpaceCategory| *4)))) (|conjugate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|AffineSpaceCategory| *3)) (|ofCategory| *3 (|Field|)))) (|conjugate| (*1 *1 *1) (AND (|ofCategory| *1 (|AffineSpaceCategory| *2)) (|ofCategory| *2 (|Field|)))) (|removeConjugate| (*1 *2 *2 *3) (AND (|isDomain| *2 (|List| *1)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|AffineSpaceCategory| *4)) (|ofCategory| *4 (|Field|)))) (|removeConjugate| (*1 *2 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|AffineSpaceCategory| *3)) (|ofCategory| *3 (|Field|)))) (|rational?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|AffineSpaceCategory| *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|Boolean|)))) (|rational?| (*1 *2 *1) (AND (|ofCategory| *1 (|AffineSpaceCategory| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Boolean|)))) (|list| (*1 *2 *1) (AND (|ofCategory| *1 (|AffineSpaceCategory| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|List| *3)))) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|AffineSpaceCategory| *2)) (|ofCategory| *2 (|Field|)))) (|setelt| (*1 *2 *1 *3 *2) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|AffineSpaceCategory| *2)) (|ofCategory| *2 (|Field|)))) (|pointValue| (*1 *2 *1) (AND (|ofCategory| *1 (|AffineSpaceCategory| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|List| *3))))) 
(|Join| (|SetCategoryWithDegree|) (CATEGORY |domain| (SIGNATURE |origin| ($)) (SIGNATURE |affinePoint| ($ (|List| |t#1|))) (SIGNATURE |definingField| (|t#1| $)) (SIGNATURE |coerce| ((|List| |t#1|) $)) (SIGNATURE |coerce| ($ (|List| |t#1|))) (SIGNATURE |orbit| ((|List| $) $)) (SIGNATURE |orbit| ((|List| $) $ (|NonNegativeInteger|))) (SIGNATURE |conjugate| ($ $ (|NonNegativeInteger|))) (SIGNATURE |conjugate| ($ $)) (SIGNATURE |removeConjugate| ((|List| $) (|List| $) (|NonNegativeInteger|))) (SIGNATURE |removeConjugate| ((|List| $) (|List| $))) (SIGNATURE |rational?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |list| ((|List| |t#1|) $)) (SIGNATURE |elt| (|t#1| $ (|Integer|))) (SIGNATURE |setelt| (|t#1| $ (|Integer|) |t#1|)) (SIGNATURE |pointValue| ((|List| |t#1|) $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|SetCategoryWithDegree|) . T)) 
((|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 16)) (|sample| (($) 10)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 15)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 14)) (|eq?| (((|Boolean|) $ $) 8)) (|empty?| (((|Boolean|) $) 13))) 
(((|Aggregate&| |#1|) (CATEGORY |domain| (SIGNATURE |sample| (|#1|)) (SIGNATURE |size?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |less?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |empty?| ((|Boolean|) |#1|)) (SIGNATURE |eq?| ((|Boolean|) |#1| |#1|))) (|Aggregate|)) (T |Aggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |sample| (|#1|)) (SIGNATURE |size?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |less?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |empty?| ((|Boolean|) |#1|)) (SIGNATURE |eq?| ((|Boolean|) |#1| |#1|))) 
((|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|sample| (($) 7 T CONST)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|copy| (($ $) 13)) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|Aggregate|) (|Category|)) (T |Aggregate|)) 
((|eq?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|Aggregate|)) (|isDomain| *2 (|Boolean|)))) (|copy| (*1 *1 *1) (|ofCategory| *1 (|Aggregate|))) (|empty| (*1 *1) (|ofCategory| *1 (|Aggregate|))) (|empty?| (*1 *2 *1) (AND (|ofCategory| *1 (|Aggregate|)) (|isDomain| *2 (|Boolean|)))) (|less?| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|Aggregate|)) (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)))) (|more?| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|Aggregate|)) (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)))) (|size?| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|Aggregate|)) (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)))) (|sample| (*1 *1) (|ofCategory| *1 (|Aggregate|))) (|#| (*1 *2 *1) (AND (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|Aggregate|)) (|isDomain| *2 (|NonNegativeInteger|))))) 
(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |eq?| ((|Boolean|) $ $)) (SIGNATURE |copy| ($ $)) (SIGNATURE |empty| ($)) (SIGNATURE |empty?| ((|Boolean|) $)) (SIGNATURE |less?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |size?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |sample| ($) |constant|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (SIGNATURE |#| ((|NonNegativeInteger|) $)) |noBranch|))) 
(((|Type|) . T)) 
((|atanh| (($ $) 11)) (|asinh| (($ $) 10)) (|asech| (($ $) 9)) (|acsch| (($ $) 8)) (|acoth| (($ $) 7)) (|acosh| (($ $) 6))) 
(((|ArcHyperbolicFunctionCategory|) (|Category|)) (T |ArcHyperbolicFunctionCategory|)) 
((|atanh| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|))) (|asinh| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|))) (|asech| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|))) (|acsch| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|))) (|acoth| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|))) (|acosh| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|)))) 
(|Join| (CATEGORY |domain| (SIGNATURE |acosh| ($ $)) (SIGNATURE |acoth| ($ $)) (SIGNATURE |acsch| ($ $)) (SIGNATURE |asech| ($ $)) (SIGNATURE |asinh| ($ $)) (SIGNATURE |atanh| ($ $)))) 
((~= (((|Boolean|) $ $) 18 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))))) (|value| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 117)) (|third| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 140)) (|tail| (($ $) 138)) (|table| (($) 66) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 65)) (|swap!| (((|Void|) $ |#1| |#1|) 93 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Void|) $ (|Integer|) (|Integer|)) 170 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|split!| (($ $ (|Integer|)) 151 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 201) (((|Boolean|) $) 195 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)))) (|sort!| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 192 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $) 191 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)) (|has| $ (ATTRIBUTE |shallowlyMutable|))))) (|sort| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 202) (($ $) 196 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setvalue!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 126 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setrest!| (($ $ $) 147 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setlast!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 149 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setfirst!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 145 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#2| $ |#1| |#2|) 67) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Integer|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 181 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|UniversalSegment| (|Integer|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 152 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ "last" (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 150 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "rest" $) 148 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ "first" (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 146 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ "value" (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 125 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) 124 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select!| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 42 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 208)) (|select| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 52 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 167 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|second| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 139)) (|search| (((|Union| |#2| "failed") |#1| $) 57)) (|sample| (($) 7 T CONST)) (|reverse!| (($ $) 193 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) 203)) (|rest| (($ $ (|NonNegativeInteger|)) 134) (($ $) 132)) (|removeDuplicates!| (($ $) 206 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (|removeDuplicates| (($ $) 55 (OR (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))) (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))))) (|remove!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 44 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 43 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| |#2| "failed") |#1| $) 58) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 212) (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 207 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (|remove| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 54 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 51 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 169 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 166 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 53 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 50 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 49 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 168 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 165 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 164 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| ((|#2| $ |#1| |#2|) 81 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Integer|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 182 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#2| $ |#1|) 82) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Integer|)) 180)) (|possiblyInfinite?| (((|Boolean|) $) 184)) (|position| (((|Integer|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 200) (((|Integer|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 199 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))) (((|Integer|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Integer|)) 198 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (|parts| (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|List| |#2|) $) 73 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 106 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) 115)) (|node?| (((|Boolean|) $ $) 123 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (|new| (($ (|NonNegativeInteger|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 161)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|minIndex| ((|#1| $) 90 (|has| |#1| (|OrderedSet|))) (((|Integer|) $) 172 (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) 190 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)))) (|merge!| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ $) 209) (($ $ $) 205 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)))) (|merge| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ $) 204) (($ $ $) 197 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)))) (|members| (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|List| |#2|) $) 74 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 107 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 27 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|Boolean|) |#2| $) 76 (AND (|has| |#2| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 109 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|maxIndex| ((|#1| $) 89 (|has| |#1| (|OrderedSet|))) (((|Integer|) $) 173 (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) 189 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)))) (|map!| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ (|Mapping| |#2| |#2|) $) 69 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 102 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 35) (($ (|Mapping| |#2| |#2|) $) 68) (($ (|Mapping| |#2| |#2| |#2|) $ $) 64) (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ $) 158) (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 101)) (|list| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 217)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|leaves| (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 120)) (|leaf?| (((|Boolean|) $) 116)) (|latex| (((|String|) $) 22 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))))) (|last| (($ $ (|NonNegativeInteger|)) 137) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 135)) (|keys| (((|List| |#1|) $) 59)) (|key?| (((|Boolean|) |#1| $) 60)) (|inspect| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 36)) (|insert!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 37) (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Integer|)) 211) (($ $ $ (|Integer|)) 210)) (|insert| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Integer|)) 154) (($ $ $ (|Integer|)) 153)) (|indices| (((|List| |#1|) $) 87) (((|List| (|Integer|)) $) 175)) (|index?| (((|Boolean|) |#1| $) 86) (((|Boolean|) (|Integer|) $) 176)) (|hash| (((|SingleInteger|) $) 21 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))))) (|first| ((|#2| $) 91 (|has| |#1| (|OrderedSet|))) (($ $ (|NonNegativeInteger|)) 131) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 129)) (|find| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 48) (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 163)) (|fill!| (($ $ |#2|) 92 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 171 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|extract!| 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(((|AssociationListAggregate| |#1| |#2|) (|Category|) (|SetCategory|) (|SetCategory|)) (T |AssociationListAggregate|)) 
((|assoc| (*1 *2 *3 *1) (|partial| AND (|ofCategory| *1 (|AssociationListAggregate| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Record| (|:| |key| *3) (|:| |entry| *4)))))) 
(|Join| (|TableAggregate| |t#1| |t#2|) (|ListAggregate| (|Record| (|:| |key| |t#1|) (|:| |entry| |t#2|))) (CATEGORY |domain| (SIGNATURE |assoc| ((|Union| (|Record| (|:| |key| |t#1|) (|:| |entry| |t#2|)) "failed") |t#1| $)))) 
(((|Aggregate|) . T) ((|BagAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|BasicType|) OR (|has| |#2| (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#2| (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|))) ((|Collection| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|ConvertibleTo| (|InputForm|)) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|ConvertibleTo| (|InputForm|))) ((|Dictionary| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|DictionaryOperations| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|Eltable| (|Integer|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|Eltable| |#1| |#2|) . T) ((|EltableAggregate| (|Integer|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|EltableAggregate| |#1| |#2|) . T) ((|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|ExtensibleLinearAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|FiniteLinearAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|HomogeneousAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|HomogeneousAggregate| |#2|) . T) ((|IndexedAggregate| (|Integer|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|IndexedAggregate| |#1| |#2|) . T) ((|InnerEvalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))) ((|InnerEvalable| |#2| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|KeyedDictionary| |#1| |#2|) . T) ((|LinearAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|ListAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|OrderedSet|) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)) ((|RecursiveAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|SetCategory|) OR (|has| |#2| (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|))) ((|StreamAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|TableAggregate| |#1| |#2|) . T) ((|Type|) . T) ((|UnaryRecursiveAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T)) 
((|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ |#2|) 10))) 
(((|Algebra&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|Algebra| |#2|) (|CommutativeRing|)) (T |Algebra&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ |#1|) 36)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 38) (($ |#1| $) 37))) 
(((|Algebra| |#1|) (|Category|) (|CommutativeRing|)) (T |Algebra|)) 
((|coerce| (*1 *1 *2) (AND (|ofCategory| *1 (|Algebra| *2)) (|ofCategory| *2 (|CommutativeRing|))))) 
(|Join| (|Ring|) (|Module| |t#1|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |t#1|)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|split| (((|Factored| |#1|) |#1|) 38)) (|factor| (((|Factored| |#1|) |#1|) 27) (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) 30)) (|doublyTransitive?| (((|Boolean|) |#1|) 54))) 
(((|AlgFactor| |#1|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|)))) (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) (SIGNATURE |split| ((|Factored| |#1|) |#1|)) (SIGNATURE |doublyTransitive?| ((|Boolean|) |#1|))) (|UnivariatePolynomialCategory| (|AlgebraicNumber|))) (T |AlgFactor|)) 
((|doublyTransitive?| (*1 *2 *3) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|AlgFactor| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|AlgebraicNumber|))))) (|split| (*1 *2 *3) (AND (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|AlgFactor| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|AlgebraicNumber|))))) (|factor| (*1 *2 *3) (AND (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|AlgFactor| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|AlgebraicNumber|))))) (|factor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| (|AlgebraicNumber|))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|AlgFactor| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|AlgebraicNumber|)))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|)))) (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) (SIGNATURE |split| ((|Factored| |#1|) |#1|)) (SIGNATURE |doublyTransitive?| ((|Boolean|) |#1|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|unitCanonical| (($ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|unit?| (((|Boolean|) $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|traceMatrix| (((|Matrix| (|Fraction| |#2|)) (|Vector| $)) NIL) (((|Matrix| (|Fraction| |#2|))) NIL)) (|trace| (((|Fraction| |#2|) $) NIL)) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|squareFree| (((|Factored| $) $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|sizeLess?| (((|Boolean|) $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|size| (((|NonNegativeInteger|)) NIL (|has| (|Fraction| |#2|) (|Finite|)))) (|singularAtInfinity?| (((|Boolean|)) NIL)) (|singular?| (((|Boolean|) |#1|) NIL) (((|Boolean|) |#2|) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (|has| (|Fraction| |#2|) (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| (|Fraction| |#2|) (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Fraction| |#2|) "failed") $) NIL)) (|retract| (((|Integer|) $) NIL (|has| (|Fraction| |#2|) (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) NIL (|has| (|Fraction| |#2|) (|RetractableTo| (|Fraction| (|Integer|))))) (((|Fraction| |#2|) $) NIL)) (|represents| (($ (|Vector| (|Fraction| |#2|)) (|Vector| $)) NIL) (($ (|Vector| (|Fraction| |#2|))) 57) (($ (|Vector| |#2|) |#2|) 124)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|rem| (($ $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|regularRepresentation| (((|Matrix| (|Fraction| |#2|)) $ (|Vector| $)) NIL) (((|Matrix| (|Fraction| |#2|)) $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| (|Fraction| |#2|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| (|Fraction| |#2|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Fraction| |#2|))) (|:| |vec| (|Vector| (|Fraction| |#2|)))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| (|Fraction| |#2|)) (|Matrix| $)) NIL)) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) NIL)) (|reduce| (($ |#3|) NIL) (((|Union| $ "failed") (|Fraction| |#3|)) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|recip| (((|Union| $ "failed") $) NIL)) (|rationalPoints| (((|List| (|List| |#1|))) NIL (|has| |#1| (|Finite|)))) (|rationalPoint?| (((|Boolean|) |#1| |#1|) NIL)) (|rank| (((|PositiveInteger|)) NIL)) (|random| (($) NIL (|has| (|Fraction| |#2|) (|Finite|)))) (|ramifiedAtInfinity?| (((|Boolean|)) NIL)) (|ramified?| (((|Boolean|) |#1|) NIL) (((|Boolean|) |#2|) NIL)) (|quo| (($ $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|primitivePart| (($ $) NIL)) (|primitiveElement| (($) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|primitive?| (((|Boolean|) $) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))) (($ $) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|prime?| (((|Boolean|) $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|order| (((|PositiveInteger|) $) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))) (((|OnePointCompletion| (|PositiveInteger|)) $) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|one?| (((|Boolean|) $) NIL)) (|numberOfComponents| (((|NonNegativeInteger|)) NIL)) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) 100)) (|norm| (((|Fraction| |#2|) $) NIL)) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) NIL (|has| |#1| (|Field|)))) (|nextItem| (((|Union| $ "failed") $) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|minimalPolynomial| ((|#3| $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|lookup| (((|PositiveInteger|) $) NIL (|has| (|Fraction| |#2|) (|Finite|)))) (|lift| ((|#3| $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|lcm| (($ (|List| $)) NIL (|has| (|Fraction| |#2|) (|Field|))) (($ $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|latex| (((|String|) $) NIL)) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) 78)) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) 51)) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) 44)) (|inv| (($ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|integralRepresents| (($ (|Vector| |#2|) |#2|) 125)) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) 45)) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) 43)) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) 122)) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) 63)) (|integralBasisAtInfinity| (((|Vector| $)) 42)) (|integralBasis| (((|Vector| $)) 41)) (|integralAtInfinity?| (((|Boolean|) $) NIL)) (|integral?| (((|Boolean|) $) NIL) (((|Boolean|) $ |#1|) NIL) (((|Boolean|) $ |#2|) NIL)) (|init| (($) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) CONST)) (|index| (($ (|PositiveInteger|)) NIL (|has| (|Fraction| |#2|) (|Finite|)))) (|hyperelliptic| (((|Union| |#2| "failed")) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|genus| (((|NonNegativeInteger|)) NIL)) (|generator| (($) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|gcd| (($ (|List| $)) NIL (|has| (|Fraction| |#2|) (|Field|))) (($ $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|factor| (((|Factored| $) $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL (|has| (|Fraction| |#2|) (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|exquo| (((|Union| $ "failed") $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|euclideanSize| (((|NonNegativeInteger|) $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|enumerate| (((|List| $)) NIL (|has| (|Fraction| |#2|) (|Finite|)))) (|elt| ((|#1| $ |#1| |#1|) NIL)) (|elliptic| (((|Union| |#2| "failed")) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|discriminant| (((|Fraction| |#2|) (|Vector| $)) NIL) (((|Fraction| |#2|)) 39)) (|discreteLog| (((|NonNegativeInteger|) $) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))) (((|Union| (|NonNegativeInteger|) "failed") $ $) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|differentiate| (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|)) (|NonNegativeInteger|)) NIL (|has| (|Fraction| |#2|) (|Field|))) (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|))) NIL (|has| (|Fraction| |#2|) (|Field|))) (($ $ (|Mapping| |#2| |#2|)) 118) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|)) NIL (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|NonNegativeInteger|)) NIL (OR (AND (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|))) (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (($ $) NIL (OR (AND (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|))) (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))))) (|derivationCoordinates| (((|Matrix| (|Fraction| |#2|)) (|Vector| $) (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|))) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|definingPolynomial| ((|#3|) 50)) (|createPrimitiveElement| (($) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|coordinates| (((|Vector| (|Fraction| |#2|)) $ (|Vector| $)) NIL) (((|Matrix| (|Fraction| |#2|)) (|Vector| $) (|Vector| $)) NIL) (((|Vector| (|Fraction| |#2|)) $) 58) (((|Matrix| (|Fraction| |#2|)) (|Vector| $)) 101)) (|convert| (((|Vector| (|Fraction| |#2|)) $) NIL) (($ (|Vector| (|Fraction| |#2|))) NIL) ((|#3| $) NIL) (($ |#3|) NIL)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|complementaryBasis| (((|Vector| $) (|Vector| $)) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ (|Fraction| |#2|)) NIL) (($ (|Fraction| (|Integer|))) NIL (OR (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|RetractableTo| (|Fraction| (|Integer|)))))) (($ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|charthRoot| (($ $) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))) (((|Union| $ "failed") $) NIL (|has| (|Fraction| |#2|) (|CharacteristicNonZero|)))) (|characteristicPolynomial| ((|#3| $) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|branchPointAtInfinity?| (((|Boolean|)) 37)) (|branchPoint?| (((|Boolean|) |#1|) 49) (((|Boolean|) |#2|) 130)) (|basis| (((|Vector| $)) 91)) (|associates?| (((|Boolean|) $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) NIL)) (|absolutelyIrreducible?| (((|Boolean|)) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|Zero| (($) 16 T CONST)) (|One| (($) 26 T CONST)) (D (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|)) (|NonNegativeInteger|)) NIL (|has| (|Fraction| |#2|) (|Field|))) (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|))) NIL (|has| (|Fraction| |#2|) (|Field|))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|)) NIL (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|NonNegativeInteger|)) NIL (OR (AND (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|))) (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (($ $) NIL (OR (AND (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|))) (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))))) (= (((|Boolean|) $ $) NIL)) (/ (($ $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| (|Fraction| |#2|) (|Field|)))) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| |#2|)) NIL) (($ (|Fraction| |#2|) $) NIL) (($ (|Fraction| (|Integer|)) $) NIL (|has| (|Fraction| |#2|) (|Field|))) (($ $ (|Fraction| (|Integer|))) NIL (|has| (|Fraction| |#2|) (|Field|))))) 
(((|AlgebraicFunctionField| |#1| |#2| |#3| |#4|) (|Join| (|FunctionFieldCategory| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |knownInfBasis| ((|Void|) (|NonNegativeInteger|))))) (|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) |#3|) (T |AlgebraicFunctionField|)) 
((|knownInfBasis| (*1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|AlgebraicFunctionField| *4 *5 *6 *7)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|ofType| *7 *6)))) 
(|Join| (|FunctionFieldCategory| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |knownInfBasis| ((|Void|) (|NonNegativeInteger|))))) 
((|rootSplit| ((|#2| |#2|) 47)) (|rootSimp| ((|#2| |#2|) 116 (AND (|has| |#2| (|FunctionSpace| |#1|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|OrderedSet|)) (|has| |#1| (|RetractableTo| (|Integer|)))))) (|rootProduct| ((|#2| |#2|) 85 (AND (|has| |#2| (|FunctionSpace| |#1|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|OrderedSet|)) (|has| |#1| (|RetractableTo| (|Integer|)))))) (|rootPower| ((|#2| |#2|) 86 (AND (|has| |#2| (|FunctionSpace| |#1|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|OrderedSet|)) (|has| |#1| (|RetractableTo| (|Integer|)))))) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) 73 (AND (|has| |#2| (|FunctionSpace| |#1|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|OrderedSet|)) (|has| |#1| (|RetractableTo| (|Integer|)))))) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) 44)) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) 17) ((|#2| |#2| (|List| |#2|)) 19) ((|#2| |#2| |#2|) 20) ((|#2| |#2|) 15))) 
(((|AlgebraicManipulations| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rootSplit| (|#2| |#2|)) (SIGNATURE |ratDenom| (|#2| |#2|)) (SIGNATURE |ratDenom| (|#2| |#2| |#2|)) (SIGNATURE |ratDenom| (|#2| |#2| (|List| |#2|))) (SIGNATURE |ratDenom| (|#2| |#2| (|List| (|Kernel| |#2|)))) (SIGNATURE |ratPoly| ((|SparseUnivariatePolynomial| |#2|) |#2|)) (IF (|has| |#1| (|OrderedSet|)) (IF (|has| |#1| (|GcdDomain|)) (IF (|has| |#1| (|RetractableTo| (|Integer|))) (IF (|has| |#2| (|FunctionSpace| |#1|)) (PROGN (SIGNATURE |rootPower| (|#2| |#2|)) (SIGNATURE |rootProduct| (|#2| |#2|)) (SIGNATURE |rootSimp| (|#2| |#2|)) (SIGNATURE |rootKerSimp| (|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)))) |noBranch|) |noBranch|) |noBranch|) |noBranch|)) (|IntegralDomain|) (|Join| (|Field|) (|ExpressionSpace|) (CATEGORY |domain| (SIGNATURE |numer| ((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $)) (SIGNATURE |denom| ((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $)) (SIGNATURE |coerce| ($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))))))) (T |AlgebraicManipulations|)) 
((|rootKerSimp| (*1 *2 *3 *2 *4) (AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *5 (|RetractableTo| (|Integer|))) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *1 (|AlgebraicManipulations| *5 *2)) (|ofCategory| *2 (|FunctionSpace| *5)) (|ofCategory| *2 (|Join| (|Field|) (|ExpressionSpace|) (CATEGORY |domain| (SIGNATURE |numer| ((|SparseMultivariatePolynomial| *5 (|Kernel| $)) $)) (SIGNATURE |denom| ((|SparseMultivariatePolynomial| *5 (|Kernel| $)) $)) (SIGNATURE |coerce| ($ (|SparseMultivariatePolynomial| *5 (|Kernel| $))))))))) (|rootSimp| (*1 *2 *2) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *3 (|RetractableTo| (|Integer|))) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|AlgebraicManipulations| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)) (|ofCategory| *2 (|Join| (|Field|) (|ExpressionSpace|) (CATEGORY |domain| (SIGNATURE |numer| ((|SparseMultivariatePolynomial| *3 (|Kernel| $)) $)) (SIGNATURE |denom| ((|SparseMultivariatePolynomial| *3 (|Kernel| $)) $)) (SIGNATURE |coerce| ($ (|SparseMultivariatePolynomial| *3 (|Kernel| $))))))))) (|rootProduct| (*1 *2 *2) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *3 (|RetractableTo| (|Integer|))) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|AlgebraicManipulations| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)) (|ofCategory| *2 (|Join| (|Field|) (|ExpressionSpace|) (CATEGORY |domain| (SIGNATURE |numer| ((|SparseMultivariatePolynomial| *3 (|Kernel| $)) $)) (SIGNATURE |denom| ((|SparseMultivariatePolynomial| *3 (|Kernel| $)) $)) (SIGNATURE |coerce| ($ (|SparseMultivariatePolynomial| *3 (|Kernel| $))))))))) (|rootPower| (*1 *2 *2) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *3 (|RetractableTo| (|Integer|))) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|AlgebraicManipulations| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)) (|ofCategory| *2 (|Join| (|Field|) (|ExpressionSpace|) (CATEGORY |domain| (SIGNATURE |numer| ((|SparseMultivariatePolynomial| *3 (|Kernel| $)) $)) (SIGNATURE |denom| ((|SparseMultivariatePolynomial| *3 (|Kernel| $)) $)) (SIGNATURE |coerce| ($ (|SparseMultivariatePolynomial| *3 (|Kernel| $))))))))) (|ratPoly| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) (|isDomain| *1 (|AlgebraicManipulations| *4 *3)) (|ofCategory| *3 (|Join| (|Field|) (|ExpressionSpace|) (CATEGORY |domain| (SIGNATURE |numer| ((|SparseMultivariatePolynomial| *4 (|Kernel| $)) $)) (SIGNATURE |denom| ((|SparseMultivariatePolynomial| *4 (|Kernel| $)) $)) (SIGNATURE |coerce| ($ (|SparseMultivariatePolynomial| *4 (|Kernel| $))))))))) (|ratDenom| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| (|Kernel| *2))) (|ofCategory| *2 (|Join| (|Field|) (|ExpressionSpace|) (CATEGORY |domain| (SIGNATURE |numer| ((|SparseMultivariatePolynomial| *4 (|Kernel| $)) $)) (SIGNATURE |denom| ((|SparseMultivariatePolynomial| *4 (|Kernel| $)) $)) (SIGNATURE |coerce| ($ (|SparseMultivariatePolynomial| *4 (|Kernel| $))))))) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *1 (|AlgebraicManipulations| *4 *2)))) (|ratDenom| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|Join| (|Field|) (|ExpressionSpace|) (CATEGORY |domain| (SIGNATURE |numer| ((|SparseMultivariatePolynomial| *4 (|Kernel| $)) $)) (SIGNATURE |denom| ((|SparseMultivariatePolynomial| *4 (|Kernel| $)) $)) (SIGNATURE |coerce| ($ (|SparseMultivariatePolynomial| *4 (|Kernel| $))))))) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *1 (|AlgebraicManipulations| *4 *2)))) (|ratDenom| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|AlgebraicManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|Field|) (|ExpressionSpace|) (CATEGORY |domain| (SIGNATURE |numer| ((|SparseMultivariatePolynomial| *3 (|Kernel| $)) $)) (SIGNATURE |denom| ((|SparseMultivariatePolynomial| *3 (|Kernel| $)) $)) (SIGNATURE |coerce| ($ (|SparseMultivariatePolynomial| *3 (|Kernel| $))))))))) (|ratDenom| (*1 *2 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|AlgebraicManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|Field|) (|ExpressionSpace|) (CATEGORY |domain| (SIGNATURE |numer| ((|SparseMultivariatePolynomial| *3 (|Kernel| $)) $)) (SIGNATURE |denom| ((|SparseMultivariatePolynomial| *3 (|Kernel| $)) $)) (SIGNATURE |coerce| ($ (|SparseMultivariatePolynomial| *3 (|Kernel| $))))))))) (|rootSplit| (*1 *2 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|AlgebraicManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|Field|) (|ExpressionSpace|) (CATEGORY |domain| (SIGNATURE |numer| ((|SparseMultivariatePolynomial| *3 (|Kernel| $)) $)) (SIGNATURE |denom| ((|SparseMultivariatePolynomial| *3 (|Kernel| $)) $)) (SIGNATURE |coerce| ($ (|SparseMultivariatePolynomial| *3 (|Kernel| $)))))))))) 
(CATEGORY |package| (SIGNATURE |rootSplit| (|#2| |#2|)) (SIGNATURE |ratDenom| (|#2| |#2|)) (SIGNATURE |ratDenom| (|#2| |#2| |#2|)) (SIGNATURE |ratDenom| (|#2| |#2| (|List| |#2|))) (SIGNATURE |ratDenom| (|#2| |#2| (|List| (|Kernel| |#2|)))) (SIGNATURE |ratPoly| ((|SparseUnivariatePolynomial| |#2|) |#2|)) (IF (|has| |#1| (|OrderedSet|)) (IF (|has| |#1| (|GcdDomain|)) (IF (|has| |#1| (|RetractableTo| (|Integer|))) (IF (|has| |#2| (|FunctionSpace| |#1|)) (PROGN (SIGNATURE |rootPower| (|#2| |#2|)) (SIGNATURE |rootProduct| (|#2| |#2|)) (SIGNATURE |rootSimp| (|#2| |#2|)) (SIGNATURE |rootKerSimp| (|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)))) |noBranch|) |noBranch|) |noBranch|) |noBranch|)) 
((|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) 22) (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) 18))) 
(((|AlgebraicMultFact| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|)))) (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))))) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|PolynomialCategory| (|AlgebraicNumber|) |#2| |#1|)) (T |AlgebraicMultFact|)) 
((|factor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| (|AlgebraicNumber|))) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|PolynomialCategory| (|AlgebraicNumber|) *6 *5)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *7))) (|isDomain| *1 (|AlgebraicMultFact| *5 *6 *7)) (|isDomain| *3 (|SparseUnivariatePolynomial| *7)))) (|factor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| (|AlgebraicNumber|))) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|AlgebraicMultFact| *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| (|AlgebraicNumber|) *6 *5))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|)))) (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))))) 
((|weakBiRank| (((|NonNegativeInteger|) |#2|) 65)) (|rightRank| (((|NonNegativeInteger|) |#2|) 68)) (|radicalOfLeftTraceForm| (((|List| |#2|)) 33)) (|leftRank| (((|NonNegativeInteger|) |#2|) 67)) (|doubleRank| (((|NonNegativeInteger|) |#2|) 64)) (|biRank| (((|NonNegativeInteger|) |#2|) 66)) (|basisOfRightNucloid| (((|List| (|Matrix| |#1|))) 60)) (|basisOfRightNucleus| (((|List| |#2|)) 55)) (|basisOfRightAnnihilator| (((|List| |#2|) |#2|) 43)) (|basisOfNucleus| (((|List| |#2|)) 57)) (|basisOfMiddleNucleus| (((|List| |#2|)) 56)) (|basisOfLeftNucloid| (((|List| (|Matrix| |#1|))) 48)) (|basisOfLeftNucleus| (((|List| |#2|)) 54)) (|basisOfLeftAnnihilator| (((|List| |#2|) |#2|) 42)) (|basisOfCommutingElements| (((|List| |#2|)) 50)) (|basisOfCentroid| (((|List| (|Matrix| |#1|))) 61)) (|basisOfCenter| (((|List| |#2|)) 59)) (|basis| (((|Vector| |#2|) (|Vector| |#2|)) 83 (|has| |#1| (|EuclideanDomain|))))) 
(((|AlgebraPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |leftRank| ((|NonNegativeInteger|) |#2|)) (SIGNATURE |rightRank| ((|NonNegativeInteger|) |#2|)) (SIGNATURE |doubleRank| ((|NonNegativeInteger|) |#2|)) (SIGNATURE |weakBiRank| ((|NonNegativeInteger|) |#2|)) (SIGNATURE |biRank| ((|NonNegativeInteger|) |#2|)) (SIGNATURE |basisOfCommutingElements| ((|List| |#2|))) (SIGNATURE |basisOfLeftAnnihilator| ((|List| |#2|) |#2|)) (SIGNATURE |basisOfRightAnnihilator| ((|List| |#2|) |#2|)) (SIGNATURE |basisOfLeftNucleus| ((|List| |#2|))) (SIGNATURE |basisOfRightNucleus| ((|List| |#2|))) (SIGNATURE |basisOfMiddleNucleus| ((|List| |#2|))) (SIGNATURE |basisOfNucleus| ((|List| |#2|))) (SIGNATURE |basisOfCenter| ((|List| |#2|))) (SIGNATURE |basisOfLeftNucloid| ((|List| (|Matrix| |#1|)))) (SIGNATURE |basisOfRightNucloid| ((|List| (|Matrix| |#1|)))) (SIGNATURE |basisOfCentroid| ((|List| (|Matrix| |#1|)))) (SIGNATURE |radicalOfLeftTraceForm| ((|List| |#2|))) (IF (|has| |#1| (|EuclideanDomain|)) (SIGNATURE |basis| ((|Vector| |#2|) (|Vector| |#2|))) |noBranch|)) (|IntegralDomain|) (|FramedNonAssociativeAlgebra| |#1|)) (T |AlgebraPackage|)) 
((|basis| (*1 *2 *2) (AND (|isDomain| *2 (|Vector| *4)) (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|AlgebraPackage| *3 *4)))) (|radicalOfLeftTraceForm| (*1 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|AlgebraPackage| *3 *4)) (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3)))) (|basisOfCentroid| (*1 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| (|Matrix| *3))) (|isDomain| *1 (|AlgebraPackage| *3 *4)) (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3)))) (|basisOfRightNucloid| (*1 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| (|Matrix| *3))) (|isDomain| *1 (|AlgebraPackage| *3 *4)) (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3)))) (|basisOfLeftNucloid| (*1 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| (|Matrix| *3))) (|isDomain| *1 (|AlgebraPackage| *3 *4)) (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3)))) (|basisOfCenter| (*1 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|AlgebraPackage| *3 *4)) (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3)))) (|basisOfNucleus| (*1 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|AlgebraPackage| *3 *4)) (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3)))) (|basisOfMiddleNucleus| (*1 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|AlgebraPackage| *3 *4)) (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3)))) (|basisOfRightNucleus| (*1 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|AlgebraPackage| *3 *4)) (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3)))) (|basisOfLeftNucleus| (*1 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|AlgebraPackage| *3 *4)) (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3)))) (|basisOfRightAnnihilator| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|AlgebraPackage| *4 *3)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4)))) (|basisOfLeftAnnihilator| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|AlgebraPackage| *4 *3)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4)))) (|basisOfCommutingElements| (*1 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|AlgebraPackage| *3 *4)) (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3)))) (|biRank| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|AlgebraPackage| *4 *3)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4)))) (|weakBiRank| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|AlgebraPackage| *4 *3)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4)))) (|doubleRank| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|AlgebraPackage| *4 *3)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4)))) (|rightRank| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|AlgebraPackage| *4 *3)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4)))) (|leftRank| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|AlgebraPackage| *4 *3)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4))))) 
(CATEGORY |package| (SIGNATURE |leftRank| ((|NonNegativeInteger|) |#2|)) (SIGNATURE |rightRank| ((|NonNegativeInteger|) |#2|)) (SIGNATURE |doubleRank| ((|NonNegativeInteger|) |#2|)) (SIGNATURE |weakBiRank| ((|NonNegativeInteger|) |#2|)) (SIGNATURE |biRank| ((|NonNegativeInteger|) |#2|)) (SIGNATURE |basisOfCommutingElements| ((|List| |#2|))) (SIGNATURE |basisOfLeftAnnihilator| ((|List| |#2|) |#2|)) (SIGNATURE |basisOfRightAnnihilator| ((|List| |#2|) |#2|)) (SIGNATURE |basisOfLeftNucleus| ((|List| |#2|))) (SIGNATURE |basisOfRightNucleus| ((|List| |#2|))) (SIGNATURE |basisOfMiddleNucleus| ((|List| |#2|))) (SIGNATURE |basisOfNucleus| ((|List| |#2|))) (SIGNATURE |basisOfCenter| ((|List| |#2|))) (SIGNATURE |basisOfLeftNucloid| ((|List| (|Matrix| |#1|)))) (SIGNATURE |basisOfRightNucloid| ((|List| (|Matrix| |#1|)))) (SIGNATURE |basisOfCentroid| ((|List| (|Matrix| |#1|)))) (SIGNATURE |radicalOfLeftTraceForm| ((|List| |#2|))) (IF (|has| |#1| (|EuclideanDomain|)) (SIGNATURE |basis| ((|Vector| |#2|) (|Vector| |#2|))) |noBranch|)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unit| (((|Union| $ "failed")) NIL (|has| |#1| (|IntegralDomain|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) NIL) (((|Vector| (|Matrix| |#1|))) 24)) (|someBasis| (((|Vector| $)) 51)) (|sample| (($) NIL T CONST)) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) NIL (|has| |#1| (|IntegralDomain|)))) (|rightUnit| (((|Union| $ "failed")) NIL (|has| |#1| (|IntegralDomain|)))) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) NIL) (((|Matrix| |#1|)) NIL)) (|rightTrace| ((|#1| $) NIL)) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) NIL) (((|Matrix| |#1|) $) NIL)) (|rightRecip| (((|Union| $ "failed") $) NIL (|has| |#1| (|IntegralDomain|)))) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) NIL (|has| |#1| (|Field|)))) (|rightPower| (($ $ (|PositiveInteger|)) NIL)) (|rightNorm| ((|#1| $) NIL)) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|rightDiscriminant| ((|#1| (|Vector| $)) NIL) ((|#1|) NIL)) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) NIL)) (|rightAlternative?| (((|Boolean|)) 88)) (|represents| (($ (|Vector| |#1|) (|Vector| $)) NIL) (($ (|Vector| |#1|)) NIL)) (|recip| (((|Union| $ "failed") $) 14 (|has| |#1| (|IntegralDomain|)))) (|rank| (((|PositiveInteger|)) 52)) (|powerAssociative?| (((|Boolean|)) NIL)) (|plenaryPower| (($ $ (|PositiveInteger|)) NIL)) (|noncommutativeJordanAlgebra?| (((|Boolean|)) NIL)) (|lieAlgebra?| (((|Boolean|)) NIL)) (|lieAdmissible?| (((|Boolean|)) 90)) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) NIL (|has| |#1| (|IntegralDomain|)))) (|leftUnit| (((|Union| $ "failed")) NIL (|has| |#1| (|IntegralDomain|)))) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) NIL) (((|Matrix| |#1|)) NIL)) (|leftTrace| ((|#1| $) NIL)) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) NIL) (((|Matrix| |#1|) $) NIL)) (|leftRecip| (((|Union| $ "failed") $) NIL (|has| |#1| (|IntegralDomain|)))) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) NIL (|has| |#1| (|Field|)))) (|leftPower| (($ $ (|PositiveInteger|)) NIL)) (|leftNorm| ((|#1| $) NIL)) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|leftDiscriminant| ((|#1| (|Vector| $)) NIL) ((|#1|) NIL)) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) NIL)) (|leftAlternative?| (((|Boolean|)) 87)) (|latex| (((|String|) $) NIL)) (|jordanAlgebra?| (((|Boolean|)) 96)) (|jordanAdmissible?| (((|Boolean|)) 94)) (|jacobiIdentity?| (((|Boolean|)) 97)) (|hash| (((|SingleInteger|) $) NIL)) (|flexible?| (((|Boolean|)) 89)) (|elt| ((|#1| $ (|Integer|)) 54)) (|coordinates| (((|Vector| |#1|) $ (|Vector| $)) 48) (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) NIL) (((|Vector| |#1|) $) 28) (((|Matrix| |#1|) (|Vector| $)) NIL)) (|convert| (((|Vector| |#1|) $) NIL) (($ (|Vector| |#1|)) NIL)) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) NIL) (((|List| (|Polynomial| |#1|))) NIL)) (|commutator| (($ $ $) NIL)) (|commutative?| (((|Boolean|)) 85)) (|coerce| (((|OutputForm|) $) 69) (($ (|Vector| |#1|)) 22)) (|basis| (((|Vector| $)) 45)) (|associatorDependence| (((|List| (|Vector| |#1|))) NIL (|has| |#1| (|IntegralDomain|)))) (|associator| (($ $ $ $) NIL)) (|associative?| (((|Boolean|)) 83)) (|apply| (($ (|Matrix| |#1|) $) 18)) (|antiCommutator| (($ $ $) NIL)) (|antiCommutative?| (((|Boolean|)) 86)) (|antiAssociative?| (((|Boolean|)) 84)) (|alternative?| (((|Boolean|)) 82)) (|Zero| (($) NIL T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 76) (($ $ |#1|) NIL) (($ |#1| $) NIL) (($ (|SquareMatrix| |#2| |#1|) $) 19))) 
(((|AlgebraGivenByStructuralConstants| |#1| |#2| |#3| |#4|) (|Join| (|FramedNonAssociativeAlgebra| |#1|) (|LeftModule| (|SquareMatrix| |#2| |#1|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| |#1|))))) (|Field|) (|PositiveInteger|) (|List| (|Symbol|)) (|Vector| (|Matrix| |#1|))) (T |AlgebraGivenByStructuralConstants|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|Field|)) (|ofType| *6 (|Vector| (|Matrix| *3))) (|isDomain| *1 (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6)) (|ofType| *4 (|PositiveInteger|)) (|ofType| *5 (|List| (|Symbol|)))))) 
(|Join| (|FramedNonAssociativeAlgebra| |#1|) (|LeftModule| (|SquareMatrix| |#2| |#1|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| |#1|))))) 
((~= (((|Boolean|) $ $) NIL (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))))) (|value| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL)) (|third| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL)) (|tail| (($ $) NIL)) (|table| (($) NIL) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL)) (|swap!| (((|Void|) $ |#1| |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|split!| (($ $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL) (((|Boolean|) $) NIL (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)))) (|sort!| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $) NIL (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|))))) (|sort| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL) (($ $) NIL (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setvalue!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setrest!| (($ $ $) 27 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setlast!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setfirst!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 29 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#2| $ |#1| |#2|) 45) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Integer|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|UniversalSegment| (|Integer|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ "last" (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "rest" $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ "first" (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ "value" (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select!| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL)) (|select| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|second| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL)) (|search| (((|Union| |#2| "failed") |#1| $) 37)) (|sample| (($) NIL T CONST)) (|reverse!| (($ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) NIL)) (|rest| (($ $ (|NonNegativeInteger|)) NIL) (($ $) 24)) (|removeDuplicates!| (($ $) NIL (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))))) (|remove!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| |#2| "failed") |#1| $) 46) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL) (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (|remove| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| 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(ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| ((|#2| $ |#1| |#2|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Integer|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#2| $ |#1|) NIL) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Integer|)) NIL)) (|possiblyInfinite?| (((|Boolean|) $) NIL)) (|position| (((|Integer|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL) (((|Integer|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))) (((|Integer|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Integer|)) NIL (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (|parts| (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 18 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|List| |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|List| 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(|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copyInto!| (($ $ $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) NIL (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL)) (|concat!| (($ $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL) (($ $ $) NIL)) (|concat| (($ $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL) (($ (|List| $)) NIL) (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 25) (($ $ $) NIL)) (|coerce| (((|OutputForm|) $) NIL (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))))) (|children| (((|List| $) $) NIL)) (|child?| (((|Boolean|) $ $) NIL (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (|bag| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL)) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) 43)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (>= (((|Boolean|) $ $) NIL (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))))) (<= (((|Boolean|) $ $) NIL (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)))) (|#| (((|NonNegativeInteger|) $) 22 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|AssociationList| |#1| |#2|) (|AssociationListAggregate| |#1| |#2|) (|SetCategory|) (|SetCategory|)) (T |AssociationList|)) 
NIL 
(|AssociationListAggregate| |#1| |#2|) 
((|monomial?| (((|Boolean|) $) 12)) (|map| (($ (|Mapping| |#2| |#2|) $) 21)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ (|Fraction| (|Integer|)) $) 24) (($ $ (|Fraction| (|Integer|))) NIL))) 
(((|AbelianMonoidRing&| |#1| |#2| |#3|) (CATEGORY |domain| (SIGNATURE * (|#1| |#1| (|Fraction| (|Integer|)))) (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)) (SIGNATURE |monomial?| ((|Boolean|) |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|AbelianMonoidRing| |#2| |#3|) (|Ring|) (|OrderedAbelianMonoid|)) (T |AbelianMonoidRing&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE * (|#1| |#1| (|Fraction| (|Integer|)))) (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)) (SIGNATURE |monomial?| ((|Boolean|) |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 50 (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) 51 (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) 53 (|has| |#1| (|IntegralDomain|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|reductum| (($ $) 59)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|monomial?| (((|Boolean|) $) 61)) (|monomial| (($ |#1| |#2|) 60)) (|map| (($ (|Mapping| |#1| |#1|) $) 62)) (|leadingMonomial| (($ $) 64)) (|leadingCoefficient| ((|#1| $) 65)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|exquo| (((|Union| $ "failed") $ $) 49 (|has| |#1| (|IntegralDomain|)))) (|degree| ((|#2| $) 63)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ (|Fraction| (|Integer|))) 56 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $) 48 (|has| |#1| (|IntegralDomain|))) (($ |#1|) 46 (|has| |#1| (|CommutativeRing|)))) (|coefficient| ((|#1| $ |#2|) 58)) (|charthRoot| (((|Union| $ "failed") $) 47 (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 52 (|has| |#1| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (/ (($ $ |#1|) 57 (|has| |#1| (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 67) (($ |#1| $) 66) (($ (|Fraction| (|Integer|)) $) 55 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) 54 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) 
(((|AbelianMonoidRing| |#1| |#2|) (|Category|) (|Ring|) (|OrderedAbelianMonoid|)) (T |AbelianMonoidRing|)) 
((|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Ring|)))) (|leadingMonomial| (*1 *1 *1) (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)))) (|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|AbelianMonoidRing| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|AbelianMonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)))) (|monomial?| (*1 *2 *1) (AND (|ofCategory| *1 (|AbelianMonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|Boolean|)))) (|monomial| (*1 *1 *2 *3) (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)))) (|reductum| (*1 *1 *1) (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)))) (|coefficient| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Ring|)))) (/ (*1 *1 *1 *2) (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Field|))))) 
(|Join| (|Ring|) (|BiModule| |t#1| |t#1|) (CATEGORY |domain| (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |leadingMonomial| ($ $)) (SIGNATURE |degree| (|t#2| $)) (SIGNATURE |map| ($ (|Mapping| |t#1| |t#1|) $)) (SIGNATURE |monomial?| ((|Boolean|) $)) (SIGNATURE |monomial| ($ |t#1| |t#2|)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |coefficient| (|t#1| $ |t#2|)) (IF (|has| |t#1| (|Field|)) (SIGNATURE / ($ $ |t#1|)) |noBranch|) (IF (|has| |t#1| (|CommutativeRing|)) (PROGN (ATTRIBUTE (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |t#1|))) |noBranch|) (IF (|has| |t#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |noBranch|) (IF (|has| |t#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (ATTRIBUTE (|IntegralDomain|)) |noBranch|) (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) (ATTRIBUTE (|Algebra| (|Fraction| (|Integer|)))) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|Module| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|RightModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) NIL) (((|List| $) (|SparseUnivariatePolynomial| $)) NIL) (((|List| $) (|Polynomial| $)) NIL)) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) NIL) (($ (|SparseUnivariatePolynomial| $)) NIL) (($ (|Polynomial| $)) NIL)) (|zero?| (((|Boolean|) $) 11)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|tower| (((|List| (|Kernel| $)) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|subst| (($ $ (|Equation| $)) NIL) (($ $ (|List| (|Equation| $))) NIL) (($ $ (|List| (|Kernel| $)) (|List| $)) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sqrt| (($ $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sample| (($) NIL T CONST)) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) NIL) (((|List| $) (|SparseUnivariatePolynomial| $)) NIL) (((|List| $) (|Polynomial| $)) NIL)) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) NIL) (($ (|SparseUnivariatePolynomial| $)) NIL) (($ (|Polynomial| $)) NIL)) (|retractIfCan| (((|Union| (|Kernel| $) "failed") $) NIL) (((|Union| (|Integer|) "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL)) (|retract| (((|Kernel| $) $) NIL) (((|Integer|) $) NIL) (((|Fraction| (|Integer|)) $) NIL)) (|rem| (($ $ $) NIL)) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| (|Integer|)) (|Matrix| $)) NIL) (((|Record| (|:| |mat| (|Matrix| (|Fraction| (|Integer|)))) (|:| |vec| (|Vector| (|Fraction| (|Integer|))))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| (|Fraction| (|Integer|))) (|Matrix| $)) NIL)) (|reduce| (($ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|paren| (($ $) NIL) (($ (|List| $)) NIL)) (|operators| (((|List| (|BasicOperator|)) $) NIL)) (|operator| (((|BasicOperator|) (|BasicOperator|)) NIL)) (|one?| (((|Boolean|) $) 14)) (|odd?| (((|Boolean|) $) NIL (|has| $ (|RetractableTo| (|Integer|))))) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) NIL)) (|nthRoot| (($ $ (|Integer|)) NIL)) (|norm| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) NIL) (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) NIL) (($ $ (|Kernel| $)) NIL) (($ $ (|List| (|Kernel| $))) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) NIL (|has| $ (|Ring|)))) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|map| (($ (|Mapping| $ $) (|Kernel| $)) NIL)) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ (|List| $)) NIL) (($ $ $) NIL)) (|latex| (((|String|) $) NIL)) (|kernels| (((|List| (|Kernel| $)) $) NIL)) (|kernel| (($ (|BasicOperator|) $) NIL) (($ (|BasicOperator|) (|List| $)) NIL)) (|is?| (((|Boolean|) $ (|BasicOperator|)) NIL) (((|Boolean|) $ (|Symbol|)) NIL)) (|inv| (($ $) NIL)) (|height| (((|NonNegativeInteger|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ (|List| $)) NIL) (($ $ $) NIL)) (|freeOf?| (((|Boolean|) $ $) NIL) (((|Boolean|) $ (|Symbol|)) NIL)) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|even?| (((|Boolean|) $) NIL (|has| $ (|RetractableTo| (|Integer|))))) (|eval| (($ $ (|Kernel| $) $) NIL) (($ $ (|List| (|Kernel| $)) (|List| $)) NIL) (($ $ (|List| (|Equation| $))) NIL) (($ $ (|Equation| $)) NIL) (($ $ $ $) NIL) (($ $ (|List| $) (|List| $)) NIL) (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) NIL) (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) NIL) (($ $ (|Symbol|) (|Mapping| $ (|List| $))) NIL) (($ $ (|Symbol|) (|Mapping| $ $)) NIL) (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) NIL) (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) NIL) (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) NIL) (($ $ (|BasicOperator|) (|Mapping| $ $)) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|elt| (($ (|BasicOperator|) $) NIL) (($ (|BasicOperator|) $ $) NIL) (($ (|BasicOperator|) $ $ $) NIL) (($ (|BasicOperator|) $ $ $ $) NIL) (($ (|BasicOperator|) (|List| $)) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|distribute| (($ $) NIL) (($ $ $) NIL)) (|differentiate| (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) NIL)) (|definingPolynomial| (($ $) NIL (|has| $ (|Ring|)))) (|convert| (((|Float|) $) NIL) (((|DoubleFloat|) $) NIL) (((|Complex| (|Float|)) $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Kernel| $)) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ $) NIL) (($ (|Integer|)) NIL) (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|box| (($ $) NIL) (($ (|List| $)) NIL)) (|belong?| (((|Boolean|) (|BasicOperator|)) NIL)) (|associates?| (((|Boolean|) $ $) NIL)) (^ (($ $ (|Integer|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|PositiveInteger|)) NIL)) (|Zero| (($) 7 T CONST)) (|One| (($) 12 T CONST)) (D (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 16)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) NIL)) (/ (($ $ $) NIL)) (- (($ $ $) 15) (($ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|Fraction| (|Integer|))) NIL) (($ $ (|Integer|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|PositiveInteger|)) NIL)) (* (($ (|Fraction| (|Integer|)) $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ $ $) NIL) (($ (|Integer|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|PositiveInteger|) $) NIL))) 
(((|AlgebraicNumber|) (|Join| (|ExpressionSpace|) (|AlgebraicallyClosedField|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))) (|LinearlyExplicitRingOver| (|Integer|)) (|RealConstant|) (|LinearlyExplicitRingOver| (|Fraction| (|Integer|))) (|CharacteristicZero|) (|ConvertibleTo| (|Complex| (|Float|))) (|DifferentialRing|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)))) (SIGNATURE |numer| ((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $)) (SIGNATURE |denom| ((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $)) (SIGNATURE |reduce| ($ $)) (SIGNATURE |norm| ((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $))) (SIGNATURE |norm| ((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $)))) (SIGNATURE |norm| ($ $ (|Kernel| $))) (SIGNATURE |norm| ($ $ (|List| (|Kernel| $))))))) (T |AlgebraicNumber|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| (|AlgebraicNumber|)))) (|isDomain| *1 (|AlgebraicNumber|)))) (|numer| (*1 *2 *1) (AND (|isDomain| *2 (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| (|AlgebraicNumber|)))) (|isDomain| *1 (|AlgebraicNumber|)))) (|denom| (*1 *2 *1) (AND (|isDomain| *2 (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| (|AlgebraicNumber|)))) (|isDomain| *1 (|AlgebraicNumber|)))) (|reduce| (*1 *1 *1) (|isDomain| *1 (|AlgebraicNumber|))) (|norm| (*1 *2 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|isDomain| *3 (|Kernel| (|AlgebraicNumber|))) (|isDomain| *1 (|AlgebraicNumber|)))) (|norm| (*1 *2 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|isDomain| *3 (|List| (|Kernel| (|AlgebraicNumber|)))) (|isDomain| *1 (|AlgebraicNumber|)))) (|norm| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Kernel| (|AlgebraicNumber|))) (|isDomain| *1 (|AlgebraicNumber|)))) (|norm| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Kernel| (|AlgebraicNumber|)))) (|isDomain| *1 (|AlgebraicNumber|))))) 
(|Join| (|ExpressionSpace|) (|AlgebraicallyClosedField|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))) (|LinearlyExplicitRingOver| (|Integer|)) (|RealConstant|) (|LinearlyExplicitRingOver| (|Fraction| (|Integer|))) (|CharacteristicZero|) (|ConvertibleTo| (|Complex| (|Float|))) (|DifferentialRing|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)))) (SIGNATURE |numer| ((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $)) (SIGNATURE |denom| ((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $)) (SIGNATURE |reduce| ($ $)) (SIGNATURE |norm| ((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $))) (SIGNATURE |norm| ((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $)))) (SIGNATURE |norm| ($ $ (|Kernel| $))) (SIGNATURE |norm| ($ $ (|List| (|Kernel| $)))))) 
((~= (((|Boolean|) $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 7)) (= (((|Boolean|) $ $) NIL))) 
(((|AnonymousFunction|) (|SetCategory|)) (T |AnonymousFunction|)) 
NIL 
(|SetCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 60)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|retractable?| (((|Boolean|) $) 20)) (|retractIfCan| (((|Union| |#1| "failed") $) 23)) (|retract| ((|#1| $) 24)) (|reductum| (($ $) 27)) (|recip| (((|Union| $ "failed") $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|leadingCoefficient| ((|#1| $) 21)) (|leadingBasisTerm| (($ $) 49)) (|latex| (((|String|) $) NIL)) (|homogeneous?| (((|Boolean|) $) 28)) (|hash| (((|SingleInteger|) $) NIL)) (|generator| (($ (|NonNegativeInteger|)) 47)) (|exp| (($ (|List| (|Integer|))) 48)) (|degree| (((|NonNegativeInteger|) $) 29)) (|coerce| (((|OutputForm|) $) 63) (($ (|Integer|)) 44) (($ |#1|) 42)) (|coefficient| ((|#1| $ $) 19)) (|characteristic| (((|NonNegativeInteger|)) 46)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 30 T CONST)) (|One| (($) 14 T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) 40)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 41) (($ |#1| $) 35))) 
(((|AntiSymm| |#1| |#2|) (|Join| (|LeftAlgebra| |#1|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |leadingCoefficient| (|#1| $)) (SIGNATURE |leadingBasisTerm| ($ $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |coefficient| (|#1| $ $)) (SIGNATURE |generator| ($ (|NonNegativeInteger|))) (SIGNATURE |exp| ($ (|List| (|Integer|)))) (SIGNATURE |homogeneous?| ((|Boolean|) $)) (SIGNATURE |retractable?| ((|Boolean|) $)) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)))) (|Ring|) (|List| (|Symbol|))) (T |AntiSymm|)) 
((|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|AntiSymm| *2 *3)) (|ofType| *3 (|List| (|Symbol|))))) (|leadingBasisTerm| (*1 *1 *1) (AND (|isDomain| *1 (|AntiSymm| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofType| *3 (|List| (|Symbol|))))) (|reductum| (*1 *1 *1) (AND (|isDomain| *1 (|AntiSymm| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofType| *3 (|List| (|Symbol|))))) (|coefficient| (*1 *2 *1 *1) (AND (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|AntiSymm| *2 *3)) (|ofType| *3 (|List| (|Symbol|))))) (|generator| (*1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|AntiSymm| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|List| (|Symbol|))))) (|exp| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|AntiSymm| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|List| (|Symbol|))))) (|homogeneous?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|AntiSymm| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|List| (|Symbol|))))) (|retractable?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|AntiSymm| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|List| (|Symbol|))))) (|degree| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|AntiSymm| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|List| (|Symbol|))))) (|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|AntiSymm| *3 *4)) (|ofType| *4 (|List| (|Symbol|)))))) 
(|Join| (|LeftAlgebra| |#1|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |leadingCoefficient| (|#1| $)) (SIGNATURE |leadingBasisTerm| ($ $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |coefficient| (|#1| $ $)) (SIGNATURE |generator| ($ (|NonNegativeInteger|))) (SIGNATURE |exp| ($ (|List| (|Integer|)))) (SIGNATURE |homogeneous?| ((|Boolean|) $)) (SIGNATURE |retractable?| ((|Boolean|) $)) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)))) 
((|retractable?| (((|Boolean|) (|Any|)) 13)) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) 21)) (|retract| ((|#1| (|Any|)) 22)) (|coerce| (((|Any|) |#1|) 18))) 
(((|AnyFunctions1| |#1|) (CATEGORY |package| (SIGNATURE |coerce| ((|Any|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#1| "failed") (|Any|))) (SIGNATURE |retractable?| ((|Boolean|) (|Any|))) (SIGNATURE |retract| (|#1| (|Any|)))) (|Type|)) (T |AnyFunctions1|)) 
((|retract| (*1 *2 *3) (AND (|isDomain| *3 (|Any|)) (|isDomain| *1 (|AnyFunctions1| *2)) (|ofCategory| *2 (|Type|)))) (|retractable?| (*1 *2 *3) (AND (|isDomain| *3 (|Any|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|AnyFunctions1| *4)) (|ofCategory| *4 (|Type|)))) (|retractIfCan| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|Any|)) (|isDomain| *1 (|AnyFunctions1| *2)) (|ofCategory| *2 (|Type|)))) (|coerce| (*1 *2 *3) (AND (|isDomain| *2 (|Any|)) (|isDomain| *1 (|AnyFunctions1| *3)) (|ofCategory| *3 (|Type|))))) 
(CATEGORY |package| (SIGNATURE |coerce| ((|Any|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#1| "failed") (|Any|))) (SIGNATURE |retractable?| ((|Boolean|) (|Any|))) (SIGNATURE |retract| (|#1| (|Any|)))) 
((~= (((|Boolean|) $ $) NIL)) (|showTypeInOutput| (((|String|) (|Boolean|)) 25)) (|objectOf| (((|OutputForm|) $) 24)) (|obj| (((|None|) $) 12)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|domainOf| (((|OutputForm|) $) 16)) (|dom| (((|SExpression|) $) 14)) (|coerce| (((|OutputForm|) $) 32)) (|any| (($ (|SExpression|) (|None|)) 33)) (= (((|Boolean|) $ $) 18))) 
(((|Any|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |any| ($ (|SExpression|) (|None|))) (SIGNATURE |domainOf| ((|OutputForm|) $)) (SIGNATURE |objectOf| ((|OutputForm|) $)) (SIGNATURE |dom| ((|SExpression|) $)) (SIGNATURE |obj| ((|None|) $)) (SIGNATURE |showTypeInOutput| ((|String|) (|Boolean|)))))) (T |Any|)) 
((|any| (*1 *1 *2 *3) (AND (|isDomain| *2 (|SExpression|)) (|isDomain| *3 (|None|)) (|isDomain| *1 (|Any|)))) (|domainOf| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|Any|)))) (|objectOf| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|Any|)))) (|dom| (*1 *2 *1) (AND (|isDomain| *2 (|SExpression|)) (|isDomain| *1 (|Any|)))) (|obj| (*1 *2 *1) (AND (|isDomain| *2 (|None|)) (|isDomain| *1 (|Any|)))) (|showTypeInOutput| (*1 *2 *3) (AND (|isDomain| *3 (|Boolean|)) (|isDomain| *2 (|String|)) (|isDomain| *1 (|Any|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |any| ($ (|SExpression|) (|None|))) (SIGNATURE |domainOf| ((|OutputForm|) $)) (SIGNATURE |objectOf| ((|OutputForm|) $)) (SIGNATURE |dom| ((|SExpression|) $)) (SIGNATURE |obj| ((|None|) $)) (SIGNATURE |showTypeInOutput| ((|String|) (|Boolean|))))) 
((|summary| (((|Void|)) 20)) (|reportInstantiations| (((|Void|) (|Boolean|)) 22)) (|getDomains| (((|Set| (|Symbol|)) (|Symbol|)) 15)) (|getAncestors| (((|Set| (|Symbol|)) (|Symbol|)) 16)) (|credits| (((|Void|)) 19))) 
(((|ApplicationProgramInterface|) (CATEGORY |package| (SIGNATURE |getDomains| ((|Set| (|Symbol|)) (|Symbol|))) (SIGNATURE |getAncestors| ((|Set| (|Symbol|)) (|Symbol|))) (SIGNATURE |credits| ((|Void|))) (SIGNATURE |summary| ((|Void|))) (SIGNATURE |reportInstantiations| ((|Void|) (|Boolean|))))) (T |ApplicationProgramInterface|)) 
((|reportInstantiations| (*1 *2 *3) (AND (|isDomain| *3 (|Boolean|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ApplicationProgramInterface|)))) (|summary| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ApplicationProgramInterface|)))) (|credits| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ApplicationProgramInterface|)))) (|getAncestors| (*1 *2 *3) (AND (|isDomain| *2 (|Set| (|Symbol|))) (|isDomain| *1 (|ApplicationProgramInterface|)) (|isDomain| *3 (|Symbol|)))) (|getDomains| (*1 *2 *3) (AND (|isDomain| *2 (|Set| (|Symbol|))) (|isDomain| *1 (|ApplicationProgramInterface|)) (|isDomain| *3 (|Symbol|))))) 
(CATEGORY |package| (SIGNATURE |getDomains| ((|Set| (|Symbol|)) (|Symbol|))) (SIGNATURE |getAncestors| ((|Set| (|Symbol|)) (|Symbol|))) (SIGNATURE |credits| ((|Void|))) (SIGNATURE |summary| ((|Void|))) (SIGNATURE |reportInstantiations| ((|Void|) (|Boolean|)))) 
((|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) 16))) 
(((|ApplyUnivariateSkewPolynomial| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |apply| (|#2| |#3| (|Mapping| |#2| |#2|) |#2|))) (|Ring|) (|LeftModule| |#1|) (|UnivariateSkewPolynomialCategory| |#1|)) (T |ApplyUnivariateSkewPolynomial|)) 
((|apply| (*1 *2 *3 *4 *2) (AND (|isDomain| *4 (|Mapping| *2 *2)) (|ofCategory| *2 (|LeftModule| *5)) (|ofCategory| *5 (|Ring|)) (|isDomain| *1 (|ApplyUnivariateSkewPolynomial| *5 *2 *3)) (|ofCategory| *3 (|UnivariateSkewPolynomialCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |apply| (|#2| |#3| (|Mapping| |#2| |#2|) |#2|))) 
((|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) 35)) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) 22) ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) 20))) 
(((|ApplyRules| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |applyRules| (|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|)) (SIGNATURE |applyRules| (|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|))) (SIGNATURE |localUnquote| (|#3| |#3| (|List| (|Symbol|))))) (|SetCategory|) (|Join| (|Ring|) (|PatternMatchable| |#1|) (|OrderedSet|) (|ConvertibleTo| (|Pattern| |#1|))) (|Join| (|FunctionSpace| |#2|) (|PatternMatchable| |#1|) (|ConvertibleTo| (|Pattern| |#1|)))) (T |ApplyRules|)) 
((|localUnquote| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|Join| (|Ring|) (|PatternMatchable| *4) (|OrderedSet|) (|ConvertibleTo| (|Pattern| *4)))) (|isDomain| *1 (|ApplyRules| *4 *5 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *5) (|PatternMatchable| *4) (|ConvertibleTo| (|Pattern| *4)))))) (|applyRules| (*1 *2 *3 *2 *4) (AND (|isDomain| *3 (|List| (|RewriteRule| *5 *6 *2))) (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|Join| (|Ring|) (|PatternMatchable| *5) (|OrderedSet|) (|ConvertibleTo| (|Pattern| *5)))) (|ofCategory| *2 (|Join| (|FunctionSpace| *6) (|PatternMatchable| *5) (|ConvertibleTo| (|Pattern| *5)))) (|isDomain| *1 (|ApplyRules| *5 *6 *2)))) (|applyRules| (*1 *2 *3 *2) (AND (|isDomain| *3 (|List| (|RewriteRule| *4 *5 *2))) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|Join| (|Ring|) (|PatternMatchable| *4) (|OrderedSet|) (|ConvertibleTo| (|Pattern| *4)))) (|ofCategory| *2 (|Join| (|FunctionSpace| *5) (|PatternMatchable| *4) (|ConvertibleTo| (|Pattern| *4)))) (|isDomain| *1 (|ApplyRules| *4 *5 *2))))) 
(CATEGORY |package| (SIGNATURE |applyRules| (|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|)) (SIGNATURE |applyRules| (|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|))) (SIGNATURE |localUnquote| (|#3| |#3| (|List| (|Symbol|))))) 
((|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 23)) (|setRow!| (($ $ (|Integer|) |#3|) 45)) (|setColumn!| (($ $ (|Integer|) |#4|) 49)) (|row| ((|#3| $ (|Integer|)) 58)) (|parts| (((|List| |#2|) $) 30)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 25)) (|member?| (((|Boolean|) |#2| $) 53)) (|map!| (($ (|Mapping| |#2| |#2|) $) 37)) (|map| (($ (|Mapping| |#2| |#2|) $) 36) (($ (|Mapping| |#2| |#2| |#2|) $ $) 39) (($ (|Mapping| |#2| |#2| |#2|) $ $ |#2|) 41)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 24)) (|fill!| (($ $ |#2|) 34)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 19)) (|elt| ((|#2| $ (|Integer|) (|Integer|)) NIL) ((|#2| $ (|Integer|) (|Integer|) |#2|) 27)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) 28) (((|NonNegativeInteger|) |#2| $) 55)) (|copy| (($ $) 33)) (|column| ((|#4| $ (|Integer|)) 61)) (|coerce| (((|OutputForm|) $) 66)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 18)) (= (((|Boolean|) $ $) 52)) (|#| (((|NonNegativeInteger|) $) 26))) 
(((|TwoDimensionalArrayCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2| |#2|) |#1| |#1| |#2|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2| |#2|) |#1| |#1|)) (SIGNATURE |map!| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |setColumn!| (|#1| |#1| (|Integer|) |#4|)) (SIGNATURE |setRow!| (|#1| |#1| (|Integer|) |#3|)) (SIGNATURE |parts| ((|List| |#2|) |#1|)) (SIGNATURE |column| (|#4| |#1| (|Integer|))) (SIGNATURE |row| (|#3| |#1| (|Integer|))) (SIGNATURE |elt| (|#2| |#1| (|Integer|) (|Integer|) |#2|)) (SIGNATURE |elt| (|#2| |#1| (|Integer|) (|Integer|))) (SIGNATURE |fill!| (|#1| |#1| |#2|)) (SIGNATURE = ((|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |member?| ((|Boolean|) |#2| |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) |#2| |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |size?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |less?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |copy| (|#1| |#1|))) (|TwoDimensionalArrayCategory| |#2| |#3| |#4|) (|Type|) (|FiniteLinearAggregate| |#2|) (|FiniteLinearAggregate| |#2|)) (T |TwoDimensionalArrayCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2| |#2|) |#1| |#1| |#2|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2| |#2|) |#1| |#1|)) (SIGNATURE |map!| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |setColumn!| (|#1| |#1| (|Integer|) |#4|)) (SIGNATURE |setRow!| (|#1| |#1| (|Integer|) |#3|)) (SIGNATURE |parts| ((|List| |#2|) |#1|)) (SIGNATURE |column| (|#4| |#1| (|Integer|))) (SIGNATURE |row| (|#3| |#1| (|Integer|))) (SIGNATURE |elt| (|#2| |#1| (|Integer|) (|Integer|) |#2|)) (SIGNATURE |elt| (|#2| |#1| (|Integer|) (|Integer|))) (SIGNATURE |fill!| (|#1| |#1| |#2|)) (SIGNATURE = ((|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |member?| ((|Boolean|) |#2| |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) |#2| |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |size?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |less?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |copy| (|#1| |#1|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) 41)) (|setRow!| (($ $ (|Integer|) |#2|) 39)) (|setColumn!| (($ $ (|Integer|) |#3|) 38)) (|sample| (($) 7 T CONST)) (|row| ((|#2| $ (|Integer|)) 43)) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) 40)) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) 45)) (|parts| (((|List| |#1|) $) 30)) (|nrows| (((|NonNegativeInteger|) $) 48)) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) 54)) (|ncols| (((|NonNegativeInteger|) $) 47)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|minRowIndex| (((|Integer|) $) 52)) (|minColIndex| (((|Integer|) $) 50)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|maxRowIndex| (((|Integer|) $) 51)) (|maxColIndex| (((|Integer|) $) 49)) (|map!| (($ (|Mapping| |#1| |#1|) $) 34)) (|map| (($ (|Mapping| |#1| |#1|) $) 35) (($ (|Mapping| |#1| |#1| |#1|) $ $) 37) (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) 36)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|fill!| (($ $ |#1|) 53)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| ((|#1| $ (|Integer|) (|Integer|)) 46) ((|#1| $ (|Integer|) (|Integer|) |#1|) 44)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|column| ((|#3| $ (|Integer|)) 42)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|TwoDimensionalArrayCategory| |#1| |#2| |#3|) (|Category|) (|Type|) (|FiniteLinearAggregate| |t#1|) (|FiniteLinearAggregate| |t#1|)) (T |TwoDimensionalArrayCategory|)) 
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*5)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|NonNegativeInteger|)))) (|elt| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|TwoDimensionalArrayCategory| *2 *4 *5)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)) (|ofCategory| *5 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|qelt| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|TwoDimensionalArrayCategory| *2 *4 *5)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)) (|ofCategory| *5 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|elt| (*1 *2 *1 *3 *3 *2) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|TwoDimensionalArrayCategory| *2 *4 *5)) (|ofCategory| *2 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)) (|ofCategory| *5 (|FiniteLinearAggregate| *2)))) (|row| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|TwoDimensionalArrayCategory| *4 *2 *5)) (|ofCategory| *4 (|Type|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *2 (|FiniteLinearAggregate| *4)))) (|column| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|TwoDimensionalArrayCategory| *4 *5 *2)) (|ofCategory| *4 (|Type|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *2 (|FiniteLinearAggregate| *4)))) (|parts| (*1 *2 *1) (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|List| *3)))) (|setelt| (*1 *2 *1 *3 *3 *2) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|TwoDimensionalArrayCategory| *2 *4 *5)) (|ofCategory| *2 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)) (|ofCategory| *5 (|FiniteLinearAggregate| *2)))) (|qsetelt!| (*1 *2 *1 *3 *3 *2) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|TwoDimensionalArrayCategory| *2 *4 *5)) (|ofCategory| *2 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)) (|ofCategory| *5 (|FiniteLinearAggregate| *2)))) (|setRow!| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|TwoDimensionalArrayCategory| *4 *3 *5)) (|ofCategory| *4 (|Type|)) (|ofCategory| *3 (|FiniteLinearAggregate| *4)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)))) (|setColumn!| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|TwoDimensionalArrayCategory| *4 *5 *3)) (|ofCategory| *4 (|Type|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *3 (|FiniteLinearAggregate| *4)))) (|map!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)))) (|map| (*1 *1 *2 *1 *1) (AND (|isDomain| *2 (|Mapping| *3 *3 *3)) (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)))) (|map| (*1 *1 *2 *1 *1 *3) (AND (|isDomain| *2 (|Mapping| *3 *3 *3)) (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3))))) 
(|Join| (|HomogeneousAggregate| |t#1|) (CATEGORY |domain| (ATTRIBUTE |shallowlyMutable|) (ATTRIBUTE |finiteAggregate|) (SIGNATURE |new| ($ (|NonNegativeInteger|) (|NonNegativeInteger|) |t#1|)) (SIGNATURE |fill!| ($ $ |t#1|)) (SIGNATURE |minRowIndex| ((|Integer|) $)) (SIGNATURE |maxRowIndex| ((|Integer|) $)) (SIGNATURE |minColIndex| ((|Integer|) $)) (SIGNATURE |maxColIndex| ((|Integer|) $)) (SIGNATURE |nrows| ((|NonNegativeInteger|) $)) (SIGNATURE |ncols| ((|NonNegativeInteger|) $)) (SIGNATURE |elt| (|t#1| $ (|Integer|) (|Integer|))) (SIGNATURE |qelt| (|t#1| $ (|Integer|) (|Integer|))) (SIGNATURE |elt| (|t#1| $ (|Integer|) (|Integer|) |t#1|)) (SIGNATURE |row| (|t#2| $ (|Integer|))) (SIGNATURE |column| (|t#3| $ (|Integer|))) (SIGNATURE |parts| ((|List| |t#1|) $)) (SIGNATURE |setelt| (|t#1| $ (|Integer|) (|Integer|) |t#1|)) (SIGNATURE |qsetelt!| (|t#1| $ (|Integer|) (|Integer|) |t#1|)) (SIGNATURE |setRow!| ($ $ (|Integer|) |t#2|)) (SIGNATURE |setColumn!| ($ $ (|Integer|) |t#3|)) (SIGNATURE |map| ($ (|Mapping| |t#1| |t#1|) $)) (SIGNATURE |map!| ($ (|Mapping| |t#1| |t#1|) $)) (SIGNATURE |map| ($ (|Mapping| |t#1| |t#1| |t#1|) $ $)) (SIGNATURE |map| ($ (|Mapping| |t#1| |t#1| |t#1|) $ $ |t#1|)))) 
(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) 16)) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) 18)) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) 13))) 
(((|OneDimensionalArrayFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |scan| ((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|)) (SIGNATURE |map| ((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)))) (|Type|) (|Type|)) (T |OneDimensionalArrayFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|OneDimensionalArray| *5)) (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|OneDimensionalArray| *6)) (|isDomain| *1 (|OneDimensionalArrayFunctions2| *5 *6)))) (|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) (|isDomain| *4 (|OneDimensionalArray| *5)) (|ofCategory| *5 (|Type|)) (|ofCategory| *2 (|Type|)) (|isDomain| *1 (|OneDimensionalArrayFunctions2| *5 *2)))) (|scan| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *5 *6 *5)) (|isDomain| *4 (|OneDimensionalArray| *6)) (|ofCategory| *6 (|Type|)) (|ofCategory| *5 (|Type|)) (|isDomain| *2 (|OneDimensionalArray| *5)) (|isDomain| *1 (|OneDimensionalArrayFunctions2| *6 *5))))) 
(CATEGORY |package| (SIGNATURE |scan| ((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|)) (SIGNATURE |map| ((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)))) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) NIL) (((|Boolean|) $) NIL (|has| |#1| (|OrderedSet|)))) (|sort!| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $) NIL (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|has| |#1| (|OrderedSet|))))) (|sort| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) NIL) (($ $) NIL (|has| |#1| (|OrderedSet|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setelt| ((|#1| $ (|Integer|) |#1|) 11 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) NIL T CONST)) (|reverse!| (($ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) NIL)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|remove| (($ |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| ((|#1| $ (|Integer|) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#1| $ (|Integer|)) NIL)) (|position| (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) NIL) (((|Integer|) |#1| $) NIL (|has| |#1| (|SetCategory|))) (((|Integer|) |#1| $ (|Integer|)) NIL (|has| |#1| (|SetCategory|)))) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|oneDimensionalArray| (($ (|List| |#1|)) 13) (($ (|NonNegativeInteger|) |#1|) 14)) (|new| (($ (|NonNegativeInteger|) |#1|) 9)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|merge| (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) NIL) (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|maxIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|insert| (($ |#1| $ (|Integer|)) NIL) (($ $ $ (|Integer|)) NIL)) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|first| ((|#1| $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) NIL)) (|fill!| (($ $ |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|entry?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|entries| (((|List| |#1|) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) 7)) (|elt| ((|#1| $ (|Integer|) |#1|) NIL) ((|#1| $ (|Integer|)) NIL) (($ $ (|UniversalSegment| (|Integer|))) NIL)) (|delete| (($ $ (|Integer|)) NIL) (($ $ (|UniversalSegment| (|Integer|))) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copyInto!| (($ $ $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) NIL)) (|concat| (($ $ |#1|) NIL) (($ |#1| $) NIL) (($ $ $) NIL) (($ (|List| $)) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|OneDimensionalArray| |#1|) (|Join| (|OneDimensionalArrayAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |oneDimensionalArray| ($ (|List| |#1|))) (SIGNATURE |oneDimensionalArray| ($ (|NonNegativeInteger|) |#1|)))) (|Type|)) (T |OneDimensionalArray|)) 
((|oneDimensionalArray| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|OneDimensionalArray| *3)))) (|oneDimensionalArray| (*1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|OneDimensionalArray| *3)) (|ofCategory| *3 (|Type|))))) 
(|Join| (|OneDimensionalArrayAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |oneDimensionalArray| ($ (|List| |#1|))) (SIGNATURE |oneDimensionalArray| ($ (|NonNegativeInteger|) |#1|)))) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) NIL)) (|setRow!| (($ $ (|Integer|) (|OneDimensionalArray| |#1|)) NIL)) (|setColumn!| (($ $ (|Integer|) (|OneDimensionalArray| |#1|)) NIL)) (|sample| (($) NIL T CONST)) (|row| (((|OneDimensionalArray| |#1|) $ (|Integer|)) NIL)) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) NIL)) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) NIL)) (|parts| (((|List| |#1|) $) NIL)) (|nrows| (((|NonNegativeInteger|) $) NIL)) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) NIL)) (|ncols| (((|NonNegativeInteger|) $) NIL)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minRowIndex| (((|Integer|) $) NIL)) (|minColIndex| (((|Integer|) $) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|maxRowIndex| (((|Integer|) $) NIL)) (|maxColIndex| (((|Integer|) $) NIL)) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|fill!| (($ $ |#1|) NIL)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#1| $ (|Integer|) (|Integer|)) NIL) ((|#1| $ (|Integer|) (|Integer|) |#1|) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) NIL)) (|column| (((|OneDimensionalArray| |#1|) $ (|Integer|)) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|TwoDimensionalArray| |#1|) (|Join| (|TwoDimensionalArrayCategory| |#1| (|OneDimensionalArray| |#1|) (|OneDimensionalArray| |#1|)) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|))) (|Type|)) (T |TwoDimensionalArray|)) 
NIL 
(|Join| (|TwoDimensionalArrayCategory| |#1| (|OneDimensionalArray| |#1|) (|OneDimensionalArray| |#1|)) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|))) 
((|retractIfCan| (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) 69) (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) 58) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) 91) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) 80) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 47) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 36)) (|retract| (($ (|Vector| (|Expression| (|Float|)))) 65) (($ (|Vector| (|Expression| (|Integer|)))) 54) (($ (|Vector| (|Polynomial| (|Float|)))) 87) (($ (|Vector| (|Polynomial| (|Integer|)))) 76) (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 43) (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 29)) (|outputAsFortran| (((|Void|) $) 118)) (|coerce| (((|OutputForm|) $) 111) (($ (|List| (|FortranCode|))) 100) (($ (|FortranCode|)) 94) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 97) (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) 28))) 
(((|Asp10| |#1|) (|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|))))))) (|Symbol|)) (T |Asp10|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) (|isDomain| *1 (|Asp10| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|))))))) 
((|outputAsFortran| (((|Void|) $) 48) (((|Void|)) 49)) (|coerce| (((|OutputForm|) $) 45))) 
(((|Asp12| |#1|) (|Join| (|FortranProgramCategory|) (CATEGORY |package| (SIGNATURE |outputAsFortran| ((|Void|))))) (|Symbol|)) (T |Asp12|)) 
((|outputAsFortran| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Asp12| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranProgramCategory|) (CATEGORY |package| (SIGNATURE |outputAsFortran| ((|Void|))))) 
((|retractIfCan| (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) 142) (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) 132) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) 163) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) 152) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 121) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 110)) (|retract| (($ (|Vector| (|Expression| (|Float|)))) 138) (($ (|Vector| (|Expression| (|Integer|)))) 128) (($ (|Vector| (|Polynomial| (|Float|)))) 159) (($ (|Vector| (|Polynomial| (|Integer|)))) 148) (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 117) (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 103)) (|outputAsFortran| (((|Void|) $) 96)) (|coerce| (((|OutputForm|) $) 90) (($ (|List| (|FortranCode|))) 28) (($ (|FortranCode|)) 34) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 31) (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) 88))) 
(((|Asp19| |#1|) (|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))))))) (|Symbol|)) (T |Asp19|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) (|isDomain| *1 (|Asp19| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))))))) 
((|retractIfCan| (((|Union| $ "failed") (|Expression| (|Float|))) 36) (((|Union| $ "failed") (|Expression| (|Integer|))) 41) (((|Union| $ "failed") (|Polynomial| (|Float|))) 46) (((|Union| $ "failed") (|Polynomial| (|Integer|))) 51) (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) 31) (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) 26)) (|retract| (($ (|Expression| (|Float|))) 34) (($ (|Expression| (|Integer|))) 39) (($ (|Polynomial| (|Float|))) 44) (($ (|Polynomial| (|Integer|))) 49) (($ (|Fraction| (|Polynomial| (|Float|)))) 29) (($ (|Fraction| (|Polynomial| (|Integer|)))) 23)) (|outputAsFortran| (((|Void|) $) 73)) (|coerce| (((|OutputForm|) $) 66) (($ (|List| (|FortranCode|))) 57) (($ (|FortranCode|)) 63) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 60) (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) 22))) 
(((|Asp1| |#1|) (|Join| (|FortranFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))))) (|Symbol|)) (T |Asp1|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) (|isDomain| *1 (|Asp1| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))))) 
((|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) 100) (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) 89) (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) 122) (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) 111) (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) 78) (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) 67)) (|retract| (($ (|Matrix| (|Expression| (|Float|)))) 96) (($ (|Matrix| (|Expression| (|Integer|)))) 85) (($ (|Matrix| (|Polynomial| (|Float|)))) 118) (($ (|Matrix| (|Polynomial| (|Integer|)))) 107) (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) 74) (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) 60)) (|outputAsFortran| (((|Void|) $) 130)) (|coerce| (((|OutputForm|) $) 124) (($ (|List| (|FortranCode|))) 27) (($ (|FortranCode|)) 33) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 30) (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) 53))) 
(((|Asp20| |#1|) (|Join| (|FortranMatrixFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|))))))) (|Symbol|)) (T |Asp20|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) (|isDomain| *1 (|Asp20| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranMatrixFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|))))))) 
((|retractIfCan| (((|Union| $ "failed") (|Expression| (|Float|))) 54) (((|Union| $ "failed") (|Expression| (|Integer|))) 59) (((|Union| $ "failed") (|Polynomial| (|Float|))) 64) (((|Union| $ "failed") (|Polynomial| (|Integer|))) 69) (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) 49) (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) 44)) (|retract| (($ (|Expression| (|Float|))) 52) (($ (|Expression| (|Integer|))) 57) (($ (|Polynomial| (|Float|))) 62) (($ (|Polynomial| (|Integer|))) 67) (($ (|Fraction| (|Polynomial| (|Float|)))) 47) (($ (|Fraction| (|Polynomial| (|Integer|)))) 41)) (|outputAsFortran| (((|Void|) $) 78)) (|coerce| (((|OutputForm|) $) 72) (($ (|List| (|FortranCode|))) 27) (($ (|FortranCode|)) 33) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 30) (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) 38))) 
(((|Asp24| |#1|) (|Join| (|FortranFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))))) (|Symbol|)) (T |Asp24|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) (|isDomain| *1 (|Asp24| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))))) 
((|outputAsFortran| (((|Void|) $) 63)) (|coerce| (((|OutputForm|) $) 57) (($ (|Matrix| (|MachineFloat|))) 49) (($ (|List| (|FortranCode|))) 48) (($ (|FortranCode|)) 55) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 53))) 
(((|Asp27| |#1|) (|FortranMatrixCategory|) (|Symbol|)) (T |Asp27|)) 
NIL 
(|FortranMatrixCategory|) 
((|outputAsFortran| (((|Void|) $) 64)) (|coerce| (((|OutputForm|) $) 58) (($ (|Matrix| (|MachineFloat|))) 50) (($ (|List| (|FortranCode|))) 49) (($ (|FortranCode|)) 52) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 55))) 
(((|Asp28| |#1|) (|FortranMatrixCategory|) (|Symbol|)) (T |Asp28|)) 
NIL 
(|FortranMatrixCategory|) 
((|outputAsFortran| (((|Void|) $) NIL) (((|Void|)) 32)) (|coerce| (((|OutputForm|) $) NIL))) 
(((|Asp29| |#1|) (|Join| (|FortranProgramCategory|) (CATEGORY |package| (SIGNATURE |outputAsFortran| ((|Void|))))) (|Symbol|)) (T |Asp29|)) 
((|outputAsFortran| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Asp29| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranProgramCategory|) (CATEGORY |package| (SIGNATURE |outputAsFortran| ((|Void|))))) 
((|outputAsFortran| (((|Void|) $) 68)) (|coerce| (((|OutputForm|) $) 62) (($ (|Matrix| (|MachineFloat|))) 53) (($ (|List| (|FortranCode|))) 56) (($ (|FortranCode|)) 59) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 52))) 
(((|Asp30| |#1|) (|FortranMatrixCategory|) (|Symbol|)) (T |Asp30|)) 
NIL 
(|FortranMatrixCategory|) 
((|retractIfCan| (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) 98) (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) 87) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) 119) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) 108) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 76) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 65)) (|retract| (($ (|Vector| (|Expression| (|Float|)))) 94) (($ (|Vector| (|Expression| (|Integer|)))) 83) (($ (|Vector| (|Polynomial| (|Float|)))) 115) (($ (|Vector| (|Polynomial| (|Integer|)))) 104) (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 72) (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 58)) (|outputAsFortran| (((|Void|) $) 133)) (|coerce| (((|OutputForm|) $) 127) (($ (|List| (|FortranCode|))) 122) (($ (|FortranCode|)) 125) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 50) (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) 51))) 
(((|Asp31| |#1|) (|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))))))) (|Symbol|)) (T |Asp31|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) (|isDomain| *1 (|Asp31| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))))))) 
((|outputAsFortran| (((|Void|) $) 32) (((|Void|)) 31)) (|coerce| (((|OutputForm|) $) 35))) 
(((|Asp33| |#1|) (|Join| (|FortranProgramCategory|) (CATEGORY |package| (SIGNATURE |outputAsFortran| ((|Void|))))) (|Symbol|)) (T |Asp33|)) 
((|outputAsFortran| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Asp33| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranProgramCategory|) (CATEGORY |package| (SIGNATURE |outputAsFortran| ((|Void|))))) 
((|outputAsFortran| (((|Void|) $) 62)) (|coerce| (((|OutputForm|) $) 56) (($ (|Matrix| (|MachineFloat|))) 47) (($ (|List| (|FortranCode|))) 50) (($ (|FortranCode|)) 53) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 46))) 
(((|Asp34| |#1|) (|FortranMatrixCategory|) (|Symbol|)) (T |Asp34|)) 
NIL 
(|FortranMatrixCategory|) 
((|retractIfCan| (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) 119) (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) 108) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) 141) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) 130) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 98) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 87)) (|retract| (($ (|Vector| (|Expression| (|Float|)))) 115) (($ (|Vector| (|Expression| (|Integer|)))) 104) (($ (|Vector| (|Polynomial| (|Float|)))) 137) (($ (|Vector| (|Polynomial| (|Integer|)))) 126) (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 94) (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 80)) (|outputAsFortran| (((|Void|) $) 73)) (|coerce| (((|OutputForm|) $) 27) (($ (|List| (|FortranCode|))) 63) (($ (|FortranCode|)) 59) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 66) (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) 60))) 
(((|Asp35| |#1|) (|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))))))) (|Symbol|)) (T |Asp35|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) (|isDomain| *1 (|Asp35| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))))))) 
((|retractIfCan| (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) 125) (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) 114) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) 147) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) 136) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 103) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 92)) (|retract| (($ (|Vector| (|Expression| (|Float|)))) 121) (($ (|Vector| (|Expression| (|Integer|)))) 110) (($ (|Vector| (|Polynomial| (|Float|)))) 143) (($ (|Vector| (|Polynomial| (|Integer|)))) 132) (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 99) (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 85)) (|outputAsFortran| (((|Void|) $) 78)) (|coerce| (((|OutputForm|) $) 70) (($ (|List| (|FortranCode|))) NIL) (($ (|FortranCode|)) NIL) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) NIL) (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE EPS)) (|construct| (QUOTE Y)) (|MachineFloat|)))) 65))) 
(((|Asp41| |#1| |#2| |#3|) (|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE EPS)) (|construct| (QUOTE Y)) (|MachineFloat|))))))) (|Symbol|) (|Symbol|) (|Symbol|)) (T |Asp41|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE EPS)) (|construct| (QUOTE Y)) (|MachineFloat|)))) (|isDomain| *1 (|Asp41| *3 *4 *5)) (|ofType| *3 (|Symbol|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 (|Symbol|))))) 
(|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE EPS)) (|construct| (QUOTE Y)) (|MachineFloat|))))))) 
((|retractIfCan| (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) 129) (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) 118) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) 151) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) 140) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 107) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 96)) (|retract| (($ (|Vector| (|Expression| (|Float|)))) 125) (($ (|Vector| (|Expression| (|Integer|)))) 114) (($ (|Vector| (|Polynomial| (|Float|)))) 147) (($ (|Vector| (|Polynomial| (|Integer|)))) 136) (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 103) (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 89)) (|outputAsFortran| (((|Void|) $) 82)) (|coerce| (((|OutputForm|) $) 74) (($ (|List| (|FortranCode|))) NIL) (($ (|FortranCode|)) NIL) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) NIL) (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) 69))) 
(((|Asp42| |#1| |#2| |#3|) (|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|))))))) (|Symbol|) (|Symbol|) (|Symbol|)) (T |Asp42|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) (|isDomain| *1 (|Asp42| *3 *4 *5)) (|ofType| *3 (|Symbol|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 (|Symbol|))))) 
(|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|))))))) 
((|retractIfCan| (((|Union| $ "failed") (|Expression| (|Float|))) 77) (((|Union| $ "failed") (|Expression| (|Integer|))) 82) (((|Union| $ "failed") (|Polynomial| (|Float|))) 87) (((|Union| $ "failed") (|Polynomial| (|Integer|))) 92) (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) 72) (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) 67)) (|retract| (($ (|Expression| (|Float|))) 75) (($ (|Expression| (|Integer|))) 80) (($ (|Polynomial| (|Float|))) 85) (($ (|Polynomial| (|Integer|))) 90) (($ (|Fraction| (|Polynomial| (|Float|)))) 70) (($ (|Fraction| (|Polynomial| (|Integer|)))) 64)) (|outputAsFortran| (((|Void|) $) 61)) (|coerce| (((|OutputForm|) $) 49) (($ (|List| (|FortranCode|))) 45) (($ (|FortranCode|)) 55) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 53) (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) 46))) 
(((|Asp49| |#1|) (|Join| (|FortranFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))))) (|Symbol|)) (T |Asp49|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) (|isDomain| *1 (|Asp49| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))))) 
((|retractIfCan| (((|Union| $ "failed") (|Expression| (|Float|))) 41) (((|Union| $ "failed") (|Expression| (|Integer|))) 46) (((|Union| $ "failed") (|Polynomial| (|Float|))) 51) (((|Union| $ "failed") (|Polynomial| (|Integer|))) 56) (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) 36) (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) 31)) (|retract| (($ (|Expression| (|Float|))) 39) (($ (|Expression| (|Integer|))) 44) (($ (|Polynomial| (|Float|))) 49) (($ (|Polynomial| (|Integer|))) 54) (($ (|Fraction| (|Polynomial| (|Float|)))) 34) (($ (|Fraction| (|Polynomial| (|Integer|)))) 28)) (|outputAsFortran| (((|Void|) $) 77)) (|coerce| (((|OutputForm|) $) 71) (($ (|List| (|FortranCode|))) 62) (($ (|FortranCode|)) 68) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 65) (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) 27))) 
(((|Asp4| |#1|) (|Join| (|FortranFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))))) (|Symbol|)) (T |Asp4|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) (|isDomain| *1 (|Asp4| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))))) 
((|retractIfCan| (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) 84) (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) 73) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) 106) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) 95) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 62) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 51)) (|retract| (($ (|Vector| (|Expression| (|Float|)))) 80) (($ (|Vector| (|Expression| (|Integer|)))) 69) (($ (|Vector| (|Polynomial| (|Float|)))) 102) (($ (|Vector| (|Polynomial| (|Integer|)))) 91) (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 58) (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 44)) (|outputAsFortran| (((|Void|) $) 122)) (|coerce| (((|OutputForm|) $) 116) (($ (|List| (|FortranCode|))) 109) (($ (|FortranCode|)) 36) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 112) (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) 37))) 
(((|Asp50| |#1|) (|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))))))) (|Symbol|)) (T |Asp50|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) (|isDomain| *1 (|Asp50| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))))))) 
((|retractIfCan| (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) 137) (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) 126) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) 158) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) 147) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 116) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 105)) (|retract| (($ (|Vector| (|Expression| (|Float|)))) 133) (($ (|Vector| (|Expression| (|Integer|)))) 122) (($ (|Vector| (|Polynomial| (|Float|)))) 154) (($ (|Vector| (|Polynomial| (|Integer|)))) 143) (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 112) (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 98)) (|outputAsFortran| (((|Void|) $) 91)) (|coerce| (((|OutputForm|) $) 85) (($ (|List| (|FortranCode|))) 76) (($ (|FortranCode|)) 83) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 81) (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) 77))) 
(((|Asp55| |#1|) (|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))))))) (|Symbol|)) (T |Asp55|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) (|isDomain| *1 (|Asp55| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))))))) 
((|retractIfCan| (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) 73) (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) 62) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) 95) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) 84) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 51) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 40)) (|retract| (($ (|Vector| (|Expression| (|Float|)))) 69) (($ (|Vector| (|Expression| (|Integer|)))) 58) (($ (|Vector| (|Polynomial| (|Float|)))) 91) (($ (|Vector| (|Polynomial| (|Integer|)))) 80) (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 47) (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 33)) (|outputAsFortran| (((|Void|) $) 121)) (|coerce| (((|OutputForm|) $) 115) (($ (|List| (|FortranCode|))) 106) (($ (|FortranCode|)) 112) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 110) (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) 32))) 
(((|Asp6| |#1|) (|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))))))) (|Symbol|)) (T |Asp6|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) (|isDomain| *1 (|Asp6| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))))))) 
((|retractIfCan| (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) 90) (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) 79) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) 112) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) 101) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 68) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 57)) (|retract| (($ (|Vector| (|Expression| (|Float|)))) 86) (($ (|Vector| (|Expression| (|Integer|)))) 75) (($ (|Vector| (|Polynomial| (|Float|)))) 108) (($ (|Vector| (|Polynomial| (|Integer|)))) 97) (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 64) (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 50)) (|outputAsFortran| (((|Void|) $) 43)) (|coerce| (((|OutputForm|) $) 36) (($ (|List| (|FortranCode|))) 26) (($ (|FortranCode|)) 29) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 32) (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) 27))) 
(((|Asp73| |#1|) (|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|))))))) (|Symbol|)) (T |Asp73|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) (|isDomain| *1 (|Asp73| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|))))))) 
((|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) 103) (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) 92) (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) 125) (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) 114) (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) 82) (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) 71)) (|retract| (($ (|Matrix| (|Expression| (|Float|)))) 99) (($ (|Matrix| (|Expression| (|Integer|)))) 88) (($ (|Matrix| (|Polynomial| (|Float|)))) 121) (($ (|Matrix| (|Polynomial| (|Integer|)))) 110) (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) 78) (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) 64)) (|outputAsFortran| (((|Void|) $) 57)) (|coerce| (((|OutputForm|) $) 43) (($ (|List| (|FortranCode|))) 50) (($ (|FortranCode|)) 39) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 47) (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) 40))) 
(((|Asp74| |#1|) (|Join| (|FortranMatrixFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|))))))) (|Symbol|)) (T |Asp74|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) (|isDomain| *1 (|Asp74| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranMatrixFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|))))))) 
((|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) 103) (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) 92) (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) 124) (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) 113) (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) 81) (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) 70)) (|retract| (($ (|Matrix| (|Expression| (|Float|)))) 99) (($ (|Matrix| (|Expression| (|Integer|)))) 88) (($ (|Matrix| (|Polynomial| (|Float|)))) 120) (($ (|Matrix| (|Polynomial| (|Integer|)))) 109) (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) 77) (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) 63)) (|outputAsFortran| (((|Void|) $) 56)) (|coerce| (((|OutputForm|) $) 50) (($ (|List| (|FortranCode|))) 44) (($ (|FortranCode|)) 47) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 40) (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) 41))) 
(((|Asp77| |#1|) (|Join| (|FortranMatrixFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))))))) (|Symbol|)) (T |Asp77|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) (|isDomain| *1 (|Asp77| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranMatrixFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))))))) 
((|retractIfCan| (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) 99) (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) 88) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) 121) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) 110) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 77) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 66)) (|retract| (($ (|Vector| (|Expression| (|Float|)))) 95) (($ (|Vector| (|Expression| (|Integer|)))) 84) (($ (|Vector| (|Polynomial| (|Float|)))) 117) (($ (|Vector| (|Polynomial| (|Integer|)))) 106) (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 73) (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 59)) (|outputAsFortran| (((|Void|) $) 45)) (|coerce| (((|OutputForm|) $) 39) (($ (|List| (|FortranCode|))) 48) (($ (|FortranCode|)) 35) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 51) (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) 36))) 
(((|Asp78| |#1|) (|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))))))) (|Symbol|)) (T |Asp78|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) (|isDomain| *1 (|Asp78| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))))))) 
((|retractIfCan| (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) 74) (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) 63) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) 96) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) 85) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 52) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 41)) (|retract| (($ (|Vector| (|Expression| (|Float|)))) 70) (($ (|Vector| (|Expression| (|Integer|)))) 59) (($ (|Vector| (|Polynomial| (|Float|)))) 92) (($ (|Vector| (|Polynomial| (|Integer|)))) 81) (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 48) (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 34)) (|outputAsFortran| (((|Void|) $) 122)) (|coerce| (((|OutputForm|) $) 116) (($ (|List| (|FortranCode|))) 107) (($ (|FortranCode|)) 113) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 111) (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) 33))) 
(((|Asp7| |#1|) (|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))))))) (|Symbol|)) (T |Asp7|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) (|isDomain| *1 (|Asp7| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranVectorFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))))))) 
((|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) 105) (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) 94) (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) 127) (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) 116) (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) 83) (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) 72)) (|retract| (($ (|Matrix| (|Expression| (|Float|)))) 101) (($ (|Matrix| (|Expression| (|Integer|)))) 90) (($ (|Matrix| (|Polynomial| (|Float|)))) 123) (($ (|Matrix| (|Polynomial| (|Integer|)))) 112) (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) 79) (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) 65)) (|outputAsFortran| (((|Void|) $) 58)) (|coerce| (((|OutputForm|) $) 52) (($ (|List| (|FortranCode|))) 42) (($ (|FortranCode|)) 49) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 47) (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) 43))) 
(((|Asp80| |#1|) (|Join| (|FortranMatrixFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|))))))) (|Symbol|)) (T |Asp80|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) (|isDomain| *1 (|Asp80| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranMatrixFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|))))))) 
((|outputAsFortran| (((|Void|) $) 44)) (|coerce| (((|OutputForm|) $) 38) (($ (|Vector| (|MachineFloat|))) 88) (($ (|List| (|FortranCode|))) 29) (($ (|FortranCode|)) 35) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 32))) 
(((|Asp8| |#1|) (|FortranVectorCategory|) (|Symbol|)) (T |Asp8|)) 
NIL 
(|FortranVectorCategory|) 
((|retractIfCan| (((|Union| $ "failed") (|Expression| (|Float|))) 42) (((|Union| $ "failed") (|Expression| (|Integer|))) 47) (((|Union| $ "failed") (|Polynomial| (|Float|))) 52) (((|Union| $ "failed") (|Polynomial| (|Integer|))) 57) (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) 37) (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) 32)) (|retract| (($ (|Expression| (|Float|))) 40) (($ (|Expression| (|Integer|))) 45) (($ (|Polynomial| (|Float|))) 50) (($ (|Polynomial| (|Integer|))) 55) (($ (|Fraction| (|Polynomial| (|Float|)))) 35) (($ (|Fraction| (|Polynomial| (|Integer|)))) 29)) (|outputAsFortran| (((|Void|) $) 88)) (|coerce| (((|OutputForm|) $) 82) (($ (|List| (|FortranCode|))) 76) (($ (|FortranCode|)) 79) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 73) (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) 28))) 
(((|Asp9| |#1|) (|Join| (|FortranFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))))) (|Symbol|)) (T |Asp9|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) (|isDomain| *1 (|Asp9| *3)) (|ofType| *3 (|Symbol|))))) 
(|Join| (|FortranFunctionCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))))) 
((|uncouplingMatrices| (((|Vector| (|Matrix| |#1|)) (|Matrix| |#1|)) 54)) (|associatedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))) |#2| (|PositiveInteger|)) 44)) (|associatedEquations| (((|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| |#2|) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| |#2|))) |#2| (|PositiveInteger|)) 62 (|has| |#1| (|Field|))))) 
(((|AssociatedEquations| |#1| |#2|) (CATEGORY |package| (SIGNATURE |associatedSystem| ((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))) |#2| (|PositiveInteger|))) (SIGNATURE |uncouplingMatrices| ((|Vector| (|Matrix| |#1|)) (|Matrix| |#1|))) (IF (|has| |#1| (|Field|)) (SIGNATURE |associatedEquations| ((|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| |#2|) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| |#2|))) |#2| (|PositiveInteger|))) |noBranch|)) (|IntegralDomain|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|)) (T |AssociatedEquations|)) 
((|associatedEquations| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Field|)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| *3) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| *3)))) (|isDomain| *1 (|AssociatedEquations| *5 *3)) (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *5)))) (|uncouplingMatrices| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Vector| (|Matrix| *4))) (|isDomain| *1 (|AssociatedEquations| *4 *5)) (|isDomain| *3 (|Matrix| *4)) (|ofCategory| *5 (|LinearOrdinaryDifferentialOperatorCategory| *4)))) (|associatedSystem| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |mat| (|Matrix| *5)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|)))))) (|isDomain| *1 (|AssociatedEquations| *5 *3)) (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |associatedSystem| ((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))) |#2| (|PositiveInteger|))) (SIGNATURE |uncouplingMatrices| ((|Vector| (|Matrix| |#1|)) (|Matrix| |#1|))) (IF (|has| |#1| (|Field|)) (SIGNATURE |associatedEquations| ((|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| |#2|) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| |#2|))) |#2| (|PositiveInteger|))) |noBranch|)) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|top| ((|#1| $) 34)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|sample| (($) NIL T CONST)) (|push!| ((|#1| |#1| $) 30)) (|pop!| ((|#1| $) 28)) (|parts| (((|List| |#1|) $) 39 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 43 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 41)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|inspect| ((|#1| $) 45)) (|insert!| (($ |#1| $) 31)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|extract!| ((|#1| $) 29)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) 16)) (|empty| (($) 38)) (|depth| (((|NonNegativeInteger|) $) 26)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) 15)) (|coerce| (((|OutputForm|) $) 25 (|has| |#1| (|SetCategory|)))) (|bag| (($ (|List| |#1|)) NIL)) (|arrayStack| (($ (|List| |#1|)) 36)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 13 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 10 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|ArrayStack| |#1|) (|Join| (|StackAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |arrayStack| ($ (|List| |#1|))) (SIGNATURE |pop!| (|#1| $)) (SIGNATURE |extract!| (|#1| $)) (SIGNATURE |push!| (|#1| |#1| $)) (SIGNATURE |insert!| ($ |#1| $)) (SIGNATURE |inspect| (|#1| $)) (SIGNATURE |top| (|#1| $)) (SIGNATURE |depth| ((|NonNegativeInteger|) $)) (SIGNATURE |less?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |size?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |bag| ($ (|List| |#1|))) (SIGNATURE |empty?| ((|Boolean|) $)) (SIGNATURE |empty| ($)) (SIGNATURE |sample| ($)) (SIGNATURE |copy| ($ $)) (SIGNATURE |eq?| ((|Boolean|) $ $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (IF (|has| $ (ATTRIBUTE |shallowlyMutable|)) (SIGNATURE |map!| ($ (|Mapping| |#1| |#1|) $)) |noBranch|) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |latex| ((|String|) $)) (SIGNATURE |hash| ((|SingleInteger|) $)) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE = ((|Boolean|) $ $)) (SIGNATURE ~= ((|Boolean|) $ $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (PROGN (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |#| ((|NonNegativeInteger|) $)) (SIGNATURE |parts| ((|List| |#1|) $)) (SIGNATURE |members| ((|List| |#1|) $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |member?| ((|Boolean|) |#1| $)) (SIGNATURE |count| ((|NonNegativeInteger|) |#1| $))) |noBranch|) |noBranch|))) (|SetCategory|)) (T |ArrayStack|)) 
((|eq?| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ArrayStack| *3)) (|ofCategory| *3 (|SetCategory|)))) (|copy| (*1 *1 *1) (AND (|isDomain| *1 (|ArrayStack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|empty| (*1 *1) (AND (|isDomain| *1 (|ArrayStack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|empty?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ArrayStack| *3)) (|ofCategory| *3 (|SetCategory|)))) (|less?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ArrayStack| *4)) (|ofCategory| *4 (|SetCategory|)))) (|more?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ArrayStack| *4)) (|ofCategory| *4 (|SetCategory|)))) (|size?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ArrayStack| *4)) (|ofCategory| *4 (|SetCategory|)))) (|sample| (*1 *1) (AND (|isDomain| *1 (|ArrayStack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|#| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ArrayStack| *3)) (|ofCategory| *3 (|SetCategory|)))) (|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|ArrayStack| *3)))) (|map!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|ArrayStack| *3)))) (|any?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ArrayStack| *4)))) (|every?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ArrayStack| *4)))) (|count| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ArrayStack| *4)))) (|parts| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|ArrayStack| *3)) (|ofCategory| *3 (|SetCategory|)))) (|members| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|ArrayStack| *3)) (|ofCategory| *3 (|SetCategory|)))) (|count| (*1 *2 *3 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ArrayStack| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|member?| (*1 *2 *3 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ArrayStack| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|latex| (*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|ArrayStack| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|hash| (*1 *2 *1) (AND (|isDomain| *2 (|SingleInteger|)) (|isDomain| *1 (|ArrayStack| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|ArrayStack| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (= (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ArrayStack| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (~= (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ArrayStack| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|bag| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|ArrayStack| *3)))) (|extract!| (*1 *2 *1) (AND (|isDomain| *1 (|ArrayStack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|insert!| (*1 *1 *2 *1) (AND (|isDomain| *1 (|ArrayStack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|inspect| (*1 *2 *1) (AND (|isDomain| *1 (|ArrayStack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|push!| (*1 *2 *2 *1) (AND (|isDomain| *1 (|ArrayStack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|pop!| (*1 *2 *1) (AND (|isDomain| *1 (|ArrayStack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|top| (*1 *2 *1) (AND (|isDomain| *1 (|ArrayStack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|depth| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ArrayStack| *3)) (|ofCategory| *3 (|SetCategory|)))) (|arrayStack| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|ArrayStack| *3))))) 
(|Join| (|StackAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |arrayStack| ($ (|List| |#1|))) (SIGNATURE |pop!| (|#1| $)) (SIGNATURE |extract!| (|#1| $)) (SIGNATURE |push!| (|#1| |#1| $)) (SIGNATURE |insert!| ($ |#1| $)) (SIGNATURE |inspect| (|#1| $)) (SIGNATURE |top| (|#1| $)) (SIGNATURE |depth| ((|NonNegativeInteger|) $)) (SIGNATURE |less?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |size?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |bag| ($ (|List| |#1|))) (SIGNATURE |empty?| ((|Boolean|) $)) (SIGNATURE |empty| ($)) (SIGNATURE |sample| ($)) (SIGNATURE |copy| ($ $)) (SIGNATURE |eq?| ((|Boolean|) $ $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (IF (|has| $ (ATTRIBUTE |shallowlyMutable|)) (SIGNATURE |map!| ($ (|Mapping| |#1| |#1|) $)) |noBranch|) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |latex| ((|String|) $)) (SIGNATURE |hash| ((|SingleInteger|) $)) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE = ((|Boolean|) $ $)) (SIGNATURE ~= ((|Boolean|) $ $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (PROGN (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |#| ((|NonNegativeInteger|) $)) (SIGNATURE |parts| ((|List| |#1|) $)) (SIGNATURE |members| ((|List| |#1|) $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |member?| ((|Boolean|) |#1| $)) (SIGNATURE |count| ((|NonNegativeInteger|) |#1| $))) |noBranch|) |noBranch|))) 
NIL 
(((|AdditiveValuationAttribute|) (|Category|)) (T |AdditiveValuationAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|ApproximateAttribute|) (|Category|)) (T |ApproximateAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|ArbitraryExponentAttribute|) (|Category|)) (T |ArbitraryExponentAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|ArbitraryPrecisionAttribute|) (|Category|)) (T |ArbitraryPrecisionAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|CanonicalClosedAttribute|) (|Category|)) (T |CanonicalClosedAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|CanonicalAttribute|) (|Category|)) (T |CanonicalAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|CentralAttribute|) (|Category|)) (T |CentralAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|CommutativeStarAttribute|) (|Category|)) (T |CommutativeStarAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|CanonicalUnitNormalAttribute|) (|Category|)) (T |CanonicalUnitNormalAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|FiniteAggregateAttribute|) (|Category|)) (T |FiniteAggregateAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|JacobiIdentityAttribute|) (|Category|)) (T |JacobiIdentityAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|LazyRepresentationAttribute|) (|Category|)) (T |LazyRepresentationAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|LeftUnitaryAttribute|) (|Category|)) (T |LeftUnitaryAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|MultiplicativeValuationAttribute|) (|Category|)) (T |MultiplicativeValuationAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|NotherianAttribute|) (|Category|)) (T |NotherianAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|NullSquareAttribute|) (|Category|)) (T |NullSquareAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|NoZeroDivisorsAttribute|) (|Category|)) (T |NoZeroDivisorsAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|PartiallyOrderedSetAttribute|) (|Category|)) (T |PartiallyOrderedSetAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
((|asec| (($ $) 10)) (|acsc| (($ $) 12))) 
(((|ArcTrigonometricFunctionCategory&| |#1|) (CATEGORY |domain| (SIGNATURE |acsc| (|#1| |#1|)) (SIGNATURE |asec| (|#1| |#1|))) (|ArcTrigonometricFunctionCategory|)) (T |ArcTrigonometricFunctionCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |acsc| (|#1| |#1|)) (SIGNATURE |asec| (|#1| |#1|))) 
((|atan| (($ $) 11)) (|asin| (($ $) 10)) (|asec| (($ $) 9)) (|acsc| (($ $) 8)) (|acot| (($ $) 7)) (|acos| (($ $) 6))) 
(((|ArcTrigonometricFunctionCategory|) (|Category|)) (T |ArcTrigonometricFunctionCategory|)) 
((|atan| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|asin| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|asec| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|acsc| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|acot| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|acos| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|)))) 
(|Join| (CATEGORY |domain| (SIGNATURE |acos| ($ $)) (SIGNATURE |acot| ($ $)) (SIGNATURE |acsc| ($ $)) (SIGNATURE |asec| ($ $)) (SIGNATURE |asin| ($ $)) (SIGNATURE |atan| ($ $)))) 
NIL 
(((|RightUnitaryAttribute|) (|Category|)) (T |RightUnitaryAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
NIL 
(((|ShallowlyMutableAttribute|) (|Category|)) (T |ShallowlyMutableAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
((~= (((|Boolean|) $ $) NIL)) (|setButtonValue| (((|Float|) (|String|) (|Float|)) 42) (((|Float|) (|String|) (|String|) (|Float|)) 41)) (|setAttributeButtonStep| (((|Float|) (|Float|)) 33)) (|resetAttributeButtons| (((|Void|)) 36)) (|latex| (((|String|) $) NIL)) (|increase| (((|Float|) (|String|) (|String|)) 46) (((|Float|) (|String|)) 48)) (|hash| (((|SingleInteger|) $) NIL)) (|getButtonValue| (((|Float|) (|String|) (|String|)) 47)) (|decrease| (((|Float|) (|String|) (|String|)) 49) (((|Float|) (|String|)) 50)) (|coerce| (((|OutputForm|) $) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|AttributeButtons|) (|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE |increase| ((|Float|) (|String|) (|String|))) (SIGNATURE |increase| ((|Float|) (|String|))) (SIGNATURE |decrease| ((|Float|) (|String|) (|String|))) (SIGNATURE |decrease| ((|Float|) (|String|))) (SIGNATURE |getButtonValue| ((|Float|) (|String|) (|String|))) (SIGNATURE |resetAttributeButtons| ((|Void|))) (SIGNATURE |setAttributeButtonStep| ((|Float|) (|Float|))) (SIGNATURE |setButtonValue| ((|Float|) (|String|) (|Float|))) (SIGNATURE |setButtonValue| ((|Float|) (|String|) (|String|) (|Float|))) (ATTRIBUTE |finiteAggregate|)))) (T |AttributeButtons|)) 
((|increase| (*1 *2 *3 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Float|)) (|isDomain| *1 (|AttributeButtons|)))) (|increase| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Float|)) (|isDomain| *1 (|AttributeButtons|)))) (|decrease| (*1 *2 *3 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Float|)) (|isDomain| *1 (|AttributeButtons|)))) (|decrease| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Float|)) (|isDomain| *1 (|AttributeButtons|)))) (|getButtonValue| (*1 *2 *3 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Float|)) (|isDomain| *1 (|AttributeButtons|)))) (|resetAttributeButtons| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|AttributeButtons|)))) (|setAttributeButtonStep| (*1 *2 *2) (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|AttributeButtons|)))) (|setButtonValue| (*1 *2 *3 *2) (AND (|isDomain| *2 (|Float|)) (|isDomain| *3 (|String|)) (|isDomain| *1 (|AttributeButtons|)))) (|setButtonValue| (*1 *2 *3 *3 *2) (AND (|isDomain| *2 (|Float|)) (|isDomain| *3 (|String|)) (|isDomain| *1 (|AttributeButtons|))))) 
(|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE |increase| ((|Float|) (|String|) (|String|))) (SIGNATURE |increase| ((|Float|) (|String|))) (SIGNATURE |decrease| ((|Float|) (|String|) (|String|))) (SIGNATURE |decrease| ((|Float|) (|String|))) (SIGNATURE |getButtonValue| ((|Float|) (|String|) (|String|))) (SIGNATURE |resetAttributeButtons| ((|Void|))) (SIGNATURE |setAttributeButtonStep| ((|Float|) (|Float|))) (SIGNATURE |setButtonValue| ((|Float|) (|String|) (|Float|))) (SIGNATURE |setButtonValue| ((|Float|) (|String|) (|String|) (|Float|))) (ATTRIBUTE |finiteAggregate|))) 
NIL 
(((|AttributeRegistry|) (|Category|)) (T |AttributeRegistry|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |finiteAggregate|) (ATTRIBUTE (|commutative| "*")) (ATTRIBUTE |shallowlyMutable|) (ATTRIBUTE |unitsKnown|) (ATTRIBUTE |leftUnitary|) (ATTRIBUTE |rightUnitary|) (ATTRIBUTE |noZeroDivisors|) (ATTRIBUTE |canonicalUnitNormal|) (ATTRIBUTE |canonicalsClosed|) (ATTRIBUTE |arbitraryPrecision|) (ATTRIBUTE |partiallyOrderedSet|) (ATTRIBUTE |central|) (ATTRIBUTE |noetherian|) (ATTRIBUTE |additiveValuation|) (ATTRIBUTE |multiplicativeValuation|) (ATTRIBUTE |NullSquare|) (ATTRIBUTE |JacobiIdentity|) (ATTRIBUTE |canonical|) (ATTRIBUTE |approximate|))) 
NIL 
(((|UnitsKnownAttribute|) (|Category|)) (T |UnitsKnownAttribute|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
((~= (((|Boolean|) $ $) NIL)) (|sample| (($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|morphism| (($ (|Mapping| |#1| |#1|)) 25) (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) 24) (($ (|Mapping| |#1| |#1| (|Integer|))) 22)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 14)) (|hash| (((|SingleInteger|) $) NIL)) (|elt| ((|#1| $ |#1|) 11)) (|conjugate| (($ $ $) NIL)) (|commutator| (($ $ $) NIL)) (|coerce| (((|OutputForm|) $) 20)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|One| (($) 8 T CONST)) (= (((|Boolean|) $ $) 10)) (/ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) 28) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) 16)) (* (($ $ $) 29))) 
(((|Automorphism| |#1|) (|Join| (|Group|) (|Eltable| |#1| |#1|) (CATEGORY |domain| (SIGNATURE |morphism| ($ (|Mapping| |#1| |#1|))) (SIGNATURE |morphism| ($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|))) (SIGNATURE |morphism| ($ (|Mapping| |#1| |#1| (|Integer|)))))) (|Ring|)) (T |Automorphism|)) 
((|morphism| (*1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|Automorphism| *3)))) (|morphism| (*1 *1 *2 *2) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|Automorphism| *3)))) (|morphism| (*1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3 (|Integer|))) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|Automorphism| *3))))) 
(|Join| (|Group|) (|Eltable| |#1| |#1|) (CATEGORY |domain| (SIGNATURE |morphism| ($ (|Mapping| |#1| |#1|))) (SIGNATURE |morphism| ($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|))) (SIGNATURE |morphism| ($ (|Mapping| |#1| |#1| (|Integer|)))))) 
((|multiServ| (((|Void|) (|SExpression|)) 20)) (|getDatabase| (((|String|) (|String|) (|String|)) 7)) (|axServer| (((|Void|) (|Integer|) (|Mapping| (|Void|) (|SExpression|))) 14))) 
(((|AxiomServer|) (CATEGORY |package| (SIGNATURE |axServer| ((|Void|) (|Integer|) (|Mapping| (|Void|) (|SExpression|)))) (SIGNATURE |multiServ| ((|Void|) (|SExpression|))) (SIGNATURE |getDatabase| ((|String|) (|String|) (|String|))))) (T |AxiomServer|)) 
((|getDatabase| (*1 *2 *2 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|AxiomServer|)))) (|multiServ| (*1 *2 *3) (AND (|isDomain| *3 (|SExpression|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|AxiomServer|)))) (|axServer| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *4 (|Mapping| (|Void|) (|SExpression|))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|AxiomServer|))))) 
(CATEGORY |package| (SIGNATURE |axServer| ((|Void|) (|Integer|) (|Mapping| (|Void|) (|SExpression|)))) (SIGNATURE |multiServ| ((|Void|) (|SExpression|))) (SIGNATURE |getDatabase| ((|String|) (|String|) (|String|)))) 
((|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) 10) (((|Factored| |#2|) |#2| |#2|) 11))) 
(((|BalancedFactorisation| |#1| |#2|) (CATEGORY |package| (SIGNATURE |balancedFactorisation| ((|Factored| |#2|) |#2| |#2|)) (SIGNATURE |balancedFactorisation| ((|Factored| |#2|) |#2| (|List| |#2|)))) (|Join| (|GcdDomain|) (|CharacteristicZero|)) (|UnivariatePolynomialCategory| |#1|)) (T |BalancedFactorisation|)) 
((|balancedFactorisation| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Join| (|GcdDomain|) (|CharacteristicZero|))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|BalancedFactorisation| *5 *3)))) (|balancedFactorisation| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|Join| (|GcdDomain|) (|CharacteristicZero|))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|BalancedFactorisation| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |balancedFactorisation| ((|Factored| |#2|) |#2| |#2|)) (SIGNATURE |balancedFactorisation| ((|Factored| |#2|) |#2| (|List| |#2|)))) 
((~= (((|Boolean|) $ $) 9))) 
(((|BasicType&| |#1|) (CATEGORY |domain| (SIGNATURE ~= ((|Boolean|) |#1| |#1|))) (|BasicType|)) (T |BasicType&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE ~= ((|Boolean|) |#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (= (((|Boolean|) $ $) 6))) 
(((|BasicType|) (|Category|)) (T |BasicType|)) 
((~= (*1 *2 *1 *1) (AND (|ofCategory| *1 (|BasicType|)) (|isDomain| *2 (|Boolean|)))) (= (*1 *2 *1 *1) (AND (|ofCategory| *1 (|BasicType|)) (|isDomain| *2 (|Boolean|))))) 
(|Join| (CATEGORY |domain| (SIGNATURE = ((|Boolean|) $ $)) (SIGNATURE ~= ((|Boolean|) $ $)))) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setvalue!| ((|#1| $ |#1|) 13 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setright!| (($ $ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setleft!| (($ $ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setleaves!| (($ $ (|List| |#1|)) 15)) (|setelt| ((|#1| $ "value" |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "left" $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "right" $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) NIL T CONST)) (|right| (($ $) 11)) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) NIL)) (|node?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|node| (($ $ |#1| $) 17)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|mapUp!| ((|#1| $ (|Mapping| |#1| |#1| |#1|)) 25) (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) 30)) (|mapDown!| (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) 31) (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) 35)) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|left| (($ $) 10)) (|leaves| (((|List| |#1|) $) NIL)) (|leaf?| (((|Boolean|) $) 12)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) 9)) (|empty| (($) 16)) (|elt| ((|#1| $ "value") NIL) (($ $ "left") NIL) (($ $ "right") NIL)) (|distance| (((|Integer|) $ $) NIL)) (|cyclic?| (((|Boolean|) $) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|)))) (|children| (((|List| $) $) NIL)) (|child?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) 19)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|BalancedBinaryTree| |#1|) (|Join| (|BinaryTreeCategory| |#1|) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (ATTRIBUTE |shallowlyMutable|) (SIGNATURE |balancedBinaryTree| ($ (|NonNegativeInteger|) |#1|)) (SIGNATURE |setleaves!| ($ $ (|List| |#1|))) (SIGNATURE |mapUp!| (|#1| $ (|Mapping| |#1| |#1| |#1|))) (SIGNATURE |mapUp!| ($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|))) (SIGNATURE |mapDown!| ($ $ |#1| (|Mapping| |#1| |#1| |#1|))) (SIGNATURE |mapDown!| ($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|))))) (|SetCategory|)) (T |BalancedBinaryTree|)) 
((|balancedBinaryTree| (*1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|BalancedBinaryTree| *3)) (|ofCategory| *3 (|SetCategory|)))) (|setleaves!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|BalancedBinaryTree| *3)))) (|mapUp!| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Mapping| *2 *2 *2)) (|isDomain| *1 (|BalancedBinaryTree| *2)) (|ofCategory| *2 (|SetCategory|)))) (|mapUp!| (*1 *1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3 *3 *3 *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|BalancedBinaryTree| *3)))) (|mapDown!| (*1 *1 *1 *2 *3) (AND (|isDomain| *3 (|Mapping| *2 *2 *2)) (|ofCategory| *2 (|SetCategory|)) (|isDomain| *1 (|BalancedBinaryTree| *2)))) (|mapDown!| (*1 *1 *1 *2 *3) (AND (|isDomain| *3 (|Mapping| (|List| *2) *2 *2 *2)) (|ofCategory| *2 (|SetCategory|)) (|isDomain| *1 (|BalancedBinaryTree| *2))))) 
(|Join| (|BinaryTreeCategory| |#1|) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (ATTRIBUTE |shallowlyMutable|) (SIGNATURE |balancedBinaryTree| ($ (|NonNegativeInteger|) |#1|)) (SIGNATURE |setleaves!| ($ $ (|List| |#1|))) (SIGNATURE |mapUp!| (|#1| $ (|Mapping| |#1| |#1| |#1|))) (SIGNATURE |mapUp!| ($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|))) (SIGNATURE |mapDown!| ($ $ |#1| (|Mapping| |#1| |#1| |#1|))) (SIGNATURE |mapDown!| ($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|))))) 
((|quadraticBezier| (((|Mapping| (|List| |#1|) |#1|) (|List| |#1|) (|List| |#1|) (|List| |#1|)) 20)) (|linearBezier| (((|Mapping| (|List| |#1|) |#1|) (|List| |#1|) (|List| |#1|)) 17)) (|cubicBezier| (((|Mapping| (|List| |#1|) |#1|) (|List| |#1|) (|List| |#1|) (|List| |#1|) (|List| |#1|)) 21))) 
(((|Bezier| |#1|) (CATEGORY |package| (SIGNATURE |linearBezier| ((|Mapping| (|List| |#1|) |#1|) (|List| |#1|) (|List| |#1|))) (SIGNATURE |quadraticBezier| ((|Mapping| (|List| |#1|) |#1|) (|List| |#1|) (|List| |#1|) (|List| |#1|))) (SIGNATURE |cubicBezier| ((|Mapping| (|List| |#1|) |#1|) (|List| |#1|) (|List| |#1|) (|List| |#1|) (|List| |#1|)))) (|Ring|)) (T |Bezier|)) 
((|cubicBezier| (*1 *2 *3 *3 *3 *3) (AND (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Mapping| (|List| *4) *4)) (|isDomain| *1 (|Bezier| *4)) (|isDomain| *3 (|List| *4)))) (|quadraticBezier| (*1 *2 *3 *3 *3) (AND (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Mapping| (|List| *4) *4)) (|isDomain| *1 (|Bezier| *4)) (|isDomain| *3 (|List| *4)))) (|linearBezier| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Mapping| (|List| *4) *4)) (|isDomain| *1 (|Bezier| *4)) (|isDomain| *3 (|List| *4))))) 
(CATEGORY |package| (SIGNATURE |linearBezier| ((|Mapping| (|List| |#1|) |#1|) (|List| |#1|) (|List| |#1|))) (SIGNATURE |quadraticBezier| ((|Mapping| (|List| |#1|) |#1|) (|List| |#1|) (|List| |#1|) (|List| |#1|))) (SIGNATURE |cubicBezier| ((|Mapping| (|List| |#1|) |#1|) (|List| |#1|) (|List| |#1|) (|List| |#1|) (|List| |#1|)))) 
((|sylvesterMatrix| ((|#3| |#2| |#2|) 28)) (|bezoutResultant| ((|#1| |#2| |#2|) 36 (|has| |#1| (ATTRIBUTE (|commutative| "*"))))) (|bezoutMatrix| ((|#3| |#2| |#2|) 29)) (|bezoutDiscriminant| ((|#1| |#2|) 40 (|has| |#1| (ATTRIBUTE (|commutative| "*")))))) 
(((|BezoutMatrix| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |sylvesterMatrix| (|#3| |#2| |#2|)) (SIGNATURE |bezoutMatrix| (|#3| |#2| |#2|)) (IF (|has| |#1| (ATTRIBUTE (|commutative| "*"))) (PROGN (SIGNATURE |bezoutResultant| (|#1| |#2| |#2|)) (SIGNATURE |bezoutDiscriminant| (|#1| |#2|))) |noBranch|)) (|Ring|) (|UnivariatePolynomialCategory| |#1|) (|MatrixCategory| |#1| |#4| |#5|) (|FiniteLinearAggregate| |#1|) (|FiniteLinearAggregate| |#1|)) (T |BezoutMatrix|)) 
((|bezoutDiscriminant| (*1 *2 *3) (AND (|has| *2 (ATTRIBUTE (|commutative| "*"))) (|ofCategory| *5 (|FiniteLinearAggregate| *2)) (|ofCategory| *6 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|BezoutMatrix| *2 *3 *4 *5 *6)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|MatrixCategory| *2 *5 *6)))) (|bezoutResultant| (*1 *2 *3 *3) (AND (|has| *2 (ATTRIBUTE (|commutative| "*"))) (|ofCategory| *5 (|FiniteLinearAggregate| *2)) (|ofCategory| *6 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|BezoutMatrix| *2 *3 *4 *5 *6)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|MatrixCategory| *2 *5 *6)))) (|bezoutMatrix| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)) (|isDomain| *1 (|BezoutMatrix| *4 *3 *2 *5 *6)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)))) (|sylvesterMatrix| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)) (|isDomain| *1 (|BezoutMatrix| *4 *3 *2 *5 *6)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4))))) 
(CATEGORY |package| (SIGNATURE |sylvesterMatrix| (|#3| |#2| |#2|)) (SIGNATURE |bezoutMatrix| (|#3| |#2| |#2|)) (IF (|has| |#1| (ATTRIBUTE (|commutative| "*"))) (PROGN (SIGNATURE |bezoutResultant| (|#1| |#2| |#2|)) (SIGNATURE |bezoutDiscriminant| (|#1| |#2|))) |noBranch|)) 
((~= (((|Boolean|) $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (|bfKeys| (((|List| (|Symbol|))) 32)) (|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) 35)) (= (((|Boolean|) $ $) NIL))) 
(((|BasicFunctions|) (|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE |bfKeys| ((|List| (|Symbol|)))) (SIGNATURE |bfEntry| ((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|))) (ATTRIBUTE |finiteAggregate|)))) (T |BasicFunctions|)) 
((|bfKeys| (*1 *2) (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *1 (|BasicFunctions|)))) (|bfEntry| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|))))) (|isDomain| *1 (|BasicFunctions|))))) 
(|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE |bfKeys| ((|List| (|Symbol|)))) (SIGNATURE |bfEntry| ((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|))) (ATTRIBUTE |finiteAggregate|))) 
((|bag| (($ (|List| |#2|)) 11))) 
(((|BagAggregate&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |bag| (|#1| (|List| |#2|)))) (|BagAggregate| |#2|) (|Type|)) (T |BagAggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |bag| (|#1| (|List| |#2|)))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|sample| (($) 7 T CONST)) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|inspect| ((|#1| $) 36)) (|insert!| (($ |#1| $) 37)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|extract!| ((|#1| $) 38)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|bag| (($ (|List| |#1|)) 39)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|BagAggregate| |#1|) (|Category|) (|Type|)) (T |BagAggregate|)) 
((|bag| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *1 (|BagAggregate| *3)))) (|extract!| (*1 *2 *1) (AND (|ofCategory| *1 (|BagAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|insert!| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|BagAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|inspect| (*1 *2 *1) (AND (|ofCategory| *1 (|BagAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|HomogeneousAggregate| |t#1|) (CATEGORY |domain| (ATTRIBUTE |shallowlyMutable|) (SIGNATURE |bag| ($ (|List| |t#1|))) (SIGNATURE |extract!| (|t#1| $)) (SIGNATURE |insert!| ($ |t#1| $)) (SIGNATURE |inspect| (|t#1| $)))) 
(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|wholePart| (((|Integer|) $) NIL (|has| (|Integer|) (|EuclideanDomain|)))) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Integer|) (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Integer|) (|PolynomialFactorizationExplicit|)))) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sign| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedIntegralDomain|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL) (((|Union| (|Symbol|) "failed") $) NIL (|has| (|Integer|) (|RetractableTo| (|Symbol|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| (|Integer|) (|RetractableTo| (|Integer|)))) (((|Union| (|Integer|) "failed") $) NIL (|has| (|Integer|) (|RetractableTo| (|Integer|))))) (|retract| (((|Integer|) $) NIL) (((|Symbol|) $) NIL (|has| (|Integer|) (|RetractableTo| (|Symbol|)))) (((|Fraction| (|Integer|)) $) NIL (|has| (|Integer|) (|RetractableTo| (|Integer|)))) (((|Integer|) $) NIL (|has| (|Integer|) (|RetractableTo| (|Integer|))))) (|rem| (($ $ $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| (|Integer|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| (|Integer|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| (|Integer|)) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) NIL (|has| (|Integer|) (|IntegerNumberSystem|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|positive?| (((|Boolean|) $) NIL (|has| (|Integer|) (|OrderedIntegralDomain|)))) (|patternMatch| (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (|has| (|Integer|) (|PatternMatchable| (|Integer|)))) (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (|has| (|Integer|) (|PatternMatchable| (|Float|))))) (|one?| (((|Boolean|) $) NIL)) (|numerator| (($ $) NIL)) (|numer| (((|Integer|) $) NIL)) (|nextItem| (((|Union| $ "failed") $) NIL (|has| (|Integer|) (|StepThrough|)))) (|negative?| (((|Boolean|) $) NIL (|has| (|Integer|) (|OrderedIntegralDomain|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|min| (($ $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|map| (($ (|Mapping| (|Integer|) (|Integer|)) $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|init| (($) NIL (|has| (|Integer|) (|StepThrough|)) CONST)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|fractionPart| (($ $) NIL (|has| (|Integer|) (|EuclideanDomain|))) (((|Fraction| (|Integer|)) $) NIL)) (|floor| (((|Integer|) $) NIL (|has| (|Integer|) (|IntegerNumberSystem|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Integer|) (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Integer|) (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|eval| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) NIL (|has| (|Integer|) (|Evalable| (|Integer|)))) (($ $ (|Integer|) (|Integer|)) NIL (|has| (|Integer|) (|Evalable| (|Integer|)))) (($ $ (|Equation| (|Integer|))) NIL (|has| (|Integer|) (|Evalable| (|Integer|)))) (($ $ (|List| (|Equation| (|Integer|)))) NIL (|has| (|Integer|) (|Evalable| (|Integer|)))) (($ $ (|List| (|Symbol|)) (|List| (|Integer|))) NIL (|has| (|Integer|) (|InnerEvalable| (|Symbol|) (|Integer|)))) (($ $ (|Symbol|) (|Integer|)) NIL (|has| (|Integer|) (|InnerEvalable| (|Symbol|) (|Integer|))))) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|elt| (($ $ (|Integer|)) NIL (|has| (|Integer|) (|Eltable| (|Integer|) (|Integer|))))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|differentiate| (($ $) NIL (|has| (|Integer|) (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|Integer|) (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| (|Integer|) (|Integer|)) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| (|Integer|) (|Integer|))) NIL)) (|denominator| (($ $) NIL)) (|denom| (((|Integer|) $) NIL)) (|convert| (((|Pattern| (|Integer|)) $) NIL (|has| (|Integer|) (|ConvertibleTo| (|Pattern| (|Integer|))))) (((|Pattern| (|Float|)) $) NIL (|has| (|Integer|) (|ConvertibleTo| (|Pattern| (|Float|))))) (((|InputForm|) $) NIL (|has| (|Integer|) (|ConvertibleTo| (|InputForm|)))) (((|Float|) $) NIL (|has| (|Integer|) (|RealConstant|))) (((|DoubleFloat|) $) NIL (|has| (|Integer|) (|RealConstant|)))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| (|Integer|) (|PolynomialFactorizationExplicit|))))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) 7) (($ (|Integer|)) NIL) (($ (|Symbol|)) NIL (|has| (|Integer|) (|RetractableTo| (|Symbol|)))) (((|Fraction| (|Integer|)) $) NIL) (((|RadixExpansion| 2) $) 9)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| (|Integer|) (|PolynomialFactorizationExplicit|))) (|has| (|Integer|) (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|ceiling| (((|Integer|) $) NIL (|has| (|Integer|) (|IntegerNumberSystem|)))) (|binary| (($ (|Fraction| (|Integer|))) 8)) (|associates?| (((|Boolean|) $ $) NIL)) (|abs| (($ $) NIL (|has| (|Integer|) (|OrderedIntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($ $) NIL (|has| (|Integer|) (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|Integer|) (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| (|Integer|) (|Integer|)) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| (|Integer|) (|Integer|))) NIL)) (>= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (/ (($ $ $) NIL) (($ (|Integer|) (|Integer|)) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ (|Integer|) $) NIL) (($ $ (|Integer|)) NIL))) 
(((|BinaryExpansion|) (|Join| (|QuotientFieldCategory| (|Integer|)) (CATEGORY |domain| (SIGNATURE |coerce| ((|Fraction| (|Integer|)) $)) (SIGNATURE |coerce| ((|RadixExpansion| 2) $)) (SIGNATURE |fractionPart| ((|Fraction| (|Integer|)) $)) (SIGNATURE |binary| ($ (|Fraction| (|Integer|))))))) (T |BinaryExpansion|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|BinaryExpansion|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|RadixExpansion| 2)) (|isDomain| *1 (|BinaryExpansion|)))) (|fractionPart| (*1 *2 *1) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|BinaryExpansion|)))) (|binary| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|BinaryExpansion|))))) 
(|Join| (|QuotientFieldCategory| (|Integer|)) (CATEGORY |domain| (SIGNATURE |coerce| ((|Fraction| (|Integer|)) $)) (SIGNATURE |coerce| ((|RadixExpansion| 2) $)) (SIGNATURE |fractionPart| ((|Fraction| (|Integer|)) $)) (SIGNATURE |binary| ($ (|Fraction| (|Integer|)))))) 
((~= (((|Boolean|) $ $) NIL)) (|write!| (((|SingleInteger|) $ (|SingleInteger|)) 23)) (|reopen!| (($ $ (|String|)) 17)) (|readIfCan!| (((|Union| (|SingleInteger|) "failed") $) 22)) (|read!| (((|SingleInteger|) $) 20)) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) 25)) (|position| (((|SingleInteger|) $) 24)) (|open| (($ (|FileName|)) NIL) (($ (|FileName|) (|String|)) 16)) (|name| (((|FileName|) $) NIL)) (|latex| (((|String|) $) NIL)) (|iomode| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|flush| (((|Void|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (|close!| (($ $) 18)) (= (((|Boolean|) $ $) NIL))) 
(((|BinaryFile|) (|Join| (|FileCategory| (|FileName|) (|SingleInteger|)) (CATEGORY |domain| (SIGNATURE |readIfCan!| ((|Union| (|SingleInteger|) "failed") $)) (SIGNATURE |position| ((|SingleInteger|) $)) (SIGNATURE |position!| ((|SingleInteger|) $ (|SingleInteger|)))))) (T |BinaryFile|)) 
((|readIfCan!| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|SingleInteger|)) (|isDomain| *1 (|BinaryFile|)))) (|position| (*1 *2 *1) (AND (|isDomain| *2 (|SingleInteger|)) (|isDomain| *1 (|BinaryFile|)))) (|position!| (*1 *2 *1 *2) (AND (|isDomain| *2 (|SingleInteger|)) (|isDomain| *1 (|BinaryFile|))))) 
(|Join| (|FileCategory| (|FileName|) (|SingleInteger|)) (CATEGORY |domain| (SIGNATURE |readIfCan!| ((|Union| (|SingleInteger|) "failed") $)) (SIGNATURE |position| ((|SingleInteger|) $)) (SIGNATURE |position!| ((|SingleInteger|) $ (|SingleInteger|))))) 
((~= (((|Boolean|) $ $) NIL)) (~ (($ $) NIL)) (|xor| (($ $ $) NIL)) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) $) NIL (|has| (|Boolean|) (|OrderedSet|))) (((|Boolean|) (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $) NIL)) (|sort!| (($ $) NIL (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|has| (|Boolean|) (|OrderedSet|)))) (($ (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sort| (($ $) NIL (|has| (|Boolean|) (|OrderedSet|))) (($ (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setelt| (((|Boolean|) $ (|UniversalSegment| (|Integer|)) (|Boolean|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Boolean|) $ (|Integer|) (|Boolean|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select| (($ (|Mapping| (|Boolean|) (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) NIL T CONST)) (|reverse!| (($ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) NIL)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Boolean|) (|SetCategory|))))) (|remove| (($ (|Mapping| (|Boolean|) (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Boolean|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Boolean|) (|SetCategory|))))) (|reduce| (((|Boolean|) (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Boolean|) (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $ (|Boolean|)) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Boolean|) (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $ (|Boolean|) (|Boolean|)) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Boolean|) (|SetCategory|))))) (|qsetelt!| (((|Boolean|) $ (|Integer|) (|Boolean|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| (((|Boolean|) $ (|Integer|)) NIL)) (|position| (((|Integer|) (|Boolean|) $ (|Integer|)) NIL (|has| (|Boolean|) (|SetCategory|))) (((|Integer|) (|Boolean|) $) NIL (|has| (|Boolean|) (|SetCategory|))) (((|Integer|) (|Mapping| (|Boolean|) (|Boolean|)) $) NIL)) (|parts| (((|List| (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|or| (($ $ $) NIL)) (|not| (($ $) NIL)) (|nor| (($ $ $) NIL)) (|new| (($ (|NonNegativeInteger|) (|Boolean|)) 8)) (|nand| (($ $ $) NIL)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL)) (|merge| (($ $ $) NIL (|has| (|Boolean|) (|OrderedSet|))) (($ (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $ $) NIL)) (|members| (((|List| (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|Boolean|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Boolean|) (|SetCategory|))))) (|maxIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL)) 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(((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copyInto!| (($ $ $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) NIL (|has| (|Boolean|) (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| (|Boolean|))) NIL)) (|concat| (($ (|List| $)) NIL) (($ $ $) NIL) (($ (|Boolean|) $) NIL) (($ $ (|Boolean|)) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) 9)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|and| (($ $ $) NIL)) (^ (($ $) NIL)) (|\\/| (($ $ $) NIL)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) NIL)) (|/\\| (($ $ $) NIL)) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|Bits|) (|Join| (|BitAggregate|) (CATEGORY |domain| (SIGNATURE |bits| ($ (|NonNegativeInteger|) (|Boolean|)))))) (T |Bits|)) 
((|bits| (*1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *3 (|Boolean|)) (|isDomain| *1 (|Bits|))))) 
(|Join| (|BitAggregate|) (CATEGORY |domain| (SIGNATURE |bits| ($ (|NonNegativeInteger|) (|Boolean|))))) 
((|zaxpy| (((|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|) (|Complex| (|DoubleFloat|)) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|)) 33)) (|izamax| (((|Integer|) (|SingleInteger|) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|)) 32)) (|isamax| (((|Integer|) (|Integer|) (|PrimitiveArray| (|Float|)) (|Integer|)) 31)) (|idamax| (((|Integer|) (|Integer|) (|PrimitiveArray| (|DoubleFloat|)) (|Integer|)) 29)) (|icamax| (((|Integer|) (|Integer|) (|PrimitiveArray| (|Complex| (|Float|))) (|Integer|)) 28)) (|dznrm2| (((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|)) 25)) (|dzasum| (((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|)) 24)) (|dswap| (((|List| (|PrimitiveArray| (|DoubleFloat|))) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|)) 22)) (|dscal| (((|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|DoubleFloat|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|)) 21)) (|drotg| (((|PrimitiveArray| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) 18)) (|drot| (((|List| (|PrimitiveArray| (|DoubleFloat|))) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|DoubleFloat|) (|DoubleFloat|)) 20)) (|dnrm2| (((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|)) 17)) (|ddot| (((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|)) 16)) (|dcopy| (((|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|)) 15)) (|dcabs1| (((|DoubleFloat|) (|Complex| (|DoubleFloat|))) 10)) (|daxpy| (((|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|DoubleFloat|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|)) 14)) (|dasum| (((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|)) 13))) 
(((|BlasLevelOne|) (CATEGORY |package| (SIGNATURE |dcabs1| ((|DoubleFloat|) (|Complex| (|DoubleFloat|)))) (SIGNATURE |dasum| ((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|))) (SIGNATURE |daxpy| ((|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|DoubleFloat|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|))) (SIGNATURE |dcopy| ((|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|))) (SIGNATURE |ddot| ((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|))) (SIGNATURE |dnrm2| ((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|))) (SIGNATURE |drotg| ((|PrimitiveArray| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |drot| ((|List| (|PrimitiveArray| (|DoubleFloat|))) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |dscal| ((|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|DoubleFloat|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|))) (SIGNATURE |dswap| ((|List| (|PrimitiveArray| (|DoubleFloat|))) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|))) (SIGNATURE |dzasum| ((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|))) (SIGNATURE |dznrm2| ((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|))) (SIGNATURE |icamax| ((|Integer|) (|Integer|) (|PrimitiveArray| (|Complex| (|Float|))) (|Integer|))) (SIGNATURE |idamax| ((|Integer|) (|Integer|) (|PrimitiveArray| (|DoubleFloat|)) (|Integer|))) (SIGNATURE |isamax| ((|Integer|) (|Integer|) (|PrimitiveArray| (|Float|)) (|Integer|))) (SIGNATURE |izamax| ((|Integer|) (|SingleInteger|) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|))) (SIGNATURE |zaxpy| ((|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|) (|Complex| (|DoubleFloat|)) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|))))) (T |BlasLevelOne|)) 
((|zaxpy| (*1 *2 *3 *4 *2 *3 *2 *3) (AND (|isDomain| *2 (|PrimitiveArray| (|Complex| (|DoubleFloat|)))) (|isDomain| *3 (|SingleInteger|)) (|isDomain| *4 (|Complex| (|DoubleFloat|))) (|isDomain| *1 (|BlasLevelOne|)))) (|izamax| (*1 *2 *3 *4 *3) (AND (|isDomain| *3 (|SingleInteger|)) (|isDomain| *4 (|PrimitiveArray| (|Complex| (|DoubleFloat|)))) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|BlasLevelOne|)))) (|isamax| (*1 *2 *2 *3 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *3 (|PrimitiveArray| (|Float|))) (|isDomain| *1 (|BlasLevelOne|)))) (|idamax| (*1 *2 *2 *3 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *3 (|PrimitiveArray| (|DoubleFloat|))) (|isDomain| *1 (|BlasLevelOne|)))) (|icamax| (*1 *2 *2 *3 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *3 (|PrimitiveArray| (|Complex| (|Float|)))) (|isDomain| *1 (|BlasLevelOne|)))) (|dznrm2| (*1 *2 *3 *4 *3) (AND (|isDomain| *3 (|SingleInteger|)) (|isDomain| *4 (|PrimitiveArray| (|Complex| (|DoubleFloat|)))) (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|BlasLevelOne|)))) (|dzasum| (*1 *2 *3 *4 *3) (AND (|isDomain| *3 (|SingleInteger|)) (|isDomain| *4 (|PrimitiveArray| (|Complex| (|DoubleFloat|)))) (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|BlasLevelOne|)))) (|dswap| (*1 *2 *3 *4 *3 *4 *3) (AND (|isDomain| *3 (|SingleInteger|)) (|isDomain| *2 (|List| (|PrimitiveArray| (|DoubleFloat|)))) (|isDomain| *1 (|BlasLevelOne|)) (|isDomain| *4 (|PrimitiveArray| (|DoubleFloat|))))) (|dscal| (*1 *2 *3 *4 *2 *3) (AND (|isDomain| *2 (|PrimitiveArray| (|DoubleFloat|))) (|isDomain| *3 (|SingleInteger|)) (|isDomain| *4 (|DoubleFloat|)) (|isDomain| *1 (|BlasLevelOne|)))) (|drot| (*1 *2 *3 *4 *3 *4 *3 *5 *5) (AND (|isDomain| *3 (|SingleInteger|)) (|isDomain| *5 (|DoubleFloat|)) (|isDomain| *2 (|List| (|PrimitiveArray| *5))) (|isDomain| *1 (|BlasLevelOne|)) (|isDomain| *4 (|PrimitiveArray| *5)))) (|drotg| (*1 *2 *3 *3 *3 *3) (AND (|isDomain| *2 (|PrimitiveArray| (|DoubleFloat|))) (|isDomain| *1 (|BlasLevelOne|)) (|isDomain| *3 (|DoubleFloat|)))) (|dnrm2| (*1 *2 *3 *4 *3) (AND (|isDomain| *3 (|SingleInteger|)) (|isDomain| *4 (|PrimitiveArray| (|DoubleFloat|))) (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|BlasLevelOne|)))) (|ddot| (*1 *2 *3 *4 *3 *4 *3) (AND (|isDomain| *3 (|SingleInteger|)) (|isDomain| *4 (|PrimitiveArray| (|DoubleFloat|))) (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|BlasLevelOne|)))) (|dcopy| (*1 *2 *3 *2 *3 *2 *3) (AND (|isDomain| *2 (|PrimitiveArray| (|DoubleFloat|))) (|isDomain| *3 (|SingleInteger|)) (|isDomain| *1 (|BlasLevelOne|)))) (|daxpy| (*1 *2 *3 *4 *2 *3 *2 *3) (AND (|isDomain| *2 (|PrimitiveArray| (|DoubleFloat|))) (|isDomain| *3 (|SingleInteger|)) (|isDomain| *4 (|DoubleFloat|)) (|isDomain| *1 (|BlasLevelOne|)))) (|dasum| (*1 *2 *3 *4 *3) (AND (|isDomain| *3 (|SingleInteger|)) (|isDomain| *4 (|PrimitiveArray| (|DoubleFloat|))) (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|BlasLevelOne|)))) (|dcabs1| (*1 *2 *3) (AND (|isDomain| *3 (|Complex| (|DoubleFloat|))) (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|BlasLevelOne|))))) 
(CATEGORY |package| (SIGNATURE |dcabs1| ((|DoubleFloat|) (|Complex| (|DoubleFloat|)))) (SIGNATURE |dasum| ((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|))) (SIGNATURE |daxpy| ((|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|DoubleFloat|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|))) (SIGNATURE |dcopy| ((|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|))) (SIGNATURE |ddot| ((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|))) (SIGNATURE |dnrm2| ((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|))) (SIGNATURE |drotg| ((|PrimitiveArray| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |drot| ((|List| (|PrimitiveArray| (|DoubleFloat|))) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |dscal| ((|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|DoubleFloat|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|))) (SIGNATURE |dswap| ((|List| (|PrimitiveArray| (|DoubleFloat|))) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|))) (SIGNATURE |dzasum| ((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|))) (SIGNATURE |dznrm2| ((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|))) (SIGNATURE |icamax| ((|Integer|) (|Integer|) (|PrimitiveArray| (|Complex| (|Float|))) (|Integer|))) (SIGNATURE |idamax| ((|Integer|) (|Integer|) (|PrimitiveArray| (|DoubleFloat|)) (|Integer|))) (SIGNATURE |isamax| ((|Integer|) (|Integer|) (|PrimitiveArray| (|Float|)) (|Integer|))) (SIGNATURE |izamax| ((|Integer|) (|SingleInteger|) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|))) (SIGNATURE |zaxpy| ((|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|) (|Complex| (|DoubleFloat|)) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|)))) 
((~= (((|Boolean|) $ $) NIL)) (|type| (((|Union| "left" "center" "right" "vertical" "horizontal") $) 17)) (|transCoord| (((|Integer|) $) 14)) (|ramifMult| (((|Integer|) $) 15)) (|quotValuation| (((|Integer|) $) 16)) (|latex| (((|String|) $) NIL)) (|infClsPt?| (((|Boolean|) $) 8)) (|hash| (((|SingleInteger|) $) NIL)) (|excepCoord| (((|Integer|) $) 12)) (|createHN| (($ (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Union| "left" "center" "right" "vertical" "horizontal")) 11)) (|coerce| (((|OutputForm|) $) 19) (($ (|List| (|Integer|))) NIL)) (|chartCoord| (((|Integer|) $) 13)) (= (((|Boolean|) $ $) NIL))) 
(((|BlowUpWithHamburgerNoether|) (|Join| (|BlowUpMethodCategory|) (CATEGORY |package| (ATTRIBUTE |HamburgerNoether|)))) (T |BlowUpWithHamburgerNoether|)) 
NIL 
(|Join| (|BlowUpMethodCategory|) (CATEGORY |package| (ATTRIBUTE |HamburgerNoether|))) 
((~= (((|Boolean|) $ $) 7)) (|type| (((|Union| "left" "center" "right" "vertical" "horizontal") $) 12)) (|transCoord| (((|Integer|) $) 17)) (|ramifMult| (((|Integer|) $) 15)) (|quotValuation| (((|Integer|) $) 13)) (|latex| (((|String|) $) 9)) (|infClsPt?| (((|Boolean|) $) 14)) (|hash| (((|SingleInteger|) $) 10)) (|excepCoord| (((|Integer|) $) 19)) (|createHN| (($ (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Union| "left" "center" "right" "vertical" "horizontal")) 16)) (|coerce| (((|OutputForm|) $) 11) (($ (|List| (|Integer|))) 20)) (|chartCoord| (((|Integer|) $) 18)) (= (((|Boolean|) $ $) 6))) 
(((|BlowUpMethodCategory|) (|Category|)) (T |BlowUpMethodCategory|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|ofCategory| *1 (|BlowUpMethodCategory|)))) (|excepCoord| (*1 *2 *1) (AND (|ofCategory| *1 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Integer|)))) (|chartCoord| (*1 *2 *1) (AND (|ofCategory| *1 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Integer|)))) (|transCoord| (*1 *2 *1) (AND (|ofCategory| *1 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Integer|)))) (|createHN| (*1 *1 *2 *2 *2 *2 *2 *3 *4) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *3 (|Boolean|)) (|isDomain| *4 (|Union| "left" "center" "right" "vertical" "horizontal")) (|ofCategory| *1 (|BlowUpMethodCategory|)))) (|ramifMult| (*1 *2 *1) (AND (|ofCategory| *1 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Integer|)))) (|infClsPt?| (*1 *2 *1) (AND (|ofCategory| *1 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Boolean|)))) (|quotValuation| (*1 *2 *1) (AND (|ofCategory| *1 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Integer|)))) (|type| (*1 *2 *1) (AND (|ofCategory| *1 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Union| "left" "center" "right" "vertical" "horizontal"))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|List| (|Integer|)))) (SIGNATURE |excepCoord| ((|Integer|) $)) (SIGNATURE |chartCoord| ((|Integer|) $)) (SIGNATURE |transCoord| ((|Integer|) $)) (SIGNATURE |createHN| ($ (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Union| "left" "center" "right" "vertical" "horizontal"))) (SIGNATURE |ramifMult| ((|Integer|) $)) (SIGNATURE |infClsPt?| ((|Boolean|) $)) (SIGNATURE |quotValuation| ((|Integer|) $)) (SIGNATURE |type| ((|Union| "left" "center" "right" "vertical" "horizontal") $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|type| (((|Union| "left" "center" "right" "vertical" "horizontal") $) NIL)) (|transCoord| (((|Integer|) $) 14)) (|ramifMult| (((|Integer|) $) 11)) (|quotValuation| (((|Integer|) $) 15)) (|latex| (((|String|) $) NIL)) (|infClsPt?| (((|Boolean|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|excepCoord| (((|Integer|) $) 12)) (|createHN| (($ (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Union| "left" "center" "right" "vertical" "horizontal")) NIL)) (|coerce| (((|OutputForm|) $) 17) (($ (|List| (|Integer|))) 10)) (|chartCoord| (((|Integer|) $) 13)) (= (((|Boolean|) $ $) NIL))) 
(((|BlowUpWithQuadTrans|) (|Join| (|BlowUpMethodCategory|) (CATEGORY |package| (ATTRIBUTE |QuadraticTransform|)))) (T |BlowUpWithQuadTrans|)) 
NIL 
(|Join| (|BlowUpMethodCategory|) (CATEGORY |package| (ATTRIBUTE |QuadraticTransform|))) 
((|stepBlowUp| (((|Record| (|:| |mult| (|NonNegativeInteger|)) (|:| |subMult| (|NonNegativeInteger|)) (|:| |blUpRec| (|List| (|Record| (|:| |recTransStr| (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|)) (|:| |recPoint| (|AffinePlane| |#1|)) (|:| |recChart| |#5|) (|:| |definingExtension| |#1|))))) (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) (|AffinePlane| |#1|) |#5| |#1|) 70)) (|quadTransform| (((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) (|NonNegativeInteger|) |#5|) 54)) (|polyRingToBlUpRing| (((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) |#3| |#5|) 99)) (|newtonPolySlope| (((|List| (|List| (|NonNegativeInteger|))) (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|)) NIL)) (|biringToPolyRing| ((|#3| (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) |#5|) 105)) (|applyTransform| ((|#3| |#3| |#5|) 107))) 
(((|BlowUpPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |applyTransform| (|#3| |#3| |#5|)) (SIGNATURE |quadTransform| ((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) (|NonNegativeInteger|) |#5|)) (SIGNATURE |stepBlowUp| ((|Record| (|:| |mult| (|NonNegativeInteger|)) (|:| |subMult| (|NonNegativeInteger|)) (|:| |blUpRec| (|List| (|Record| (|:| |recTransStr| (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|)) (|:| |recPoint| (|AffinePlane| |#1|)) (|:| |recChart| |#5|) (|:| |definingExtension| |#1|))))) (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) (|AffinePlane| |#1|) |#5| |#1|)) (SIGNATURE |newtonPolySlope| ((|List| (|List| (|NonNegativeInteger|))) (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|))) (SIGNATURE |polyRingToBlUpRing| ((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) |#3| |#5|)) (SIGNATURE |biringToPolyRing| (|#3| (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) |#5|))) (|Field|) (|List| (|Symbol|)) (|FiniteAbelianMonoidRing| |#1| |#4|) (|DirectProductCategory| (|#| |#2|) (|NonNegativeInteger|)) (|BlowUpMethodCategory|)) (T |BlowUpPackage|)) 
((|biringToPolyRing| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) *5)) (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *2 (|FiniteAbelianMonoidRing| *5 *7)) (|isDomain| *1 (|BlowUpPackage| *5 *6 *2 *7 *4)) (|ofCategory| *7 (|DirectProductCategory| (|#| *6) (|NonNegativeInteger|))) (|ofCategory| *4 (|BlowUpMethodCategory|)))) (|polyRingToBlUpRing| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|DirectProductCategory| (|#| *6) (|NonNegativeInteger|))) (|isDomain| *2 (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) *5)) (|isDomain| *1 (|BlowUpPackage| *5 *6 *3 *7 *4)) (|ofCategory| *3 (|FiniteAbelianMonoidRing| *5 *7)) (|ofCategory| *4 (|BlowUpMethodCategory|)))) (|newtonPolySlope| (*1 *2 *3) (AND (|isDomain| *3 (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) *4)) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|isDomain| *2 (|List| (|List| (|NonNegativeInteger|)))) (|isDomain| *1 (|BlowUpPackage| *4 *5 *6 *7 *8)) (|ofCategory| *6 (|FiniteAbelianMonoidRing| *4 *7)) (|ofCategory| *8 (|BlowUpMethodCategory|)))) (|stepBlowUp| (*1 *2 *3 *4 *5 *6) (AND (|ofCategory| *6 (|Field|)) (|ofType| *7 (|List| (|Symbol|))) (|ofCategory| *9 (|DirectProductCategory| (|#| *7) (|NonNegativeInteger|))) (|isDomain| *2 (|Record| (|:| |mult| (|NonNegativeInteger|)) (|:| |subMult| (|NonNegativeInteger|)) (|:| |blUpRec| (|List| (|Record| (|:| |recTransStr| (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) *6)) (|:| |recPoint| (|AffinePlane| *6)) (|:| |recChart| *5) (|:| |definingExtension| *6)))))) (|isDomain| *1 (|BlowUpPackage| *6 *7 *8 *9 *5)) (|isDomain| *3 (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) *6)) (|isDomain| *4 (|AffinePlane| *6)) (|ofCategory| *8 (|FiniteAbelianMonoidRing| *6 *9)) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|quadTransform| (*1 *2 *2 *3 *4) (AND (|isDomain| *2 (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *8 (|DirectProductCategory| (|#| *6) *3)) (|isDomain| *1 (|BlowUpPackage| *5 *6 *7 *8 *4)) (|ofCategory| *7 (|FiniteAbelianMonoidRing| *5 *8)) (|ofCategory| *4 (|BlowUpMethodCategory|)))) (|applyTransform| (*1 *2 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|isDomain| *1 (|BlowUpPackage| *4 *5 *2 *6 *3)) (|ofCategory| *2 (|FiniteAbelianMonoidRing| *4 *6)) (|ofCategory| *3 (|BlowUpMethodCategory|))))) 
(CATEGORY |package| (SIGNATURE |applyTransform| (|#3| |#3| |#5|)) (SIGNATURE |quadTransform| ((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) (|NonNegativeInteger|) |#5|)) (SIGNATURE |stepBlowUp| ((|Record| (|:| |mult| (|NonNegativeInteger|)) (|:| |subMult| (|NonNegativeInteger|)) (|:| |blUpRec| (|List| (|Record| (|:| |recTransStr| (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|)) (|:| |recPoint| (|AffinePlane| |#1|)) (|:| |recChart| |#5|) (|:| |definingExtension| |#1|))))) (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) (|AffinePlane| |#1|) |#5| |#1|)) (SIGNATURE |newtonPolySlope| ((|List| (|List| (|NonNegativeInteger|))) (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|))) (SIGNATURE |polyRingToBlUpRing| ((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) |#3| |#5|)) (SIGNATURE |biringToPolyRing| (|#3| (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) |#5|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ |#1| $) 22) (($ $ |#2|) 24))) 
(((|BiModule| |#1| |#2|) (|Category|) (|Ring|) (|Ring|)) (T |BiModule|)) 
NIL 
(|Join| (|LeftModule| |t#1|) (|RightModule| |t#2|) (CATEGORY |package| (ATTRIBUTE |leftUnitary|) (ATTRIBUTE |rightUnitary|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| |#1|) . T) ((|RightModule| |#2|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (~ (($ $) 12)) (|xor| (($ $ $) 17)) (|true| (($) 8 T CONST)) (|test| (((|Boolean|) $) 7)) (|size| (((|NonNegativeInteger|)) 24)) (|random| (($) 30)) (|or| (($ $ $) 15)) (|not| (($ $) 10)) (|nor| (($ $ $) 18)) (|nand| (($ $ $) 19)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|lookup| (((|PositiveInteger|) $) 29)) (|latex| (((|String|) $) NIL)) (|index| (($ (|PositiveInteger|)) 28)) (|implies| (($ $ $) 21)) (|hash| (((|SingleInteger|) $) NIL)) (|false| (($) 9 T CONST)) (|enumerate| (((|List| $)) NIL)) (|convert| (((|InputForm|) $) 36)) (|coerce| (((|OutputForm|) $) 39)) (|and| (($ $ $) 13)) (^ (($ $) 11)) (|\\/| (($ $ $) 16)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 20)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 22)) (|/\\| (($ $ $) 14))) 
(((|Boolean|) (|Join| (|OrderedSet|) (|Finite|) (|Logic|) (|ConvertibleTo| (|InputForm|)) (CATEGORY |domain| (SIGNATURE |true| ($) |constant|) (SIGNATURE |false| ($) |constant|) (SIGNATURE ^ ($ $)) (SIGNATURE |not| ($ $)) (SIGNATURE |and| ($ $ $)) (SIGNATURE |or| ($ $ $)) (SIGNATURE |xor| ($ $ $)) (SIGNATURE |nand| ($ $ $)) (SIGNATURE |nor| ($ $ $)) (SIGNATURE |implies| ($ $ $)) (SIGNATURE |test| ((|Boolean|) $))))) (T |Boolean|)) 
((|true| (*1 *1) (|isDomain| *1 (|Boolean|))) (|false| (*1 *1) (|isDomain| *1 (|Boolean|))) (^ (*1 *1 *1) (|isDomain| *1 (|Boolean|))) (|not| (*1 *1 *1) (|isDomain| *1 (|Boolean|))) (|and| (*1 *1 *1 *1) (|isDomain| *1 (|Boolean|))) (|or| (*1 *1 *1 *1) (|isDomain| *1 (|Boolean|))) (|xor| (*1 *1 *1 *1) (|isDomain| *1 (|Boolean|))) (|nand| (*1 *1 *1 *1) (|isDomain| *1 (|Boolean|))) (|nor| (*1 *1 *1 *1) (|isDomain| *1 (|Boolean|))) (|implies| (*1 *1 *1 *1) (|isDomain| *1 (|Boolean|))) (|test| (*1 *1 *1) (|isDomain| *1 (|Boolean|)))) 
(|Join| (|OrderedSet|) (|Finite|) (|Logic|) (|ConvertibleTo| (|InputForm|)) (CATEGORY |domain| (SIGNATURE |true| ($) |constant|) (SIGNATURE |false| ($) |constant|) (SIGNATURE ^ ($ $)) (SIGNATURE |not| ($ $)) (SIGNATURE |and| ($ $ $)) (SIGNATURE |or| ($ $ $)) (SIGNATURE |xor| ($ $ $)) (SIGNATURE |nand| ($ $ $)) (SIGNATURE |nor| ($ $ $)) (SIGNATURE |implies| ($ $ $)) (SIGNATURE |test| ((|Boolean|) $)))) 
((|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) 18) (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) 13) (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) 11) (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) 20)) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) 24) (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) 30) (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) 26)) (|constantOperator| (((|BasicOperator|) |#1|) 53 (|has| |#1| (|OrderedSet|)))) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) 48 (|has| |#1| (|OrderedSet|))))) 
(((|BasicOperatorFunctions1| |#1|) (CATEGORY |package| (SIGNATURE |evaluate| ((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|))) (SIGNATURE |evaluate| ((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|)))) (SIGNATURE |evaluate| ((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|))) (SIGNATURE |evaluate| ((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|))) (SIGNATURE |derivative| ((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|))))) (SIGNATURE |derivative| ((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|))) (SIGNATURE |derivative| ((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|))) (IF (|has| |#1| (|OrderedSet|)) (PROGN (SIGNATURE |constantOperator| ((|BasicOperator|) |#1|)) (SIGNATURE |constantOpIfCan| ((|Union| |#1| "failed") (|BasicOperator|)))) |noBranch|)) (|SetCategory|)) (T |BasicOperatorFunctions1|)) 
((|constantOpIfCan| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|OrderedSet|)) (|isDomain| *1 (|BasicOperatorFunctions1| *2)))) (|constantOperator| (*1 *2 *3) (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *1 (|BasicOperatorFunctions1| *3)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *3 (|SetCategory|)))) (|derivative| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *2 (|List| (|Mapping| *4 (|List| *4)))) (|isDomain| *1 (|BasicOperatorFunctions1| *4)) (|ofCategory| *4 (|SetCategory|)))) (|derivative| (*1 *2 *2 *3) (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|Mapping| *4 *4)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *1 (|BasicOperatorFunctions1| *4)))) (|derivative| (*1 *2 *2 *3) (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|List| (|Mapping| *4 (|List| *4)))) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *1 (|BasicOperatorFunctions1| *4)))) (|evaluate| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *2 (|Mapping| *4 (|List| *4))) (|isDomain| *1 (|BasicOperatorFunctions1| *4)) (|ofCategory| *4 (|SetCategory|)))) (|evaluate| (*1 *2 *2 *3) (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|Mapping| *4 *4)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *1 (|BasicOperatorFunctions1| *4)))) (|evaluate| (*1 *2 *2 *3) (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|Mapping| *4 (|List| *4))) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *1 (|BasicOperatorFunctions1| *4)))) (|evaluate| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *4 (|List| *2)) (|isDomain| *1 (|BasicOperatorFunctions1| *2)) (|ofCategory| *2 (|SetCategory|))))) 
(CATEGORY |package| (SIGNATURE |evaluate| ((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|))) (SIGNATURE |evaluate| ((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|)))) (SIGNATURE |evaluate| ((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|))) (SIGNATURE |evaluate| ((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|))) (SIGNATURE |derivative| ((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|))))) (SIGNATURE |derivative| ((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|))) (SIGNATURE |derivative| ((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|))) (IF (|has| |#1| (|OrderedSet|)) (PROGN (SIGNATURE |constantOperator| ((|BasicOperator|) |#1|)) (SIGNATURE |constantOpIfCan| ((|Union| |#1| "failed") (|BasicOperator|)))) |noBranch|)) 
((~= (((|Boolean|) $ $) NIL)) (|weight| (((|NonNegativeInteger|) $) 68) (($ $ (|NonNegativeInteger|)) 30)) (|unary?| (((|Boolean|) $) 32)) (|setProperty| (($ $ (|String|) (|None|)) 26)) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) 13)) (|property| (((|Union| (|None|) "failed") $ (|String|)) 24)) (|properties| (((|AssociationList| (|String|) (|None|)) $) 12)) (|operator| (($ (|Symbol|)) 15) (($ (|Symbol|) (|NonNegativeInteger|)) 20)) (|nullary?| (((|Boolean|) $) 31)) (|nary?| (((|Boolean|) $) 33)) (|name| (((|Symbol|) $) 8)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|latex| (((|String|) $) NIL)) (|is?| (((|Boolean|) $ (|Symbol|)) 10)) (|input| (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) 50) (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) 54)) (|hash| (((|SingleInteger|) $) NIL)) (|has?| (((|Boolean|) $ (|String|)) 29)) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) 35)) (|display| (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) 52) (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) 41) (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) 43)) (|deleteProperty!| (($ $ (|String|)) 45)) (|copy| (($ $) 61)) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) 36)) (|coerce| (((|OutputForm|) $) 48)) (|assert| (($ $ (|String|)) 27)) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) 56)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 67)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 72))) 
(((|BasicOperator|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |name| ((|Symbol|) $)) (SIGNATURE |properties| ((|AssociationList| (|String|) (|None|)) $)) (SIGNATURE |copy| ($ $)) (SIGNATURE |operator| ($ (|Symbol|))) (SIGNATURE |operator| ($ (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |arity| ((|Union| (|NonNegativeInteger|) "failed") $)) (SIGNATURE |nullary?| ((|Boolean|) $)) (SIGNATURE |unary?| ((|Boolean|) $)) (SIGNATURE |nary?| ((|Boolean|) $)) (SIGNATURE |weight| ((|NonNegativeInteger|) $)) (SIGNATURE |weight| ($ $ (|NonNegativeInteger|))) (SIGNATURE |equality| ($ $ (|Mapping| (|Boolean|) $ $))) (SIGNATURE |comparison| ($ $ (|Mapping| (|Boolean|) $ $))) (SIGNATURE |display| ((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $)) (SIGNATURE |display| ($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|))))) (SIGNATURE |display| ($ $ (|Mapping| (|OutputForm|) (|OutputForm|)))) (SIGNATURE |input| ($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|))))) (SIGNATURE |input| ((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $)) (SIGNATURE |is?| ((|Boolean|) $ (|Symbol|))) (SIGNATURE |has?| ((|Boolean|) $ (|String|))) (SIGNATURE |assert| ($ $ (|String|))) (SIGNATURE |deleteProperty!| ($ $ (|String|))) (SIGNATURE |property| ((|Union| (|None|) "failed") $ (|String|))) (SIGNATURE |setProperty| ($ $ (|String|) (|None|))) (SIGNATURE |setProperties| ($ $ (|AssociationList| (|String|) (|None|))))))) (T |BasicOperator|)) 
((|name| (*1 *2 *1) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|BasicOperator|)))) (|properties| (*1 *2 *1) (AND (|isDomain| *2 (|AssociationList| (|String|) (|None|))) (|isDomain| *1 (|BasicOperator|)))) (|copy| (*1 *1 *1) (|isDomain| *1 (|BasicOperator|))) (|operator| (*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|BasicOperator|)))) (|operator| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|BasicOperator|)))) (|arity| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|BasicOperator|)))) (|nullary?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|BasicOperator|)))) (|unary?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|BasicOperator|)))) (|nary?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|BasicOperator|)))) (|weight| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|BasicOperator|)))) (|weight| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|BasicOperator|)))) (|equality| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| (|Boolean|) (|BasicOperator|) (|BasicOperator|))) (|isDomain| *1 (|BasicOperator|)))) (|comparison| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| (|Boolean|) (|BasicOperator|) (|BasicOperator|))) (|isDomain| *1 (|BasicOperator|)))) (|display| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) (|isDomain| *1 (|BasicOperator|)))) (|display| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) (|isDomain| *1 (|BasicOperator|)))) (|display| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| (|OutputForm|) (|OutputForm|))) (|isDomain| *1 (|BasicOperator|)))) (|input| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| (|InputForm|) (|List| (|InputForm|)))) (|isDomain| *1 (|BasicOperator|)))) (|input| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|Mapping| (|InputForm|) (|List| (|InputForm|)))) (|isDomain| *1 (|BasicOperator|)))) (|is?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|BasicOperator|)))) (|has?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|BasicOperator|)))) (|assert| (*1 *1 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|BasicOperator|)))) (|deleteProperty!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|BasicOperator|)))) (|property| (*1 *2 *1 *3) (|partial| AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|None|)) (|isDomain| *1 (|BasicOperator|)))) (|setProperty| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|String|)) (|isDomain| *3 (|None|)) (|isDomain| *1 (|BasicOperator|)))) (|setProperties| (*1 *1 *1 *2) (AND (|isDomain| *2 (|AssociationList| (|String|) (|None|))) (|isDomain| *1 (|BasicOperator|))))) 
(|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |name| ((|Symbol|) $)) (SIGNATURE |properties| ((|AssociationList| (|String|) (|None|)) $)) (SIGNATURE |copy| ($ $)) (SIGNATURE |operator| ($ (|Symbol|))) (SIGNATURE |operator| ($ (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |arity| ((|Union| (|NonNegativeInteger|) "failed") $)) (SIGNATURE |nullary?| ((|Boolean|) $)) (SIGNATURE |unary?| ((|Boolean|) $)) (SIGNATURE |nary?| ((|Boolean|) $)) (SIGNATURE |weight| ((|NonNegativeInteger|) $)) (SIGNATURE |weight| ($ $ (|NonNegativeInteger|))) (SIGNATURE |equality| ($ $ (|Mapping| (|Boolean|) $ $))) (SIGNATURE |comparison| ($ $ (|Mapping| (|Boolean|) $ $))) (SIGNATURE |display| ((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $)) (SIGNATURE |display| ($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|))))) (SIGNATURE |display| ($ $ (|Mapping| (|OutputForm|) (|OutputForm|)))) (SIGNATURE |input| ($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|))))) (SIGNATURE |input| ((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $)) (SIGNATURE |is?| ((|Boolean|) $ (|Symbol|))) (SIGNATURE |has?| ((|Boolean|) $ (|String|))) (SIGNATURE |assert| ($ $ (|String|))) (SIGNATURE |deleteProperty!| ($ $ (|String|))) (SIGNATURE |property| ((|Union| (|None|) "failed") $ (|String|))) (SIGNATURE |setProperty| ($ $ (|String|) (|None|))) (SIGNATURE |setProperties| ($ $ (|AssociationList| (|String|) (|None|)))))) 
((|integerBound| (((|Integer|) |#2|) 36))) 
(((|BoundIntegerRoots| |#1| |#2|) (CATEGORY |package| (SIGNATURE |integerBound| ((|Integer|) |#2|))) (|Join| (|Field|) (|RetractableTo| (|Fraction| (|Integer|)))) (|UnivariatePolynomialCategory| |#1|)) (T |BoundIntegerRoots|)) 
((|integerBound| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|Field|) (|RetractableTo| (|Fraction| *2)))) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|BoundIntegerRoots| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |integerBound| ((|Integer|) |#2|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sqrt| (($ $ (|Integer|)) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sample| (($) NIL T CONST)) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) NIL)) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|quotientByP| (($ $) NIL)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|order| (((|NonNegativeInteger|) $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|modulus| (((|Integer|)) NIL)) (|moduloP| (((|Integer|) $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|extend| (($ $ (|Integer|)) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|digits| (((|Stream| (|Integer|)) $) NIL)) (|complete| (($ $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|associates?| (((|Boolean|) $ $) NIL)) (|approximate| (((|Integer|) $ (|Integer|)) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL))) 
(((|BalancedPAdicInteger| |#1|) (|PAdicIntegerCategory| |#1|) (|Integer|)) (T |BalancedPAdicInteger|)) 
NIL 
(|PAdicIntegerCategory| |#1|) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|wholePart| (((|BalancedPAdicInteger| |#1|) $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|EuclideanDomain|)))) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|PolynomialFactorizationExplicit|)))) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sign| (((|Integer|) $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|OrderedIntegralDomain|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|BalancedPAdicInteger| |#1|) "failed") $) NIL) (((|Union| (|Symbol|) "failed") $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|RetractableTo| (|Symbol|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|RetractableTo| (|Integer|)))) (((|Union| (|Integer|) "failed") $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|RetractableTo| (|Integer|))))) (|retract| (((|BalancedPAdicInteger| |#1|) $) NIL) (((|Symbol|) $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|RetractableTo| (|Symbol|)))) (((|Fraction| (|Integer|)) $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|RetractableTo| (|Integer|)))) (((|Integer|) $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|RetractableTo| (|Integer|))))) (|removeZeroes| (($ $) NIL) (($ (|Integer|) $) NIL)) (|rem| (($ $ $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|BalancedPAdicInteger| |#1|))) (|:| |vec| (|Vector| (|BalancedPAdicInteger| |#1|)))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| (|BalancedPAdicInteger| |#1|)) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) NIL (|has| (|BalancedPAdicInteger| |#1|) (|IntegerNumberSystem|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|positive?| (((|Boolean|) $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|OrderedIntegralDomain|)))) (|patternMatch| (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|PatternMatchable| (|Integer|)))) (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|PatternMatchable| (|Float|))))) (|one?| (((|Boolean|) $) NIL)) (|numerator| (($ $) NIL)) (|numer| (((|BalancedPAdicInteger| |#1|) $) NIL)) (|nextItem| (((|Union| $ "failed") $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|StepThrough|)))) (|negative?| (((|Boolean|) $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|OrderedIntegralDomain|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|min| (($ $ $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|OrderedSet|)))) (|map| (($ (|Mapping| (|BalancedPAdicInteger| |#1|) (|BalancedPAdicInteger| |#1|)) $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|init| (($) NIL (|has| (|BalancedPAdicInteger| |#1|) (|StepThrough|)) CONST)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|fractionPart| (($ $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|EuclideanDomain|)))) (|floor| (((|BalancedPAdicInteger| |#1|) $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|IntegerNumberSystem|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|eval| (($ $ (|List| (|BalancedPAdicInteger| |#1|)) (|List| (|BalancedPAdicInteger| |#1|))) NIL (|has| (|BalancedPAdicInteger| |#1|) (|Evalable| (|BalancedPAdicInteger| |#1|)))) (($ $ (|BalancedPAdicInteger| |#1|) (|BalancedPAdicInteger| |#1|)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|Evalable| (|BalancedPAdicInteger| |#1|)))) (($ $ (|Equation| (|BalancedPAdicInteger| |#1|))) NIL (|has| (|BalancedPAdicInteger| |#1|) (|Evalable| (|BalancedPAdicInteger| |#1|)))) (($ $ (|List| (|Equation| (|BalancedPAdicInteger| |#1|)))) NIL (|has| (|BalancedPAdicInteger| |#1|) (|Evalable| (|BalancedPAdicInteger| |#1|)))) (($ $ (|List| (|Symbol|)) (|List| (|BalancedPAdicInteger| |#1|))) NIL (|has| (|BalancedPAdicInteger| |#1|) (|InnerEvalable| (|Symbol|) (|BalancedPAdicInteger| |#1|)))) (($ $ (|Symbol|) (|BalancedPAdicInteger| |#1|)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|InnerEvalable| (|Symbol|) (|BalancedPAdicInteger| |#1|))))) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|elt| (($ $ (|BalancedPAdicInteger| |#1|)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|Eltable| (|BalancedPAdicInteger| |#1|) (|BalancedPAdicInteger| |#1|))))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|differentiate| (($ $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| (|BalancedPAdicInteger| |#1|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| (|BalancedPAdicInteger| |#1|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| (|BalancedPAdicInteger| |#1|) (|BalancedPAdicInteger| |#1|)) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| (|BalancedPAdicInteger| |#1|) (|BalancedPAdicInteger| |#1|))) NIL)) (|denominator| (($ $) NIL)) (|denom| (((|BalancedPAdicInteger| |#1|) $) NIL)) (|convert| (((|Pattern| (|Integer|)) $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|ConvertibleTo| (|Pattern| (|Integer|))))) (((|Pattern| (|Float|)) $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|ConvertibleTo| (|Pattern| (|Float|))))) (((|InputForm|) $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|ConvertibleTo| (|InputForm|)))) (((|Float|) $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|RealConstant|))) (((|DoubleFloat|) $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|RealConstant|)))) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) NIL)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| (|BalancedPAdicInteger| |#1|) (|PolynomialFactorizationExplicit|))))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ (|BalancedPAdicInteger| |#1|)) NIL) (($ (|Symbol|)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|RetractableTo| (|Symbol|))))) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| (|BalancedPAdicInteger| |#1|) (|PolynomialFactorizationExplicit|))) (|has| (|BalancedPAdicInteger| |#1|) (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|ceiling| (((|BalancedPAdicInteger| |#1|) $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|IntegerNumberSystem|)))) (|associates?| (((|Boolean|) $ $) NIL)) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) NIL)) (|abs| (($ $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|OrderedIntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($ $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| (|BalancedPAdicInteger| |#1|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| (|BalancedPAdicInteger| |#1|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| (|BalancedPAdicInteger| |#1|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| (|BalancedPAdicInteger| |#1|) (|BalancedPAdicInteger| |#1|)) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| (|BalancedPAdicInteger| |#1|) (|BalancedPAdicInteger| |#1|))) NIL)) (>= (((|Boolean|) $ $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| (|BalancedPAdicInteger| |#1|) (|OrderedSet|)))) (/ (($ $ $) NIL) (($ (|BalancedPAdicInteger| |#1|) (|BalancedPAdicInteger| |#1|)) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ (|BalancedPAdicInteger| |#1|) $) NIL) (($ $ (|BalancedPAdicInteger| |#1|)) NIL))) 
(((|BalancedPAdicRational| |#1|) (|Join| (|QuotientFieldCategory| (|BalancedPAdicInteger| |#1|)) (CATEGORY |domain| (SIGNATURE |approximate| ((|Fraction| (|Integer|)) $ (|Integer|))) (SIGNATURE |continuedFraction| ((|ContinuedFraction| (|Fraction| (|Integer|))) $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |removeZeroes| ($ (|Integer|) $)))) (|Integer|)) (T |BalancedPAdicRational|)) 
((|approximate| (*1 *2 *1 *3) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|BalancedPAdicRational| *4)) (|ofType| *4 *3) (|isDomain| *3 (|Integer|)))) (|continuedFraction| (*1 *2 *1) (AND (|isDomain| *2 (|ContinuedFraction| (|Fraction| (|Integer|)))) (|isDomain| *1 (|BalancedPAdicRational| *3)) (|ofType| *3 (|Integer|)))) (|removeZeroes| (*1 *1 *1) (AND (|isDomain| *1 (|BalancedPAdicRational| *2)) (|ofType| *2 (|Integer|)))) (|removeZeroes| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|BalancedPAdicRational| *3)) (|ofType| *3 *2)))) 
(|Join| (|QuotientFieldCategory| (|BalancedPAdicInteger| |#1|)) (CATEGORY |domain| (SIGNATURE |approximate| ((|Fraction| (|Integer|)) $ (|Integer|))) (SIGNATURE |continuedFraction| ((|ContinuedFraction| (|Fraction| (|Integer|))) $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |removeZeroes| ($ (|Integer|) $)))) 
((|setelt| ((|#2| $ "value" |#2|) NIL) (($ $ "left" $) 48) (($ $ "right" $) 50)) (|nodes| (((|List| $) $) 27)) (|node?| (((|Boolean|) $ $) 32)) (|member?| (((|Boolean|) |#2| $) 36)) (|leaves| (((|List| |#2|) $) 22)) (|leaf?| (((|Boolean|) $) 16)) (|elt| ((|#2| $ "value") NIL) (($ $ "left") 10) (($ $ "right") 13)) (|cyclic?| (((|Boolean|) $) 45)) (|coerce| (((|OutputForm|) $) 41)) (|children| (((|List| $) $) 28)) (= (((|Boolean|) $ $) 34)) (|#| (((|NonNegativeInteger|) $) 43))) 
(((|BinaryRecursiveAggregate&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |setelt| (|#1| |#1| "right" |#1|)) (SIGNATURE |setelt| (|#1| |#1| "left" |#1|)) (SIGNATURE |elt| (|#1| |#1| "right")) (SIGNATURE |elt| (|#1| |#1| "left")) (SIGNATURE |setelt| (|#2| |#1| "value" |#2|)) (SIGNATURE |node?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |leaves| ((|List| |#2|) |#1|)) (SIGNATURE |cyclic?| ((|Boolean|) |#1|)) (SIGNATURE |elt| (|#2| |#1| "value")) (SIGNATURE |leaf?| ((|Boolean|) |#1|)) (SIGNATURE |nodes| ((|List| |#1|) |#1|)) (SIGNATURE |children| ((|List| |#1|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |member?| ((|Boolean|) |#2| |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) |#1|))) (|BinaryRecursiveAggregate| |#2|) (|Type|)) (T |BinaryRecursiveAggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |setelt| (|#1| |#1| "right" |#1|)) (SIGNATURE |setelt| (|#1| |#1| "left" |#1|)) (SIGNATURE |elt| (|#1| |#1| "right")) (SIGNATURE |elt| (|#1| |#1| "left")) (SIGNATURE |setelt| (|#2| |#1| "value" |#2|)) (SIGNATURE |node?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |leaves| ((|List| |#2|) |#1|)) (SIGNATURE |cyclic?| ((|Boolean|) |#1|)) (SIGNATURE |elt| (|#2| |#1| "value")) (SIGNATURE |leaf?| ((|Boolean|) |#1|)) (SIGNATURE |nodes| ((|List| |#1|) |#1|)) (SIGNATURE |children| ((|List| |#1|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |member?| ((|Boolean|) |#2| |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) |#1|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) 45)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setvalue!| ((|#1| $ |#1|) 36 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setright!| (($ $ $) 49 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setleft!| (($ $ $) 51 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "left" $) 52 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "right" $) 50 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) 7 T CONST)) (|right| (($ $) 54)) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) 47)) (|node?| (((|Boolean|) $ $) 39 (|has| |#1| (|SetCategory|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|left| (($ $) 56)) (|leaves| (((|List| |#1|) $) 42)) (|leaf?| (((|Boolean|) $) 46)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| ((|#1| $ "value") 44) (($ $ "left") 55) (($ $ "right") 53)) (|distance| (((|Integer|) $ $) 41)) (|cyclic?| (((|Boolean|) $) 43)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|children| (((|List| $) $) 48)) (|child?| (((|Boolean|) $ $) 40 (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|BinaryRecursiveAggregate| |#1|) (|Category|) (|Type|)) (T |BinaryRecursiveAggregate|)) 
((|left| (*1 *1 *1) (AND (|ofCategory| *1 (|BinaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|elt| (*1 *1 *1 *2) (AND (|isDomain| *2 "left") (|ofCategory| *1 (|BinaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|right| (*1 *1 *1) (AND (|ofCategory| *1 (|BinaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|elt| (*1 *1 *1 *2) (AND (|isDomain| *2 "right") (|ofCategory| *1 (|BinaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|setelt| (*1 *1 *1 *2 *1) (AND (|isDomain| *2 "left") (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|BinaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|setleft!| (*1 *1 *1 *1) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|BinaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setelt| (*1 *1 *1 *2 *1) (AND (|isDomain| *2 "right") (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|BinaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|setright!| (*1 *1 *1 *1) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|BinaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|RecursiveAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |left| ($ $)) (SIGNATURE |elt| ($ $ "left")) (SIGNATURE |right| ($ $)) (SIGNATURE |elt| ($ $ "right")) (IF (|has| $ (ATTRIBUTE |shallowlyMutable|)) (PROGN (SIGNATURE |setelt| ($ $ "left" $)) (SIGNATURE |setleft!| ($ $ $)) (SIGNATURE |setelt| ($ $ "right" $)) (SIGNATURE |setright!| ($ $ $))) |noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((|noLinearFactor?| (((|Boolean|) |#1|) 24)) (|brillhartTrials| (((|NonNegativeInteger|) (|NonNegativeInteger|)) 23) (((|NonNegativeInteger|)) 22)) (|brillhartIrreducible?| (((|Boolean|) |#1| (|Boolean|)) 25) (((|Boolean|) |#1|) 26))) 
(((|BrillhartTests| |#1|) (CATEGORY |package| (SIGNATURE |brillhartIrreducible?| ((|Boolean|) |#1|)) (SIGNATURE |brillhartIrreducible?| ((|Boolean|) |#1| (|Boolean|))) (SIGNATURE |brillhartTrials| ((|NonNegativeInteger|))) (SIGNATURE |brillhartTrials| ((|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |noLinearFactor?| ((|Boolean|) |#1|))) (|UnivariatePolynomialCategory| (|Integer|))) (T |BrillhartTests|)) 
((|noLinearFactor?| (*1 *2 *3) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|BrillhartTests| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|brillhartTrials| (*1 *2 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|BrillhartTests| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|brillhartTrials| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|BrillhartTests| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|brillhartIrreducible?| (*1 *2 *3 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|BrillhartTests| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|brillhartIrreducible?| (*1 *2 *3) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|BrillhartTests| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(CATEGORY |package| (SIGNATURE |brillhartIrreducible?| ((|Boolean|) |#1|)) (SIGNATURE |brillhartIrreducible?| ((|Boolean|) |#1| (|Boolean|))) (SIGNATURE |brillhartTrials| ((|NonNegativeInteger|))) (SIGNATURE |brillhartTrials| ((|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |noLinearFactor?| ((|Boolean|) |#1|))) 
((~= (((|Boolean|) $ $) NIL)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|latex| (((|String|) $) NIL)) (|introduce!| (((|Union| $ "failed") (|Symbol|) (|Symbol|)) 31)) (|hash| (((|SingleInteger|) $) NIL)) (|getSmgl| (((|Union| (|Symbol|) "failed") $) 45)) (|d| (((|Union| $ (|Integer|)) (|Symbol|)) 36)) (|copyIto| (((|Table| (|Symbol|) $)) 42)) (|copyBSD| (((|List| $)) 40)) (|convertIfCan| (((|Union| $ "failed") (|Symbol|)) 19)) (|convert| (($ (|Symbol|)) 27) (((|Symbol|) $) NIL)) (|coerce| (((|OutputForm|) $) 21)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) NIL))) 
(((|BasicStochasticDifferential|) (|Join| (|OrderedSet|) (CATEGORY |domain| (ATTRIBUTE (|ConvertibleTo| (|Symbol|))) (SIGNATURE |convertIfCan| ((|Union| $ "failed") (|Symbol|))) (SIGNATURE |convert| ($ (|Symbol|))) (SIGNATURE |introduce!| ((|Union| $ "failed") (|Symbol|) (|Symbol|))) (SIGNATURE |d| ((|Union| $ (|Integer|)) (|Symbol|))) (SIGNATURE |copyBSD| ((|List| $))) (SIGNATURE |copyIto| ((|Table| (|Symbol|) $))) (SIGNATURE |getSmgl| ((|Union| (|Symbol|) "failed") $))))) (T |BasicStochasticDifferential|)) 
((|convertIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|BasicStochasticDifferential|)))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|BasicStochasticDifferential|)))) (|introduce!| (*1 *1 *2 *2) (|partial| AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|BasicStochasticDifferential|)))) (|d| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Union| (|BasicStochasticDifferential|) (|Integer|))) (|isDomain| *1 (|BasicStochasticDifferential|)))) (|copyBSD| (*1 *2) (AND (|isDomain| *2 (|List| (|BasicStochasticDifferential|))) (|isDomain| *1 (|BasicStochasticDifferential|)))) (|copyIto| (*1 *2) (AND (|isDomain| *2 (|Table| (|Symbol|) (|BasicStochasticDifferential|))) (|isDomain| *1 (|BasicStochasticDifferential|)))) (|getSmgl| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|BasicStochasticDifferential|))))) 
(|Join| (|OrderedSet|) (CATEGORY |domain| (ATTRIBUTE (|ConvertibleTo| (|Symbol|))) (SIGNATURE |convertIfCan| ((|Union| $ "failed") (|Symbol|))) (SIGNATURE |convert| ($ (|Symbol|))) (SIGNATURE |introduce!| ((|Union| $ "failed") (|Symbol|) (|Symbol|))) (SIGNATURE |d| ((|Union| $ (|Integer|)) (|Symbol|))) (SIGNATURE |copyBSD| ((|List| $))) (SIGNATURE |copyIto| ((|Table| (|Symbol|) $))) (SIGNATURE |getSmgl| ((|Union| (|Symbol|) "failed") $)))) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) 15)) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) 22)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setvalue!| ((|#1| $ |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setright!| (($ $ $) 18 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setleft!| (($ $ $) 20 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "left" $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "right" $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) NIL T CONST)) (|right| (($ $) 17)) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) NIL)) (|node?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|node| (($ $ |#1| $) 23)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|left| (($ $) 19)) (|leaves| (((|List| |#1|) $) NIL)) (|leaf?| (((|Boolean|) $) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|insertRoot!| (($ |#1| $) 24)) (|insert!| (($ |#1| $) 10)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) 14)) (|empty| (($) 8)) (|elt| ((|#1| $ "value") NIL) (($ $ "left") NIL) (($ $ "right") NIL)) (|distance| (((|Integer|) $ $) NIL)) (|cyclic?| (((|Boolean|) $) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|)))) (|children| (((|List| $) $) NIL)) (|child?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|binarySearchTree| (($ (|List| |#1|)) 12)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|BinarySearchTree| |#1|) (|Join| (|BinaryTreeCategory| |#1|) (CATEGORY |domain| (ATTRIBUTE |shallowlyMutable|) (ATTRIBUTE |finiteAggregate|) (SIGNATURE |binarySearchTree| ($ (|List| |#1|))) (SIGNATURE |insert!| ($ |#1| $)) (SIGNATURE |insertRoot!| ($ |#1| $)) (SIGNATURE |split| ((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $)))) (|OrderedSet|)) (T |BinarySearchTree|)) 
((|binarySearchTree| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|BinarySearchTree| *3)))) (|insert!| (*1 *1 *2 *1) (AND (|isDomain| *1 (|BinarySearchTree| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|insertRoot!| (*1 *1 *2 *1) (AND (|isDomain| *1 (|BinarySearchTree| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|split| (*1 *2 *3 *1) (AND (|isDomain| *2 (|Record| (|:| |less| (|BinarySearchTree| *3)) (|:| |greater| (|BinarySearchTree| *3)))) (|isDomain| *1 (|BinarySearchTree| *3)) (|ofCategory| *3 (|OrderedSet|))))) 
(|Join| (|BinaryTreeCategory| |#1|) (CATEGORY |domain| (ATTRIBUTE |shallowlyMutable|) (ATTRIBUTE |finiteAggregate|) (SIGNATURE |binarySearchTree| ($ (|List| |#1|))) (SIGNATURE |insert!| ($ |#1| $)) (SIGNATURE |insertRoot!| ($ |#1| $)) (SIGNATURE |split| ((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $)))) 
((~ (($ $) 14)) (|not| (($ $) 11)) (|nor| (($ $ $) 24)) (|nand| (($ $ $) 22)) (^ (($ $) 12)) (|\\/| (($ $ $) 20)) (|/\\| (($ $ $) 18))) 
(((|BitAggregate&| |#1|) (CATEGORY |domain| (SIGNATURE |nor| (|#1| |#1| |#1|)) (SIGNATURE |nand| (|#1| |#1| |#1|)) (SIGNATURE ^ (|#1| |#1|)) (SIGNATURE |not| (|#1| |#1|)) (SIGNATURE ~ (|#1| |#1|)) (SIGNATURE |/\\| (|#1| |#1| |#1|)) (SIGNATURE |\\/| (|#1| |#1| |#1|))) (|BitAggregate|)) (T |BitAggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |nor| (|#1| |#1| |#1|)) (SIGNATURE |nand| (|#1| |#1| |#1|)) (SIGNATURE ^ (|#1| |#1|)) (SIGNATURE |not| (|#1| |#1|)) (SIGNATURE ~ (|#1| |#1|)) (SIGNATURE |/\\| (|#1| |#1| |#1|)) (SIGNATURE |\\/| (|#1| |#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (~ (($ $) 103)) (|xor| (($ $ $) 24)) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) 66 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) $) 98 (|has| (|Boolean|) (|OrderedSet|))) (((|Boolean|) (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $) 92)) (|sort!| (($ $) 102 (AND (|has| (|Boolean|) (|OrderedSet|)) (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (($ (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $) 101 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sort| (($ $) 97 (|has| (|Boolean|) (|OrderedSet|))) (($ (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $) 91)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 37)) (|setelt| (((|Boolean|) $ (|UniversalSegment| (|Integer|)) (|Boolean|)) 88 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Boolean|) $ (|Integer|) (|Boolean|)) 54 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select| (($ (|Mapping| (|Boolean|) (|Boolean|)) $) 71 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) 38 T CONST)) (|reverse!| (($ $) 100 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) 90)) (|removeDuplicates| (($ $) 68 (AND (|has| (|Boolean|) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove| (($ (|Mapping| (|Boolean|) (|Boolean|)) $) 72 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Boolean|) $) 69 (AND (|has| (|Boolean|) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|reduce| (((|Boolean|) (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $) 74 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Boolean|) (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $ (|Boolean|)) 73 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Boolean|) (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $ (|Boolean|) (|Boolean|)) 70 (AND (|has| (|Boolean|) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|qsetelt!| (((|Boolean|) $ (|Integer|) (|Boolean|)) 53 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| (((|Boolean|) $ (|Integer|)) 55)) (|position| (((|Integer|) (|Boolean|) $ (|Integer|)) 95 (|has| (|Boolean|) (|SetCategory|))) (((|Integer|) (|Boolean|) $) 94 (|has| (|Boolean|) (|SetCategory|))) (((|Integer|) (|Mapping| (|Boolean|) (|Boolean|)) $) 93)) (|parts| (((|List| (|Boolean|)) $) 45 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|or| (($ $ $) 25)) (|not| (($ $) 30)) (|nor| (($ $ $) 27)) (|new| (($ (|NonNegativeInteger|) (|Boolean|)) 77)) (|nand| (($ $ $) 28)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 36)) (|minIndex| (((|Integer|) $) 63 (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) 12)) (|merge| (($ $ $) 96 (|has| (|Boolean|) (|OrderedSet|))) (($ (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $ $) 89)) (|members| (((|List| (|Boolean|)) $) 46 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|Boolean|) $) 48 (AND (|has| (|Boolean|) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|maxIndex| (((|Integer|) $) 62 (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) 13)) (|map!| (($ (|Mapping| (|Boolean|) (|Boolean|)) $) 41 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $ $) 82) (($ (|Mapping| (|Boolean|) (|Boolean|)) $) 40)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 35)) (|latex| (((|String|) $) 9)) (|insert| (($ $ $ (|Integer|)) 87) (($ (|Boolean|) $ (|Integer|)) 86)) (|indices| (((|List| (|Integer|)) $) 60)) (|index?| (((|Boolean|) (|Integer|) $) 59)) (|hash| (((|SingleInteger|) $) 10)) (|first| (((|Boolean|) $) 64 (|has| (|Integer|) (|OrderedSet|)))) (|find| (((|Union| (|Boolean|) "failed") (|Mapping| (|Boolean|) (|Boolean|)) $) 75)) (|fill!| (($ $ (|Boolean|)) 65 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) (|Boolean|)) $) 43 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Boolean|)) (|List| (|Boolean|))) 52 (AND (|has| (|Boolean|) (|Evalable| (|Boolean|))) (|has| (|Boolean|) (|SetCategory|)))) (($ $ (|Boolean|) (|Boolean|)) 51 (AND (|has| (|Boolean|) (|Evalable| (|Boolean|))) (|has| (|Boolean|) (|SetCategory|)))) (($ $ (|Equation| (|Boolean|))) 50 (AND (|has| (|Boolean|) (|Evalable| (|Boolean|))) (|has| (|Boolean|) (|SetCategory|)))) (($ $ (|List| (|Equation| (|Boolean|)))) 49 (AND (|has| (|Boolean|) (|Evalable| (|Boolean|))) (|has| (|Boolean|) (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 31)) (|entry?| (((|Boolean|) (|Boolean|) $) 61 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Boolean|) (|SetCategory|))))) (|entries| (((|List| (|Boolean|)) $) 58)) (|empty?| (((|Boolean|) $) 34)) (|empty| (($) 33)) (|elt| (($ $ (|UniversalSegment| (|Integer|))) 83) (((|Boolean|) $ (|Integer|)) 57) (((|Boolean|) $ (|Integer|) (|Boolean|)) 56)) (|delete| (($ $ (|UniversalSegment| (|Integer|))) 85) (($ $ (|Integer|)) 84)) (|count| (((|NonNegativeInteger|) (|Boolean|) $) 47 (AND (|has| (|Boolean|) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|Boolean|)) $) 44 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copyInto!| (($ $ $ (|Integer|)) 99 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) 32)) (|convert| (((|InputForm|) $) 67 (|has| (|Boolean|) (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| (|Boolean|))) 76)) (|concat| (($ (|List| $)) 81) (($ $ $) 80) (($ (|Boolean|) $) 79) (($ $ (|Boolean|)) 78)) (|coerce| (((|OutputForm|) $) 11)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|Boolean|)) $) 42 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|and| (($ $ $) 26)) (^ (($ $) 29)) (|\\/| (($ $ $) 105)) (>= (((|Boolean|) $ $) 15)) (> (((|Boolean|) $ $) 16)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 14)) (< (((|Boolean|) $ $) 17)) (|/\\| (($ $ $) 104)) (|#| (((|NonNegativeInteger|) $) 39 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|BitAggregate|) (|Category|)) (T |BitAggregate|)) 
((|not| (*1 *1 *1) (|ofCategory| *1 (|BitAggregate|))) (^ (*1 *1 *1) (|ofCategory| *1 (|BitAggregate|))) (|nand| (*1 *1 *1 *1) (|ofCategory| *1 (|BitAggregate|))) (|nor| (*1 *1 *1 *1) (|ofCategory| *1 (|BitAggregate|))) (|and| (*1 *1 *1 *1) (|ofCategory| *1 (|BitAggregate|))) (|or| (*1 *1 *1 *1) (|ofCategory| *1 (|BitAggregate|))) (|xor| (*1 *1 *1 *1) (|ofCategory| *1 (|BitAggregate|)))) 
(|Join| (|OrderedSet|) (|Logic|) (|OneDimensionalArrayAggregate| (|Boolean|)) (CATEGORY |domain| (SIGNATURE |not| ($ $)) (SIGNATURE ^ ($ $)) (SIGNATURE |nand| ($ $ $)) (SIGNATURE |nor| ($ $ $)) (SIGNATURE |and| ($ $ $)) (SIGNATURE |or| ($ $ $)) (SIGNATURE |xor| ($ $ $)))) 
(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| (|Boolean|)) . T) ((|ConvertibleTo| (|InputForm|)) |has| (|Boolean|) (|ConvertibleTo| (|InputForm|))) ((|Eltable| (|Integer|) (|Boolean|)) . T) ((|EltableAggregate| (|Integer|) (|Boolean|)) . T) ((|Evalable| (|Boolean|)) AND (|has| (|Boolean|) (|Evalable| (|Boolean|))) (|has| (|Boolean|) (|SetCategory|))) ((|FiniteLinearAggregate| (|Boolean|)) . T) ((|HomogeneousAggregate| (|Boolean|)) . T) ((|IndexedAggregate| (|Integer|) (|Boolean|)) . T) ((|InnerEvalable| (|Boolean|) (|Boolean|)) AND (|has| (|Boolean|) (|Evalable| (|Boolean|))) (|has| (|Boolean|) (|SetCategory|))) ((|LinearAggregate| (|Boolean|)) . T) ((|Logic|) . T) ((|OneDimensionalArrayAggregate| (|Boolean|)) . T) ((|OrderedSet|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|map!| (($ (|Mapping| |#2| |#2|) $) 22)) (|copy| (($ $) 16)) (|#| (((|NonNegativeInteger|) $) 24))) 
(((|BinaryTreeCategory&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |map!| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |copy| (|#1| |#1|))) (|BinaryTreeCategory| |#2|) (|SetCategory|)) (T |BinaryTreeCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |map!| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |copy| (|#1| |#1|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) 45)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setvalue!| ((|#1| $ |#1|) 36 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setright!| (($ $ $) 49 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setleft!| (($ $ $) 51 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "left" $) 52 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "right" $) 50 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) 7 T CONST)) (|right| (($ $) 54)) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) 47)) (|node?| (((|Boolean|) $ $) 39 (|has| |#1| (|SetCategory|)))) (|node| (($ $ |#1| $) 57)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|left| (($ $) 56)) (|leaves| (((|List| |#1|) $) 42)) (|leaf?| (((|Boolean|) $) 46)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| ((|#1| $ "value") 44) (($ $ "left") 55) (($ $ "right") 53)) (|distance| (((|Integer|) $ $) 41)) (|cyclic?| (((|Boolean|) $) 43)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|children| (((|List| $) $) 48)) (|child?| (((|Boolean|) $ $) 40 (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|BinaryTreeCategory| |#1|) (|Category|) (|SetCategory|)) (T |BinaryTreeCategory|)) 
((|node| (*1 *1 *1 *2 *1) (AND (|ofCategory| *1 (|BinaryTreeCategory| *2)) (|ofCategory| *2 (|SetCategory|))))) 
(|Join| (|BinaryRecursiveAggregate| |t#1|) (CATEGORY |domain| (ATTRIBUTE |shallowlyMutable|) (ATTRIBUTE |finiteAggregate|) (SIGNATURE |node| ($ $ |t#1| $)))) 
(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|BinaryRecursiveAggregate| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) 15)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setvalue!| ((|#1| $ |#1|) 19 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setright!| (($ $ $) 20 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setleft!| (($ $ $) 18 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "left" $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "right" $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) NIL T CONST)) (|right| (($ $) 21)) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) NIL)) (|node?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|node| (($ $ |#1| $) NIL)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|left| (($ $) NIL)) (|leaves| (((|List| |#1|) $) NIL)) (|leaf?| (((|Boolean|) $) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|insert!| (($ |#1| $) 10)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) 14)) (|empty| (($) 8)) (|elt| ((|#1| $ "value") NIL) (($ $ "left") NIL) (($ $ "right") NIL)) (|distance| (((|Integer|) $ $) NIL)) (|cyclic?| (((|Boolean|) $) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) 17)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|)))) (|children| (((|List| $) $) NIL)) (|child?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|binaryTournament| (($ (|List| |#1|)) 12)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|BinaryTournament| |#1|) (|Join| (|BinaryTreeCategory| |#1|) (CATEGORY |domain| (ATTRIBUTE |shallowlyMutable|) (SIGNATURE |binaryTournament| ($ (|List| |#1|))) (SIGNATURE |insert!| ($ |#1| $)))) (|OrderedSet|)) (T |BinaryTournament|)) 
((|binaryTournament| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|BinaryTournament| *3)))) (|insert!| (*1 *1 *2 *1) (AND (|isDomain| *1 (|BinaryTournament| *2)) (|ofCategory| *2 (|OrderedSet|))))) 
(|Join| (|BinaryTreeCategory| |#1|) (CATEGORY |domain| (ATTRIBUTE |shallowlyMutable|) (SIGNATURE |binaryTournament| ($ (|List| |#1|))) (SIGNATURE |insert!| ($ |#1| $)))) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) 24)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setvalue!| ((|#1| $ |#1|) 26 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setright!| (($ $ $) 30 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setleft!| (($ $ $) 28 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "left" $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "right" $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) NIL T CONST)) (|right| (($ $) 20)) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) NIL)) (|node?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|node| (($ $ |#1| $) 15)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|left| (($ $) 19)) (|leaves| (((|List| |#1|) $) NIL)) (|leaf?| (((|Boolean|) $) 21)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) 18)) (|empty| (($) 11)) (|elt| ((|#1| $ "value") NIL) (($ $ "left") NIL) (($ $ "right") NIL)) (|distance| (((|Integer|) $ $) NIL)) (|cyclic?| (((|Boolean|) $) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|)))) (|children| (((|List| $) $) NIL)) (|child?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|binaryTree| (($ |#1|) 17) (($ $ |#1| $) 16)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 10 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|BinaryTree| |#1|) (|Join| (|BinaryTreeCategory| |#1|) (CATEGORY |domain| (SIGNATURE |binaryTree| ($ |#1|)) (SIGNATURE |binaryTree| ($ $ |#1| $)))) (|SetCategory|)) (T |BinaryTree|)) 
((|binaryTree| (*1 *1 *2) (AND (|isDomain| *1 (|BinaryTree| *2)) (|ofCategory| *2 (|SetCategory|)))) (|binaryTree| (*1 *1 *1 *2 *1) (AND (|isDomain| *1 (|BinaryTree| *2)) (|ofCategory| *2 (|SetCategory|))))) 
(|Join| (|BinaryTreeCategory| |#1|) (CATEGORY |domain| (SIGNATURE |binaryTree| ($ |#1|)) (SIGNATURE |binaryTree| ($ $ |#1| $)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (+ (($ $ $) 13)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14))) 
(((|CancellationAbelianMonoid|) (|Category|)) (T |CancellationAbelianMonoid|)) 
((|subtractIfCan| (*1 *1 *1 *1) (|partial| |ofCategory| *1 (|CancellationAbelianMonoid|)))) 
(|Join| (|AbelianMonoid|) (CATEGORY |domain| (SIGNATURE |subtractIfCan| ((|Union| $ "failed") $ $)))) 
(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) 7)) (|setPosition| (((|Void|) $ (|NonNegativeInteger|)) 18)) (|position| (((|NonNegativeInteger|) $) 19)) (|min| (($ $ $) 12)) (|max| (($ $ $) 13)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (>= (((|Boolean|) $ $) 15)) (> (((|Boolean|) $ $) 16)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 14)) (< (((|Boolean|) $ $) 17))) 
(((|CachableSet|) (|Category|)) (T |CachableSet|)) 
((|position| (*1 *2 *1) (AND (|ofCategory| *1 (|CachableSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|setPosition| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|CachableSet|)) (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Void|))))) 
(|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |position| ((|NonNegativeInteger|) $)) (SIGNATURE |setPosition| ((|Void|) $ (|NonNegativeInteger|))))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|OrderedSet|) . T) ((|SetCategory|) . T)) 
((|specialise| (((|List| (|SparseUnivariatePolynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|Cell| |#1|)) 33)) (|resultantSet| (((|List| (|Polynomial| |#1|)) (|List| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)))) 61)) (|projectionSet| (((|List| (|Polynomial| |#1|)) (|List| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)))) 32)) (|principalSubResultantSet| (((|List| (|Polynomial| |#1|)) (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|SparseUnivariatePolynomial| (|Polynomial| |#1|))) 60)) (|discriminantSet| (((|List| (|Polynomial| |#1|)) (|List| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)))) 57)) (|cylindricalDecomposition| (((|List| (|Cell| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) 16) (((|List| (|Cell| |#1|)) (|List| (|Polynomial| |#1|))) 17)) (|coefficientSet| (((|List| (|Polynomial| |#1|)) (|SparseUnivariatePolynomial| (|Polynomial| |#1|))) 45))) 
(((|CylindricalAlgebraicDecompositionPackage| |#1|) (CATEGORY |package| (SIGNATURE |cylindricalDecomposition| ((|List| (|Cell| |#1|)) (|List| (|Polynomial| |#1|)))) (SIGNATURE |cylindricalDecomposition| ((|List| (|Cell| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)))) (SIGNATURE |projectionSet| ((|List| (|Polynomial| |#1|)) (|List| (|SparseUnivariatePolynomial| (|Polynomial| |#1|))))) (SIGNATURE |coefficientSet| ((|List| (|Polynomial| |#1|)) (|SparseUnivariatePolynomial| (|Polynomial| |#1|)))) (SIGNATURE |discriminantSet| ((|List| (|Polynomial| |#1|)) (|List| (|SparseUnivariatePolynomial| (|Polynomial| |#1|))))) (SIGNATURE |resultantSet| ((|List| (|Polynomial| |#1|)) (|List| (|SparseUnivariatePolynomial| (|Polynomial| |#1|))))) (SIGNATURE |principalSubResultantSet| ((|List| (|Polynomial| |#1|)) (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|SparseUnivariatePolynomial| (|Polynomial| |#1|)))) (SIGNATURE |specialise| ((|List| (|SparseUnivariatePolynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|Cell| |#1|)))) (|RealClosedField|)) (T |CylindricalAlgebraicDecompositionPackage|)) 
((|specialise| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|Cell| *5)) (|ofCategory| *5 (|RealClosedField|)) (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *5))) (|isDomain| *1 (|CylindricalAlgebraicDecompositionPackage| *5)))) (|principalSubResultantSet| (*1 *2 *3 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| (|Polynomial| *4))) (|ofCategory| *4 (|RealClosedField|)) (|isDomain| *2 (|List| (|Polynomial| *4))) (|isDomain| *1 (|CylindricalAlgebraicDecompositionPackage| *4)))) (|resultantSet| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|SparseUnivariatePolynomial| (|Polynomial| *4)))) (|ofCategory| *4 (|RealClosedField|)) (|isDomain| *2 (|List| (|Polynomial| *4))) (|isDomain| *1 (|CylindricalAlgebraicDecompositionPackage| *4)))) (|discriminantSet| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|SparseUnivariatePolynomial| (|Polynomial| *4)))) (|ofCategory| *4 (|RealClosedField|)) (|isDomain| *2 (|List| (|Polynomial| *4))) (|isDomain| *1 (|CylindricalAlgebraicDecompositionPackage| *4)))) (|coefficientSet| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| (|Polynomial| *4))) (|ofCategory| *4 (|RealClosedField|)) (|isDomain| *2 (|List| (|Polynomial| *4))) (|isDomain| *1 (|CylindricalAlgebraicDecompositionPackage| *4)))) (|projectionSet| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|SparseUnivariatePolynomial| (|Polynomial| *4)))) (|ofCategory| *4 (|RealClosedField|)) (|isDomain| *2 (|List| (|Polynomial| *4))) (|isDomain| *1 (|CylindricalAlgebraicDecompositionPackage| *4)))) (|cylindricalDecomposition| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|RealClosedField|)) (|isDomain| *2 (|List| (|Cell| *5))) (|isDomain| *1 (|CylindricalAlgebraicDecompositionPackage| *5)))) (|cylindricalDecomposition| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Polynomial| *4))) (|ofCategory| *4 (|RealClosedField|)) (|isDomain| *2 (|List| (|Cell| *4))) (|isDomain| *1 (|CylindricalAlgebraicDecompositionPackage| *4))))) 
(CATEGORY |package| (SIGNATURE |cylindricalDecomposition| ((|List| (|Cell| |#1|)) (|List| (|Polynomial| |#1|)))) (SIGNATURE |cylindricalDecomposition| ((|List| (|Cell| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)))) (SIGNATURE |projectionSet| ((|List| (|Polynomial| |#1|)) (|List| (|SparseUnivariatePolynomial| (|Polynomial| |#1|))))) (SIGNATURE |coefficientSet| ((|List| (|Polynomial| |#1|)) (|SparseUnivariatePolynomial| (|Polynomial| |#1|)))) (SIGNATURE |discriminantSet| ((|List| (|Polynomial| |#1|)) (|List| (|SparseUnivariatePolynomial| (|Polynomial| |#1|))))) (SIGNATURE |resultantSet| ((|List| (|Polynomial| |#1|)) (|List| (|SparseUnivariatePolynomial| (|Polynomial| |#1|))))) (SIGNATURE |principalSubResultantSet| ((|List| (|Polynomial| |#1|)) (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|SparseUnivariatePolynomial| (|Polynomial| |#1|)))) (SIGNATURE |specialise| ((|List| (|SparseUnivariatePolynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|Cell| |#1|)))) 
((|squareFreeBasis| (((|List| |#2|) (|List| |#2|)) 13)) (|gcdBasisAdd| (((|List| |#2|) |#2| (|List| |#2|)) 19)) (|gcdBasis| (((|List| |#2|) (|List| |#2|)) 14))) 
(((|CylindricalAlgebraicDecompositionUtilities| |#1| |#2|) (CATEGORY |package| (SIGNATURE |squareFreeBasis| ((|List| |#2|) (|List| |#2|))) (SIGNATURE |gcdBasis| ((|List| |#2|) (|List| |#2|))) (SIGNATURE |gcdBasisAdd| ((|List| |#2|) |#2| (|List| |#2|)))) (|GcdDomain|) (|UnivariatePolynomialCategory| |#1|)) (T |CylindricalAlgebraicDecompositionUtilities|)) 
((|gcdBasisAdd| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|GcdDomain|)) (|isDomain| *1 (|CylindricalAlgebraicDecompositionUtilities| *4 *3)))) (|gcdBasis| (*1 *2 *2) (AND (|isDomain| *2 (|List| *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|GcdDomain|)) (|isDomain| *1 (|CylindricalAlgebraicDecompositionUtilities| *3 *4)))) (|squareFreeBasis| (*1 *2 *2) (AND (|isDomain| *2 (|List| *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|GcdDomain|)) (|isDomain| *1 (|CylindricalAlgebraicDecompositionUtilities| *3 *4))))) 
(CATEGORY |package| (SIGNATURE |squareFreeBasis| ((|List| |#2|) (|List| |#2|))) (SIGNATURE |gcdBasis| ((|List| |#2|) (|List| |#2|))) (SIGNATURE |gcdBasisAdd| ((|List| |#2|) |#2| (|List| |#2|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|NonNegativeInteger|) "failed") $) 38)) (|retract| (((|NonNegativeInteger|) $) 36)) (|recip| (((|Union| $ "failed") $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|min| (($ $ $) NIL)) (|max| (($ $ $) 26)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) 39)) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) 41)) (|finite?| (((|Boolean|) $) 23)) (|countable?| (((|Boolean|) $) 35)) (|coerce| (((|OutputForm|) $) 22) (($ (|NonNegativeInteger|)) 14)) (^ (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|PositiveInteger|)) NIL)) (|Zero| (($) 12 T CONST)) (|One| (($) 11 T CONST)) (|Aleph| (($ (|NonNegativeInteger|)) 15)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 24)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 25)) (- (((|Union| $ "failed") $ $) 29)) (+ (($ $ $) 27)) (** (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|PositiveInteger|)) NIL) (($ $ $) 34)) (* (($ (|NonNegativeInteger|) $) 32) (($ (|PositiveInteger|) $) NIL) (($ $ $) 30))) 
(((|CardinalNumber|) (|Join| (|OrderedSet|) (|AbelianMonoid|) (|Monoid|) (|RetractableTo| (|NonNegativeInteger|)) (CATEGORY |domain| (ATTRIBUTE (|commutative| "*")) (SIGNATURE - ((|Union| $ "failed") $ $)) (SIGNATURE ** ($ $ $)) (SIGNATURE |Aleph| ($ (|NonNegativeInteger|))) (SIGNATURE |finite?| ((|Boolean|) $)) (SIGNATURE |countable?| ((|Boolean|) $)) (SIGNATURE |generalizedContinuumHypothesisAssumed?| ((|Boolean|))) (SIGNATURE |generalizedContinuumHypothesisAssumed| ((|Boolean|) (|Boolean|)))))) (T |CardinalNumber|)) 
((- (*1 *1 *1 *1) (|partial| |isDomain| *1 (|CardinalNumber|))) (** (*1 *1 *1 *1) (|isDomain| *1 (|CardinalNumber|))) (|Aleph| (*1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|CardinalNumber|)))) (|finite?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|CardinalNumber|)))) (|countable?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|CardinalNumber|)))) (|generalizedContinuumHypothesisAssumed?| (*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|CardinalNumber|)))) (|generalizedContinuumHypothesisAssumed| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|CardinalNumber|))))) 
(|Join| (|OrderedSet|) (|AbelianMonoid|) (|Monoid|) (|RetractableTo| (|NonNegativeInteger|)) (CATEGORY |domain| (ATTRIBUTE (|commutative| "*")) (SIGNATURE - ((|Union| $ "failed") $ $)) (SIGNATURE ** ($ $ $)) (SIGNATURE |Aleph| ($ (|NonNegativeInteger|))) (SIGNATURE |finite?| ((|Boolean|) $)) (SIGNATURE |countable?| ((|Boolean|) $)) (SIGNATURE |generalizedContinuumHypothesisAssumed?| ((|Boolean|))) (SIGNATURE |generalizedContinuumHypothesisAssumed| ((|Boolean|) (|Boolean|))))) 
((|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) 14)) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) 18))) 
(((|CartesianTensorFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |reshape| ((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|))) (SIGNATURE |map| ((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)))) (|Integer|) (|NonNegativeInteger|) (|CommutativeRing|) (|CommutativeRing|)) (T |CartesianTensorFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *8 *7)) (|isDomain| *4 (|CartesianTensor| *5 *6 *7)) (|ofType| *5 (|Integer|)) (|ofType| *6 (|NonNegativeInteger|)) (|ofCategory| *7 (|CommutativeRing|)) (|ofCategory| *8 (|CommutativeRing|)) (|isDomain| *2 (|CartesianTensor| *5 *6 *8)) (|isDomain| *1 (|CartesianTensorFunctions2| *5 *6 *7 *8)))) (|reshape| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|CartesianTensor| *5 *6 *7)) (|ofType| *5 (|Integer|)) (|ofType| *6 (|NonNegativeInteger|)) (|ofCategory| *7 (|CommutativeRing|)) (|ofCategory| *8 (|CommutativeRing|)) (|isDomain| *2 (|CartesianTensor| *5 *6 *8)) (|isDomain| *1 (|CartesianTensorFunctions2| *5 *6 *7 *8))))) 
(CATEGORY |package| (SIGNATURE |reshape| ((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|))) (SIGNATURE |map| ((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)))) 
((~= (((|Boolean|) $ $) NIL)) (|unravel| (($ (|List| |#3|)) 38)) (|transpose| (($ $) 97) (($ $ (|Integer|) (|Integer|)) 96)) (|sample| (($) 17)) (|retractIfCan| (((|Union| |#3| "failed") $) 58)) (|retract| ((|#3| $) NIL)) (|reindex| (($ $ (|List| (|Integer|))) 98)) (|ravel| (((|List| |#3|) $) 34)) (|rank| (((|NonNegativeInteger|) $) 42)) (|product| (($ $ $) 91)) (|leviCivitaSymbol| (($) 41)) (|latex| (((|String|) $) NIL)) (|kroneckerDelta| (($) 16)) (|hash| (((|SingleInteger|) $) NIL)) (|elt| ((|#3| $) 44) ((|#3| $ (|Integer|)) 45) ((|#3| $ (|Integer|) (|Integer|)) 46) ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) 47) ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) 48) ((|#3| $ (|List| (|Integer|))) 50)) (|degree| (((|NonNegativeInteger|) $) 43)) (|contract| (($ $ (|Integer|) $ (|Integer|)) 92) (($ $ (|Integer|) (|Integer|)) 94)) (|coerce| (((|OutputForm|) $) 65) (($ |#3|) 66) (($ (|DirectProduct| |#2| |#3|)) 73) (($ (|SquareMatrix| |#2| |#3|)) 76) (($ (|List| |#3|)) 51) (($ (|List| $)) 56)) (|Zero| (($) 67 T CONST)) (|One| (($) 68 T CONST)) (= (((|Boolean|) $ $) 78)) (- (($ $) 84) (($ $ $) 82)) (+ (($ $ $) 80)) (* (($ |#3| $) 89) (($ $ |#3|) 90) (($ $ (|Integer|)) 87) (($ (|Integer|) $) 86) (($ $ $) 93))) 
(((|CartesianTensor| |#1| |#2| |#3|) (|Join| (|GradedAlgebra| |#3| (|NonNegativeInteger|)) (|GradedModule| (|Integer|) (|NonNegativeInteger|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|DirectProduct| |#2| |#3|))) (SIGNATURE |coerce| ($ (|SquareMatrix| |#2| |#3|))) (SIGNATURE |coerce| ($ (|List| |#3|))) (SIGNATURE |coerce| ($ (|List| $))) (SIGNATURE |rank| ((|NonNegativeInteger|) $)) (SIGNATURE |elt| (|#3| $)) (SIGNATURE |elt| (|#3| $ (|Integer|))) (SIGNATURE |elt| (|#3| $ (|Integer|) (|Integer|))) (SIGNATURE |elt| (|#3| $ (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |elt| (|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |elt| (|#3| $ (|List| (|Integer|)))) (SIGNATURE |product| ($ $ $)) (SIGNATURE * ($ $ $)) (SIGNATURE |contract| ($ $ (|Integer|) $ (|Integer|))) (SIGNATURE |contract| ($ $ (|Integer|) (|Integer|))) (SIGNATURE |transpose| ($ $)) (SIGNATURE |transpose| ($ $ (|Integer|) (|Integer|))) (SIGNATURE |reindex| ($ $ (|List| (|Integer|)))) (SIGNATURE |kroneckerDelta| ($)) (SIGNATURE |leviCivitaSymbol| ($)) (SIGNATURE |ravel| ((|List| |#3|) $)) (SIGNATURE |unravel| ($ (|List| |#3|))) (SIGNATURE |sample| ($)))) (|Integer|) (|NonNegativeInteger|) (|CommutativeRing|)) (T |CartesianTensor|)) 
((|product| (*1 *1 *1 *1) (AND (|isDomain| *1 (|CartesianTensor| *2 *3 *4)) (|ofType| *2 (|Integer|)) (|ofType| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|CommutativeRing|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|DirectProduct| *4 *5)) (|ofType| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|CommutativeRing|)) (|isDomain| *1 (|CartesianTensor| *3 *4 *5)) (|ofType| *3 (|Integer|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|SquareMatrix| *4 *5)) (|ofType| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|CommutativeRing|)) (|isDomain| *1 (|CartesianTensor| *3 *4 *5)) (|ofType| *3 (|Integer|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| *5)) (|ofCategory| *5 (|CommutativeRing|)) (|isDomain| *1 (|CartesianTensor| *3 *4 *5)) (|ofType| *3 (|Integer|)) (|ofType| *4 (|NonNegativeInteger|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|CartesianTensor| *3 *4 *5))) (|isDomain| *1 (|CartesianTensor| *3 *4 *5)) (|ofType| *3 (|Integer|)) (|ofType| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|CommutativeRing|)))) (|rank| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|CartesianTensor| *3 *4 *5)) (|ofType| *3 (|Integer|)) (|ofType| *4 *2) (|ofCategory| *5 (|CommutativeRing|)))) (|elt| (*1 *2 *1) (AND (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|CartesianTensor| *3 *4 *2)) (|ofType| *3 (|Integer|)) (|ofType| *4 (|NonNegativeInteger|)))) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|CartesianTensor| *4 *5 *2)) (|ofType| *4 *3) (|ofType| *5 (|NonNegativeInteger|)))) (|elt| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|CartesianTensor| *4 *5 *2)) (|ofType| *4 *3) (|ofType| *5 (|NonNegativeInteger|)))) (|elt| (*1 *2 *1 *3 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|CartesianTensor| *4 *5 *2)) (|ofType| *4 *3) (|ofType| *5 (|NonNegativeInteger|)))) (|elt| (*1 *2 *1 *3 *3 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|CartesianTensor| *4 *5 *2)) (|ofType| *4 *3) (|ofType| *5 (|NonNegativeInteger|)))) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|CartesianTensor| *4 *5 *2)) (|ofType| *4 (|Integer|)) (|ofType| *5 (|NonNegativeInteger|)))) (* (*1 *1 *1 *1) (AND (|isDomain| *1 (|CartesianTensor| *2 *3 *4)) (|ofType| *2 (|Integer|)) (|ofType| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|CommutativeRing|)))) (|contract| (*1 *1 *1 *2 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|CartesianTensor| *3 *4 *5)) (|ofType| *3 *2) (|ofType| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|CommutativeRing|)))) (|contract| (*1 *1 *1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|CartesianTensor| *3 *4 *5)) (|ofType| *3 *2) (|ofType| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|CommutativeRing|)))) (|transpose| (*1 *1 *1) (AND (|isDomain| *1 (|CartesianTensor| *2 *3 *4)) (|ofType| *2 (|Integer|)) (|ofType| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|CommutativeRing|)))) (|transpose| (*1 *1 *1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|CartesianTensor| *3 *4 *5)) (|ofType| *3 *2) (|ofType| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|CommutativeRing|)))) (|reindex| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|CartesianTensor| *3 *4 *5)) (|ofType| *3 (|Integer|)) (|ofType| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|CommutativeRing|)))) (|kroneckerDelta| (*1 *1) (AND (|isDomain| *1 (|CartesianTensor| *2 *3 *4)) (|ofType| *2 (|Integer|)) (|ofType| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|CommutativeRing|)))) (|leviCivitaSymbol| (*1 *1) (AND (|isDomain| *1 (|CartesianTensor| *2 *3 *4)) (|ofType| *2 (|Integer|)) (|ofType| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|CommutativeRing|)))) (|ravel| (*1 *2 *1) (AND (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|CartesianTensor| *3 *4 *5)) (|ofType| *3 (|Integer|)) (|ofType| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|CommutativeRing|)))) (|unravel| (*1 *1 *2) (AND (|isDomain| *2 (|List| *5)) (|ofCategory| *5 (|CommutativeRing|)) (|isDomain| *1 (|CartesianTensor| *3 *4 *5)) (|ofType| *3 (|Integer|)) (|ofType| *4 (|NonNegativeInteger|)))) (|sample| (*1 *1) (AND (|isDomain| *1 (|CartesianTensor| *2 *3 *4)) (|ofType| *2 (|Integer|)) (|ofType| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|CommutativeRing|))))) 
(|Join| (|GradedAlgebra| |#3| (|NonNegativeInteger|)) (|GradedModule| (|Integer|) (|NonNegativeInteger|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|DirectProduct| |#2| |#3|))) (SIGNATURE |coerce| ($ (|SquareMatrix| |#2| |#3|))) (SIGNATURE |coerce| ($ (|List| |#3|))) (SIGNATURE |coerce| ($ (|List| $))) (SIGNATURE |rank| ((|NonNegativeInteger|) $)) (SIGNATURE |elt| (|#3| $)) (SIGNATURE |elt| (|#3| $ (|Integer|))) (SIGNATURE |elt| (|#3| $ (|Integer|) (|Integer|))) (SIGNATURE |elt| (|#3| $ (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |elt| (|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |elt| (|#3| $ (|List| (|Integer|)))) (SIGNATURE |product| ($ $ $)) (SIGNATURE * ($ $ $)) (SIGNATURE |contract| ($ $ (|Integer|) $ (|Integer|))) (SIGNATURE |contract| ($ $ (|Integer|) (|Integer|))) (SIGNATURE |transpose| ($ $)) (SIGNATURE |transpose| ($ $ (|Integer|) (|Integer|))) (SIGNATURE |reindex| ($ $ (|List| (|Integer|)))) (SIGNATURE |kroneckerDelta| ($)) (SIGNATURE |leviCivitaSymbol| ($)) (SIGNATURE |ravel| ((|List| |#3|) $)) (SIGNATURE |unravel| ($ (|List| |#3|))) (SIGNATURE |sample| ($)))) 
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(((|CharacterClass|) (|Join| (|SetCategory|) (|ConvertibleTo| (|String|)) (|FiniteSetAggregate| (|Character|)) (|ConvertibleTo| (|List| (|Character|))) (CATEGORY |domain| (SIGNATURE |charClass| ($ (|String|))) (SIGNATURE |charClass| ($ (|List| (|Character|)))) (SIGNATURE |digit| ($) |constant|) (SIGNATURE |hexDigit| ($) |constant|) (SIGNATURE |upperCase| ($) |constant|) (SIGNATURE |lowerCase| ($) |constant|) (SIGNATURE |alphabetic| ($) |constant|) (SIGNATURE |alphanumeric| ($) |constant|)))) (T |CharacterClass|)) 
((|charClass| (*1 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|CharacterClass|)))) (|charClass| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Character|))) (|isDomain| *1 (|CharacterClass|)))) (|digit| (*1 *1) (|isDomain| *1 (|CharacterClass|))) (|hexDigit| (*1 *1) (|isDomain| *1 (|CharacterClass|))) (|upperCase| (*1 *1) (|isDomain| *1 (|CharacterClass|))) (|lowerCase| (*1 *1) (|isDomain| *1 (|CharacterClass|))) (|alphabetic| (*1 *1) (|isDomain| *1 (|CharacterClass|))) (|alphanumeric| (*1 *1) (|isDomain| *1 (|CharacterClass|)))) 
(|Join| (|SetCategory|) (|ConvertibleTo| (|String|)) (|FiniteSetAggregate| (|Character|)) (|ConvertibleTo| (|List| (|Character|))) (CATEGORY |domain| (SIGNATURE |charClass| ($ (|String|))) (SIGNATURE |charClass| ($ (|List| (|Character|)))) (SIGNATURE |digit| ($) |constant|) (SIGNATURE |hexDigit| ($) |constant|) (SIGNATURE |upperCase| ($) |constant|) (SIGNATURE |lowerCase| ($) |constant|) (SIGNATURE |alphabetic| ($) |constant|) (SIGNATURE |alphanumeric| ($) |constant|))) 
((|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) 17)) (|commonDenominator| ((|#1| |#3|) 9)) (|clearDenominator| ((|#3| |#3|) 15))) 
(((|CommonDenominator| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |commonDenominator| (|#1| |#3|)) (SIGNATURE |clearDenominator| (|#3| |#3|)) (SIGNATURE |splitDenominator| ((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|))) (|IntegralDomain|) (|QuotientFieldCategory| |#1|) (|FiniteLinearAggregate| |#2|)) (T |CommonDenominator|)) 
((|splitDenominator| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|QuotientFieldCategory| *4)) (|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| *4))) (|isDomain| *1 (|CommonDenominator| *4 *5 *3)) (|ofCategory| *3 (|FiniteLinearAggregate| *5)))) (|clearDenominator| (*1 *2 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|QuotientFieldCategory| *3)) (|isDomain| *1 (|CommonDenominator| *3 *4 *2)) (|ofCategory| *2 (|FiniteLinearAggregate| *4)))) (|commonDenominator| (*1 *2 *3) (AND (|ofCategory| *4 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|isDomain| *1 (|CommonDenominator| *2 *4 *3)) (|ofCategory| *3 (|FiniteLinearAggregate| *4))))) 
(CATEGORY |package| (SIGNATURE |commonDenominator| (|#1| |#3|)) (SIGNATURE |clearDenominator| (|#3| |#3|)) (SIGNATURE |splitDenominator| ((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|))) 
((~= (((|Boolean|) $ $) NIL (|has| (|Complex| (|DoubleFloat|)) (|SetCategory|)))) (|zero?| (((|Boolean|) $) NIL)) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) NIL)) (|vertConcat| (($ $ $) NIL)) (|transpose| (($ (|ComplexDoubleFloatVector|)) NIL) (($ $) NIL)) (|symmetric?| (((|Boolean|) $) NIL)) (|swapRows!| (($ $ (|Integer|) (|Integer|)) NIL)) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) NIL)) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) NIL)) (|squareTop| (($ $) NIL)) (|square?| (((|Boolean|) $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) NIL)) (|setelt| (((|Complex| (|DoubleFloat|)) $ (|Integer|) (|Integer|) (|Complex| (|DoubleFloat|))) NIL) (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) NIL)) (|setRow!| (($ $ (|Integer|) (|ComplexDoubleFloatVector|)) NIL)) (|setColumn!| (($ $ (|Integer|) (|ComplexDoubleFloatVector|)) NIL)) (|scalarMatrix| (($ (|NonNegativeInteger|) 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(((|ComplexDoubleFloatVector|) (|Join| (|VectorCategory| (|Complex| (|DoubleFloat|))) (CATEGORY |domain| (SIGNATURE |qnew| ($ (|Integer|))) (SIGNATURE |vector| ($ (|List| (|Complex| (|DoubleFloat|)))))))) (T |ComplexDoubleFloatVector|)) 
((|qnew| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|ComplexDoubleFloatVector|)))) (|vector| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Complex| (|DoubleFloat|)))) (|isDomain| *1 (|ComplexDoubleFloatVector|))))) 
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((|permutation| (($ $ $) 8)) (|factorial| (($ $) 7)) (|binomial| (($ $ $) 6))) 
(((|CombinatorialFunctionCategory|) (|Category|)) (T |CombinatorialFunctionCategory|)) 
((|permutation| (*1 *1 *1 *1) (|ofCategory| *1 (|CombinatorialFunctionCategory|))) (|factorial| (*1 *1 *1) (|ofCategory| *1 (|CombinatorialFunctionCategory|))) (|binomial| (*1 *1 *1 *1) (|ofCategory| *1 (|CombinatorialFunctionCategory|)))) 
(|Join| (CATEGORY |domain| (SIGNATURE |binomial| ($ $ $)) (SIGNATURE |factorial| ($ $)) (SIGNATURE |permutation| ($ $ $)))) 
((~= (((|Boolean|) $ $) NIL)) (|upperCase?| (((|Boolean|) $) 38)) (|upperCase| (($ $) 50)) (|space| (($) 25)) (|size| (((|NonNegativeInteger|)) 16)) (|random| (($) 24)) (|quote| (($) 26)) (|ord| (((|Integer|) $) 21)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|lowerCase?| (((|Boolean|) $) 40)) (|lowerCase| (($ $) 51)) (|lookup| (((|PositiveInteger|) $) 22)) (|latex| (((|String|) $) 46)) (|index| (($ (|PositiveInteger|)) 20)) (|hexDigit?| (((|Boolean|) $) 36)) (|hash| (((|SingleInteger|) $) NIL)) (|escape| (($) 27)) (|enumerate| (((|List| $)) NIL)) (|digit?| (((|Boolean|) $) 34)) (|coerce| (((|OutputForm|) $) 29)) (|char| (($ (|Integer|)) 18) (($ (|String|)) 49)) (|alphanumeric?| (((|Boolean|) $) 44)) (|alphabetic?| (((|Boolean|) $) 42)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 13)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 14))) 
(((|Character|) (|Join| (|OrderedFinite|) (CATEGORY |domain| (SIGNATURE |ord| ((|Integer|) $)) (SIGNATURE |char| ($ (|Integer|))) (SIGNATURE |char| ($ (|String|))) (SIGNATURE |space| ($)) (SIGNATURE |quote| ($)) (SIGNATURE |escape| ($)) (SIGNATURE |upperCase| ($ $)) (SIGNATURE |lowerCase| ($ $)) (SIGNATURE |digit?| ((|Boolean|) $)) (SIGNATURE |hexDigit?| ((|Boolean|) $)) (SIGNATURE |alphabetic?| ((|Boolean|) $)) (SIGNATURE |upperCase?| ((|Boolean|) $)) (SIGNATURE |lowerCase?| ((|Boolean|) $)) (SIGNATURE |alphanumeric?| ((|Boolean|) $))))) (T |Character|)) 
((|ord| (*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Character|)))) (|char| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Character|)))) (|char| (*1 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|Character|)))) (|space| (*1 *1) (|isDomain| *1 (|Character|))) (|quote| (*1 *1) (|isDomain| *1 (|Character|))) (|escape| (*1 *1) (|isDomain| *1 (|Character|))) (|upperCase| (*1 *1 *1) (|isDomain| *1 (|Character|))) (|lowerCase| (*1 *1 *1) (|isDomain| *1 (|Character|))) (|digit?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Character|)))) (|hexDigit?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Character|)))) (|alphabetic?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Character|)))) (|upperCase?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Character|)))) (|lowerCase?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Character|)))) (|alphanumeric?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Character|))))) 
(|Join| (|OrderedFinite|) (CATEGORY |domain| (SIGNATURE |ord| ((|Integer|) $)) (SIGNATURE |char| ($ (|Integer|))) (SIGNATURE |char| ($ (|String|))) (SIGNATURE |space| ($)) (SIGNATURE |quote| ($)) (SIGNATURE |escape| ($)) (SIGNATURE |upperCase| ($ $)) (SIGNATURE |lowerCase| ($ $)) (SIGNATURE |digit?| ((|Boolean|) $)) (SIGNATURE |hexDigit?| ((|Boolean|) $)) (SIGNATURE |alphabetic?| ((|Boolean|) $)) (SIGNATURE |upperCase?| ((|Boolean|) $)) (SIGNATURE |lowerCase?| ((|Boolean|) $)) (SIGNATURE |alphanumeric?| ((|Boolean|) $)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27)) (|charthRoot| (((|Union| $ "failed") $) 34)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|CharacteristicNonZero|) (|Category|)) (T |CharacteristicNonZero|)) 
((|charthRoot| (*1 *1 *1) (|partial| |ofCategory| *1 (|CharacteristicNonZero|)))) 
(|Join| (|Ring|) (CATEGORY |domain| (SIGNATURE |charthRoot| ((|Union| $ "failed") $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) 17))) 
(((|CharacteristicPolynomialPackage| |#1|) (CATEGORY |package| (SIGNATURE |characteristicPolynomial| (|#1| (|Matrix| |#1|) |#1|))) (|CommutativeRing|)) (T |CharacteristicPolynomialPackage|)) 
((|characteristicPolynomial| (*1 *2 *3 *2) (AND (|isDomain| *3 (|Matrix| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|CharacteristicPolynomialPackage| *2))))) 
(CATEGORY |package| (SIGNATURE |characteristicPolynomial| (|#1| (|Matrix| |#1|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|CharacteristicZero|) (|Category|)) (T |CharacteristicZero|)) 
NIL 
(|Join| (|Ring|)) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) 69)) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) 51)) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) 36)) (|goodPoint| ((|#1| |#3| |#3|) 39)) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) 19)) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) 48))) 
(((|ChangeOfVariable| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |mkIntegral| ((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|)) (SIGNATURE |radPoly| ((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|)) (SIGNATURE |rootPoly| ((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|))) (SIGNATURE |goodPoint| (|#1| |#3| |#3|)) (SIGNATURE |eval| (|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|))) (SIGNATURE |chvar| ((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|))) (|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|))) (T |ChangeOfVariable|)) 
((|chvar| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Record| (|:| |func| *3) (|:| |poly| *3) (|:| |c1| (|Fraction| *5)) (|:| |c2| (|Fraction| *5)) (|:| |deg| (|NonNegativeInteger|)))) (|isDomain| *1 (|ChangeOfVariable| *4 *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| *5))))) (|eval| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 (|Fraction| *5)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|ChangeOfVariable| *4 *5 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|goodPoint| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|UniqueFactorizationDomain|)) (|isDomain| *1 (|ChangeOfVariable| *2 *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|rootPoly| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| *6)) (|ofCategory| *5 (|UniqueFactorizationDomain|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| *3) (|:| |radicand| *6))) (|isDomain| *1 (|ChangeOfVariable| *5 *6 *7)) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *3)))) (|radPoly| (*1 *2 *3) (|partial| AND (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Record| (|:| |radicand| (|Fraction| *5)) (|:| |deg| (|NonNegativeInteger|)))) (|isDomain| *1 (|ChangeOfVariable| *4 *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| *5))))) (|mkIntegral| (*1 *2 *3) (AND (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Record| (|:| |coef| (|Fraction| *5)) (|:| |poly| *3))) (|isDomain| *1 (|ChangeOfVariable| *4 *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| *5)))))) 
(CATEGORY |package| (SIGNATURE |mkIntegral| ((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|)) (SIGNATURE |radPoly| ((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|)) (SIGNATURE |rootPoly| ((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|))) (SIGNATURE |goodPoint| (|#1| |#3| |#3|)) (SIGNATURE |eval| (|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|))) (SIGNATURE |chvar| ((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|))) 
((|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) 31))) 
(((|ComplexIntegerSolveLinearPolynomialEquation| |#1| |#2|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquation| ((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)))) (|IntegerNumberSystem|) (|ComplexCategory| |#1|)) (T |ComplexIntegerSolveLinearPolynomialEquation|)) 
((|solveLinearPolynomialEquation| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *5))) (|isDomain| *3 (|SparseUnivariatePolynomial| *5)) (|ofCategory| *5 (|ComplexCategory| *4)) (|ofCategory| *4 (|IntegerNumberSystem|)) (|isDomain| *1 (|ComplexIntegerSolveLinearPolynomialEquation| *4 *5))))) 
(CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquation| ((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)))) 
((|select| (($ (|Mapping| (|Boolean|) |#2|) $) 29)) (|removeDuplicates| (($ $) 36)) (|remove| (($ (|Mapping| (|Boolean|) |#2|) $) 27) (($ |#2| $) 32)) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $) 22) ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) 24) ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) 34)) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) 19)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 16)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) 13) (((|NonNegativeInteger|) |#2| $) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 15)) (|#| (((|NonNegativeInteger|) $) 11))) 
(((|Collection&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |removeDuplicates| (|#1| |#1|)) (SIGNATURE |remove| (|#1| |#2| |#1|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2| |#2|)) (SIGNATURE |select| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |remove| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1|)) (SIGNATURE |find| ((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) |#2| |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) |#1|))) (|Collection| |#2|) (|Type|)) (T |Collection&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |removeDuplicates| (|#1| |#1|)) (SIGNATURE |remove| (|#1| |#2| |#1|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2| |#2|)) (SIGNATURE |select| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |remove| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1|)) (SIGNATURE |find| ((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) |#2| |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) |#1|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 41 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) 7 T CONST)) (|removeDuplicates| (($ $) 38 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) 42 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ |#1| $) 39 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $) 44 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 43 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 40 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) 45)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|convert| (((|InputForm|) $) 37 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 46)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|Collection| |#1|) (|Category|) (|Type|)) (T |Collection|)) 
((|construct| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *1 (|Collection| *3)))) (|find| (*1 *2 *3 *1) (|partial| AND (|isDomain| *3 (|Mapping| (|Boolean|) *2)) (|ofCategory| *1 (|Collection| *2)) (|ofCategory| *2 (|Type|)))) (|reduce| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| *2 *2 *2)) (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|Collection| *2)) (|ofCategory| *2 (|Type|)))) (|reduce| (*1 *2 *3 *1 *2) (AND (|isDomain| *3 (|Mapping| *2 *2 *2)) (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|Collection| *2)) (|ofCategory| *2 (|Type|)))) (|remove| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|Collection| *3)) (|ofCategory| *3 (|Type|)))) (|select| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|Collection| *3)) (|ofCategory| *3 (|Type|)))) (|reduce| (*1 *2 *3 *1 *2 *2) (AND (|isDomain| *3 (|Mapping| *2 *2 *2)) (|ofCategory| *2 (|SetCategory|)) (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|Collection| *2)) (|ofCategory| *2 (|Type|)))) (|remove| (*1 *1 *2 *1) (AND (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|Collection| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|SetCategory|)))) (|removeDuplicates| (*1 *1 *1) (AND (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|Collection| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|SetCategory|))))) 
(|Join| (|HomogeneousAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |construct| ($ (|List| |t#1|))) (SIGNATURE |find| ((|Union| |t#1| "failed") (|Mapping| (|Boolean|) |t#1|) $)) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (PROGN (SIGNATURE |reduce| (|t#1| (|Mapping| |t#1| |t#1| |t#1|) $)) (SIGNATURE |reduce| (|t#1| (|Mapping| |t#1| |t#1| |t#1|) $ |t#1|)) (SIGNATURE |remove| ($ (|Mapping| (|Boolean|) |t#1|) $)) (SIGNATURE |select| ($ (|Mapping| (|Boolean|) |t#1|) $)) (IF (|has| |t#1| (|SetCategory|)) (PROGN (SIGNATURE |reduce| (|t#1| (|Mapping| |t#1| |t#1| |t#1|) $ |t#1| |t#1|)) (SIGNATURE |remove| ($ |t#1| $)) (SIGNATURE |removeDuplicates| ($ $))) |noBranch|)) |noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) 85)) (|one?| (((|Boolean|) $) NIL)) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) 56)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|e| (($ (|PositiveInteger|)) 48)) (|dimension| (((|CardinalNumber|)) 23)) (|coerce| (((|OutputForm|) $) 68) (($ (|Integer|)) 46) (($ |#2|) 47)) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) 58)) (|characteristic| (((|NonNegativeInteger|)) 20)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 40 T CONST)) (|One| (($) 44 T CONST)) (= (((|Boolean|) $ $) 26)) (/ (($ $ |#2|) NIL)) (- (($ $) 34) (($ $ $) 32)) (+ (($ $ $) 30)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 37) (($ $ $) 52) (($ |#2| $) 39) (($ $ |#2|) NIL))) 
(((|CliffordAlgebra| |#1| |#2| |#3|) (|Join| (|Ring|) (|Algebra| |#2|) (|VectorSpace| |#2|) (CATEGORY |domain| (SIGNATURE |e| ($ (|PositiveInteger|))) (SIGNATURE |monomial| ($ |#2| (|List| (|PositiveInteger|)))) (SIGNATURE |coefficient| (|#2| $ (|List| (|PositiveInteger|)))) (SIGNATURE |recip| ((|Union| $ "failed") $)))) (|PositiveInteger|) (|Field|) (|QuadraticForm| |#1| |#2|)) (T |CliffordAlgebra|)) 
((|recip| (*1 *1 *1) (|partial| AND (|isDomain| *1 (|CliffordAlgebra| *2 *3 *4)) (|ofType| *2 (|PositiveInteger|)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|QuadraticForm| *2 *3)))) (|e| (*1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|CliffordAlgebra| *3 *4 *5)) (|ofType| *3 *2) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|QuadraticForm| *3 *4)))) (|monomial| (*1 *1 *2 *3) (AND (|isDomain| *3 (|List| (|PositiveInteger|))) (|isDomain| *1 (|CliffordAlgebra| *4 *2 *5)) (|ofType| *4 (|PositiveInteger|)) (|ofCategory| *2 (|Field|)) (|ofType| *5 (|QuadraticForm| *4 *2)))) (|coefficient| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| (|PositiveInteger|))) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|CliffordAlgebra| *4 *2 *5)) (|ofType| *4 (|PositiveInteger|)) (|ofType| *5 (|QuadraticForm| *4 *2))))) 
(|Join| (|Ring|) (|Algebra| |#2|) (|VectorSpace| |#2|) (CATEGORY |domain| (SIGNATURE |e| ($ (|PositiveInteger|))) (SIGNATURE |monomial| ($ |#2| (|List| (|PositiveInteger|)))) (SIGNATURE |coefficient| (|#2| $ (|List| (|PositiveInteger|)))) (SIGNATURE |recip| ((|Union| $ "failed") $)))) 
((|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) 38)) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) 62) (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) 63)) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) 66) (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) 65) (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) 57) (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) 58))) 
(((|TwoDimensionalPlotClipping|) (CATEGORY |package| (SIGNATURE |clip| ((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|))) (SIGNATURE |clip| ((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|)))) (SIGNATURE |clipParametric| ((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|))) (SIGNATURE |clipParametric| ((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|)))) (SIGNATURE |clipWithRanges| ((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |clip| ((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|))))) (SIGNATURE |clip| ((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))))))) (T |TwoDimensionalPlotClipping|)) 
((|clip| (*1 *2 *3) (AND (|isDomain| *2 (|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|))))) (|isDomain| *1 (|TwoDimensionalPlotClipping|)) (|isDomain| *3 (|List| (|List| (|Point| (|DoubleFloat|))))))) (|clip| (*1 *2 *3) (AND (|isDomain| *2 (|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|))))) (|isDomain| *1 (|TwoDimensionalPlotClipping|)) (|isDomain| *3 (|List| (|Point| (|DoubleFloat|)))))) (|clipWithRanges| (*1 *2 *3 *4 *4 *4 *4) (AND (|isDomain| *4 (|DoubleFloat|)) (|isDomain| *2 (|Record| (|:| |brans| (|List| (|List| (|Point| *4)))) (|:| |xValues| (|Segment| *4)) (|:| |yValues| (|Segment| *4)))) (|isDomain| *1 (|TwoDimensionalPlotClipping|)) (|isDomain| *3 (|List| (|List| (|Point| *4)))))) (|clipParametric| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|Plot|)) (|isDomain| *4 (|Fraction| (|Integer|))) (|isDomain| *2 (|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|))))) (|isDomain| *1 (|TwoDimensionalPlotClipping|)))) (|clipParametric| (*1 *2 *3) (AND (|isDomain| *3 (|Plot|)) (|isDomain| *2 (|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|))))) (|isDomain| *1 (|TwoDimensionalPlotClipping|)))) (|clip| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|Plot|)) (|isDomain| *4 (|Fraction| (|Integer|))) (|isDomain| *2 (|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|))))) (|isDomain| *1 (|TwoDimensionalPlotClipping|)))) (|clip| (*1 *2 *3) (AND (|isDomain| *3 (|Plot|)) (|isDomain| *2 (|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|))))) (|isDomain| *1 (|TwoDimensionalPlotClipping|))))) 
(CATEGORY |package| (SIGNATURE |clip| ((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|))) (SIGNATURE |clip| ((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|)))) (SIGNATURE |clipParametric| ((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|))) (SIGNATURE |clipParametric| ((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|)))) (SIGNATURE |clipWithRanges| ((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |clip| ((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|))))) (SIGNATURE |clip| ((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))))) 
((|complexZeros| (((|List| (|Complex| |#2|)) |#1| |#2|) 45))) 
(((|ComplexRootPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |complexZeros| ((|List| (|Complex| |#2|)) |#1| |#2|))) (|UnivariatePolynomialCategory| (|Complex| (|Integer|))) (|Join| (|Field|) (|OrderedRing|))) (T |ComplexRootPackage|)) 
((|complexZeros| (*1 *2 *3 *4) (AND (|isDomain| *2 (|List| (|Complex| *4))) (|isDomain| *1 (|ComplexRootPackage| *3 *4)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| (|Integer|)))) (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))) 
(CATEGORY |package| (SIGNATURE |complexZeros| ((|List| (|Complex| |#2|)) |#1| |#2|))) 
((~= (((|Boolean|) $ $) NIL)) (|yellow| (($) 15)) (|red| (($) 14)) (|numberOfHues| (((|PositiveInteger|)) 22)) (|latex| (((|String|) $) NIL)) (|hue| (((|Integer|) $) 19)) (|hash| (((|SingleInteger|) $) NIL)) (|green| (($) 16)) (|color| (($ (|Integer|)) 23)) (|coerce| (((|OutputForm|) $) 29)) (|blue| (($) 17)) (= (((|Boolean|) $ $) 13)) (+ (($ $ $) 11)) (* (($ (|PositiveInteger|) $) 21) (($ (|DoubleFloat|) $) 8))) 
(((|Color|) (|Join| (|AbelianSemiGroup|) (CATEGORY |domain| (SIGNATURE * ($ (|PositiveInteger|) $)) (SIGNATURE * ($ (|DoubleFloat|) $)) (SIGNATURE + ($ $ $)) (SIGNATURE |red| ($)) (SIGNATURE |yellow| ($)) (SIGNATURE |green| ($)) (SIGNATURE |blue| ($)) (SIGNATURE |hue| ((|Integer|) $)) (SIGNATURE |numberOfHues| ((|PositiveInteger|))) (SIGNATURE |color| ($ (|Integer|)))))) (T |Color|)) 
((+ (*1 *1 *1 *1) (|isDomain| *1 (|Color|))) (* (*1 *1 *2 *1) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|Color|)))) (* (*1 *1 *2 *1) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|Color|)))) (|red| (*1 *1) (|isDomain| *1 (|Color|))) (|yellow| (*1 *1) (|isDomain| *1 (|Color|))) (|green| (*1 *1) (|isDomain| *1 (|Color|))) (|blue| (*1 *1) (|isDomain| *1 (|Color|))) (|hue| (*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Color|)))) (|numberOfHues| (*1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|Color|)))) (|color| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Color|))))) 
(|Join| (|AbelianSemiGroup|) (CATEGORY |domain| (SIGNATURE * ($ (|PositiveInteger|) $)) (SIGNATURE * ($ (|DoubleFloat|) $)) (SIGNATURE + ($ $ $)) (SIGNATURE |red| ($)) (SIGNATURE |yellow| ($)) (SIGNATURE |green| ($)) (SIGNATURE |blue| ($)) (SIGNATURE |hue| ((|Integer|) $)) (SIGNATURE |numberOfHues| ((|PositiveInteger|))) (SIGNATURE |color| ($ (|Integer|))))) 
((|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) 87) ((|#2| |#2| (|Symbol|)) 67)) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) 86) ((|#2| |#2| (|Symbol|)) 66)) (|permutation| ((|#2| |#2| |#2|) 27)) (|operator| (((|BasicOperator|) (|BasicOperator|)) 97)) (|ipow| ((|#2| (|List| |#2|)) 116)) (|iipow| ((|#2| (|List| |#2|)) 134)) (|iiperm| ((|#2| (|List| |#2|)) 124)) (|iifact| ((|#2| |#2|) 122)) (|iidsum| ((|#2| (|List| |#2|)) 109)) (|iidprod| ((|#2| (|List| |#2|)) 110)) (|iibinom| ((|#2| (|List| |#2|)) 132)) (|factorials| ((|#2| |#2| (|Symbol|)) 54) ((|#2| |#2|) 53)) (|factorial| ((|#2| |#2|) 23)) (|binomial| ((|#2| |#2| |#2|) 26)) (|belong?| (((|Boolean|) (|BasicOperator|)) 47)) (** ((|#2| |#2| |#2|) 38))) 
(((|CombinatorialFunction| |#1| |#2|) (CATEGORY |package| (SIGNATURE |belong?| ((|Boolean|) (|BasicOperator|))) (SIGNATURE |operator| ((|BasicOperator|) (|BasicOperator|))) (SIGNATURE ** (|#2| |#2| |#2|)) (SIGNATURE |binomial| (|#2| |#2| |#2|)) (SIGNATURE |permutation| (|#2| |#2| |#2|)) (SIGNATURE |factorial| (|#2| |#2|)) (SIGNATURE |factorials| (|#2| |#2|)) (SIGNATURE |factorials| (|#2| |#2| (|Symbol|))) (SIGNATURE |summation| (|#2| |#2| (|Symbol|))) (SIGNATURE |summation| (|#2| |#2| (|SegmentBinding| |#2|))) (SIGNATURE |product| (|#2| |#2| (|Symbol|))) (SIGNATURE |product| (|#2| |#2| (|SegmentBinding| |#2|))) (SIGNATURE |iifact| (|#2| |#2|)) (SIGNATURE |iibinom| (|#2| (|List| |#2|))) (SIGNATURE |iiperm| (|#2| (|List| |#2|))) (SIGNATURE |iipow| (|#2| (|List| |#2|))) (SIGNATURE |iidsum| (|#2| (|List| |#2|))) (SIGNATURE |iidprod| (|#2| (|List| |#2|))) (SIGNATURE |ipow| (|#2| (|List| |#2|)))) (|Join| (|OrderedSet|) (|IntegralDomain|)) (|FunctionSpace| |#1|)) (T |CombinatorialFunction|)) 
((|ipow| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4)) (|isDomain| *1 (|CombinatorialFunction| *4 *2)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|iidprod| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4)) (|isDomain| *1 (|CombinatorialFunction| *4 *2)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|iidsum| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4)) (|isDomain| *1 (|CombinatorialFunction| *4 *2)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|iipow| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4)) (|isDomain| *1 (|CombinatorialFunction| *4 *2)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|iiperm| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4)) (|isDomain| *1 (|CombinatorialFunction| *4 *2)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|iibinom| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4)) (|isDomain| *1 (|CombinatorialFunction| *4 *2)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|iifact| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|CombinatorialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|product| (*1 *2 *2 *3) (AND (|isDomain| *3 (|SegmentBinding| *2)) (|ofCategory| *2 (|FunctionSpace| *4)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|CombinatorialFunction| *4 *2)))) (|product| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|CombinatorialFunction| *4 *2)) (|ofCategory| *2 (|FunctionSpace| *4)))) (|summation| (*1 *2 *2 *3) (AND (|isDomain| *3 (|SegmentBinding| *2)) (|ofCategory| *2 (|FunctionSpace| *4)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|CombinatorialFunction| *4 *2)))) (|summation| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|CombinatorialFunction| *4 *2)) (|ofCategory| *2 (|FunctionSpace| *4)))) (|factorials| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|CombinatorialFunction| *4 *2)) (|ofCategory| *2 (|FunctionSpace| *4)))) (|factorials| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|CombinatorialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|factorial| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|CombinatorialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|permutation| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|CombinatorialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|binomial| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|CombinatorialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (** (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|CombinatorialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|operator| (*1 *2 *2) (AND (|isDomain| *2 (|BasicOperator|)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|CombinatorialFunction| *3 *4)) (|ofCategory| *4 (|FunctionSpace| *3)))) (|belong?| (*1 *2 *3) (AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|CombinatorialFunction| *4 *5)) (|ofCategory| *5 (|FunctionSpace| *4))))) 
(CATEGORY |package| (SIGNATURE |belong?| ((|Boolean|) (|BasicOperator|))) (SIGNATURE |operator| ((|BasicOperator|) (|BasicOperator|))) (SIGNATURE ** (|#2| |#2| |#2|)) (SIGNATURE |binomial| (|#2| |#2| |#2|)) (SIGNATURE |permutation| (|#2| |#2| |#2|)) (SIGNATURE |factorial| (|#2| |#2|)) (SIGNATURE |factorials| (|#2| |#2|)) (SIGNATURE |factorials| (|#2| |#2| (|Symbol|))) (SIGNATURE |summation| (|#2| |#2| (|Symbol|))) (SIGNATURE |summation| (|#2| |#2| (|SegmentBinding| |#2|))) (SIGNATURE |product| (|#2| |#2| (|Symbol|))) (SIGNATURE |product| (|#2| |#2| (|SegmentBinding| |#2|))) (SIGNATURE |iifact| (|#2| |#2|)) (SIGNATURE |iibinom| (|#2| (|List| |#2|))) (SIGNATURE |iiperm| (|#2| (|List| |#2|))) (SIGNATURE |iipow| (|#2| (|List| |#2|))) (SIGNATURE |iidsum| (|#2| (|List| |#2|))) (SIGNATURE |iidprod| (|#2| (|List| |#2|))) (SIGNATURE |ipow| (|#2| (|List| |#2|)))) 
((|stirling2| ((|#1| |#1| |#1|) 52)) (|stirling1| ((|#1| |#1| |#1|) 49)) (|permutation| ((|#1| |#1| |#1|) 43)) (|partition| ((|#1| |#1|) 34)) (|multinomial| ((|#1| |#1| (|List| |#1|)) 42)) (|factorial| ((|#1| |#1|) 36)) (|binomial| ((|#1| |#1| |#1|) 39))) 
(((|IntegerCombinatoricFunctions| |#1|) (CATEGORY |package| (SIGNATURE |binomial| (|#1| |#1| |#1|)) (SIGNATURE |factorial| (|#1| |#1|)) (SIGNATURE |multinomial| (|#1| |#1| (|List| |#1|))) (SIGNATURE |partition| (|#1| |#1|)) (SIGNATURE |permutation| (|#1| |#1| |#1|)) (SIGNATURE |stirling1| (|#1| |#1| |#1|)) (SIGNATURE |stirling2| (|#1| |#1| |#1|))) (|IntegerNumberSystem|)) (T |IntegerCombinatoricFunctions|)) 
((|stirling2| (*1 *2 *2 *2) (AND (|isDomain| *1 (|IntegerCombinatoricFunctions| *2)) (|ofCategory| *2 (|IntegerNumberSystem|)))) (|stirling1| (*1 *2 *2 *2) (AND (|isDomain| *1 (|IntegerCombinatoricFunctions| *2)) (|ofCategory| *2 (|IntegerNumberSystem|)))) (|permutation| (*1 *2 *2 *2) (AND (|isDomain| *1 (|IntegerCombinatoricFunctions| *2)) (|ofCategory| *2 (|IntegerNumberSystem|)))) (|partition| (*1 *2 *2) (AND (|isDomain| *1 (|IntegerCombinatoricFunctions| *2)) (|ofCategory| *2 (|IntegerNumberSystem|)))) (|multinomial| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|IntegerNumberSystem|)) (|isDomain| *1 (|IntegerCombinatoricFunctions| *2)))) (|factorial| (*1 *2 *2) (AND (|isDomain| *1 (|IntegerCombinatoricFunctions| *2)) (|ofCategory| *2 (|IntegerNumberSystem|)))) (|binomial| (*1 *2 *2 *2) (AND (|isDomain| *1 (|IntegerCombinatoricFunctions| *2)) (|ofCategory| *2 (|IntegerNumberSystem|))))) 
(CATEGORY |package| (SIGNATURE |binomial| (|#1| |#1| |#1|)) (SIGNATURE |factorial| (|#1| |#1|)) (SIGNATURE |multinomial| (|#1| |#1| (|List| |#1|))) (SIGNATURE |partition| (|#1| |#1|)) (SIGNATURE |permutation| (|#1| |#1| |#1|)) (SIGNATURE |stirling1| (|#1| |#1| |#1|)) (SIGNATURE |stirling2| (|#1| |#1| |#1|))) 
((|summation| (($ $ (|Symbol|)) 12) (($ $ (|SegmentBinding| $)) 11)) (|product| (($ $ (|Symbol|)) 10) (($ $ (|SegmentBinding| $)) 9)) (|permutation| (($ $ $) 8)) (|factorials| (($ $) 14) (($ $ (|Symbol|)) 13)) (|factorial| (($ $) 7)) (|binomial| (($ $ $) 6))) 
(((|CombinatorialOpsCategory|) (|Category|)) (T |CombinatorialOpsCategory|)) 
((|factorials| (*1 *1 *1) (|ofCategory| *1 (|CombinatorialOpsCategory|))) (|factorials| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|CombinatorialOpsCategory|)) (|isDomain| *2 (|Symbol|)))) (|summation| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|CombinatorialOpsCategory|)) (|isDomain| *2 (|Symbol|)))) (|summation| (*1 *1 *1 *2) (AND (|isDomain| *2 (|SegmentBinding| *1)) (|ofCategory| *1 (|CombinatorialOpsCategory|)))) (|product| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|CombinatorialOpsCategory|)) (|isDomain| *2 (|Symbol|)))) (|product| (*1 *1 *1 *2) (AND (|isDomain| *2 (|SegmentBinding| *1)) (|ofCategory| *1 (|CombinatorialOpsCategory|))))) 
(|Join| (|CombinatorialFunctionCategory|) (CATEGORY |domain| (SIGNATURE |factorials| ($ $)) (SIGNATURE |factorials| ($ $ (|Symbol|))) (SIGNATURE |summation| ($ $ (|Symbol|))) (SIGNATURE |summation| ($ $ (|SegmentBinding| $))) (SIGNATURE |product| ($ $ (|Symbol|))) (SIGNATURE |product| ($ $ (|SegmentBinding| $))))) 
(((|CombinatorialFunctionCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|mkcomm| (($ (|Integer|)) 13) (($ $ $) 14)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 17)) (= (((|Boolean|) $ $) 9))) 
(((|Commutator|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |mkcomm| ($ (|Integer|))) (SIGNATURE |mkcomm| ($ $ $))))) (T |Commutator|)) 
((|mkcomm| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Commutator|)))) (|mkcomm| (*1 *1 *1 *1) (|isDomain| *1 (|Commutator|)))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |mkcomm| ($ (|Integer|))) (SIGNATURE |mkcomm| ($ $ $)))) 
((|operator| (((|BasicOperator|) (|Symbol|)) 99))) 
(((|CommonOperators|) (CATEGORY |package| (SIGNATURE |operator| ((|BasicOperator|) (|Symbol|))))) (T |CommonOperators|)) 
((|operator| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|BasicOperator|)) (|isDomain| *1 (|CommonOperators|))))) 
(CATEGORY |package| (SIGNATURE |operator| ((|BasicOperator|) (|Symbol|)))) 
((|swap| ((|#3| |#3|) 19))) 
(((|CommuteUnivariatePolynomialCategory| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |swap| (|#3| |#3|))) (|Ring|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| |#2|)) (T |CommuteUnivariatePolynomialCategory|)) 
((|swap| (*1 *2 *2) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *1 (|CommuteUnivariatePolynomialCategory| *3 *4 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |swap| (|#3| |#3|))) 
((~= (((|Boolean|) $ $) 7)) (|smaller?| (((|Boolean|) $ $) 12)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (= (((|Boolean|) $ $) 6))) 
(((|Comparable|) (|Category|)) (T |Comparable|)) 
((|smaller?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|Comparable|)) (|isDomain| *2 (|Boolean|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |smaller?| ((|Boolean|) $ $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 215)) (|trace| ((|#2| $) 95)) (|tanh| (($ $) 242)) (|tan| (($ $) 236)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 39)) (|sinh| (($ $) 240)) (|sin| (($ $) 234)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL) (((|Union| |#2| "failed") $) 139)) (|retract| (((|Integer|) $) NIL) (((|Fraction| (|Integer|)) $) NIL) ((|#2| $) 137)) (|rem| (($ $ $) 220)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| $) (|Vector| $)) 153) (((|Matrix| |#2|) (|Matrix| $)) 147)) (|reduce| (($ (|SparseUnivariatePolynomial| |#2|)) 118) (((|Union| $ "failed") (|Fraction| (|SparseUnivariatePolynomial| |#2|))) NIL)) (|recip| (((|Union| $ "failed") $) 207)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 197)) (|rational?| (((|Boolean|) $) 192)) (|rational| (((|Fraction| (|Integer|)) $) 195)) (|rank| (((|PositiveInteger|)) 88)) (|quo| (($ $ $) 222)) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) 258)) (|pi| (($) 231)) (|patternMatch| (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) 184) (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) 189)) (|norm| ((|#2| $) 93)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) 120)) (|map| (($ (|Mapping| |#2| |#2|) $) 101)) (|log| (($ $) 233)) (|lift| (((|SparseUnivariatePolynomial| |#2|) $) 119)) (|inv| (($ $) 200)) (|imaginary| (($) 96)) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 87)) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 56)) (|exquo| (((|Union| $ "failed") $ |#2|) 202) (((|Union| $ "failed") $ $) 205)) (|exp| (($ $) 232)) (|euclideanSize| (((|NonNegativeInteger|) $) 217)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 226)) (|discriminant| ((|#2| (|Vector| $)) NIL) ((|#2|) 90)) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#2| |#2|)) 112) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|))) NIL) (($ $ (|Symbol|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) 113)) (|cosh| (($ $) 241)) (|cos| (($ $) 235)) (|coordinates| (((|Vector| |#2|) $ (|Vector| $)) 126) (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) NIL) (((|Vector| |#2|) $) 109) (((|Matrix| |#2|) (|Vector| $)) NIL)) (|convert| (((|Vector| |#2|) $) NIL) (($ (|Vector| |#2|)) NIL) (((|SparseUnivariatePolynomial| |#2|) $) NIL) (($ (|SparseUnivariatePolynomial| |#2|)) NIL) (((|Pattern| (|Integer|)) $) 175) (((|Pattern| (|Float|)) $) 179) (((|Complex| (|Float|)) $) 165) (((|Complex| (|DoubleFloat|)) $) 160) (((|InputForm|) $) 171)) (|conjugate| (($ $) 97)) (|coerce| (((|OutputForm|) $) 136) (($ (|Integer|)) NIL) (($ |#2|) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ $) NIL)) (|characteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) 23)) (|characteristic| (((|NonNegativeInteger|)) 99)) (|atanh| (($ $) 245)) (|atan| (($ $) 239)) (|asinh| (($ $) 243)) (|asin| (($ $) 237)) (|argument| ((|#2| $) 230)) (|acosh| (($ $) 244)) (|acos| (($ $) 238)) (|abs| (($ $) 155)) (= (((|Boolean|) $ $) 103)) (< (((|Boolean|) $ $) 191)) (- (($ $) 105) (($ $ $) NIL)) (+ (($ $ $) 104)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Fraction| (|Integer|))) 264) (($ $ $) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 111) (($ $ $) 140) (($ $ |#2|) NIL) (($ |#2| $) 107) (($ (|Fraction| (|Integer|)) $) NIL) (($ $ (|Fraction| (|Integer|))) NIL))) 
(((|ComplexCategory&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |coerce| (|#1| |#1|)) (SIGNATURE |exquo| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE |unitNormal| ((|Record| (|:| |unit| |#1|) (|:| |canonical| |#1|) (|:| |associate| |#1|)) |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |euclideanSize| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |divide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |quo| (|#1| |#1| |#1|)) (SIGNATURE |rem| (|#1| |#1| |#1|)) (SIGNATURE |inv| (|#1| |#1|)) (SIGNATURE ** (|#1| |#1| (|Integer|))) (SIGNATURE * (|#1| |#1| (|Fraction| (|Integer|)))) (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |convert| ((|Complex| (|DoubleFloat|)) |#1|)) (SIGNATURE |convert| ((|Complex| (|Float|)) |#1|)) (SIGNATURE |tan| (|#1| |#1|)) (SIGNATURE |sin| (|#1| |#1|)) (SIGNATURE |cos| (|#1| |#1|)) (SIGNATURE |acos| (|#1| |#1|)) (SIGNATURE |asin| (|#1| |#1|)) (SIGNATURE |atan| (|#1| |#1|)) (SIGNATURE |cosh| (|#1| |#1|)) (SIGNATURE |sinh| (|#1| |#1|)) (SIGNATURE |tanh| (|#1| |#1|)) (SIGNATURE |acosh| (|#1| |#1|)) (SIGNATURE |asinh| (|#1| |#1|)) (SIGNATURE |atanh| (|#1| |#1|)) (SIGNATURE |log| (|#1| |#1|)) (SIGNATURE |exp| (|#1| |#1|)) (SIGNATURE ** (|#1| |#1| |#1|)) (SIGNATURE |pi| (|#1|)) (SIGNATURE ** (|#1| |#1| (|Fraction| (|Integer|)))) (SIGNATURE |factorPolynomial| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |factorSquareFreePolynomial| ((|Factored| 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119) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 127 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 128 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) 129 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|)) 130 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|NonNegativeInteger|)) 132 (OR (|and| (|has| |#1| (|Field|)) (|has| |#1| (|DifferentialRing|))) (|has| |#1| (|DifferentialRing|)) (|and| (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|))))) (($ $) 134 (OR (|and| (|has| |#1| (|Field|)) (|has| |#1| (|DifferentialRing|))) (|has| |#1| (|DifferentialRing|)) (|and| (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|)))))) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) 151 (|has| |#1| (|Field|)))) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) 156)) (|csch| (($ $) 212 (|has| |#1| 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(|Symbol|)))) (($ $ (|NonNegativeInteger|)) 131 (OR (|and| (|has| |#1| (|Field|)) (|has| |#1| (|DifferentialRing|))) (|has| |#1| (|DifferentialRing|)) (|and| (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|))))) (($ $) 133 (OR (|and| (|has| |#1| (|Field|)) (|has| |#1| (|DifferentialRing|))) (|has| |#1| (|DifferentialRing|)) (|and| (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|)))))) (>= (((|Boolean|) $ $) 191 (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) 190 (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 192 (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) 189 (|has| |#1| (|OrderedSet|)))) (/ (($ $ $) 118 (|has| |#1| (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Fraction| (|Integer|))) 226 (AND (|has| |#1| (|RadicalCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|)))) (($ $ $) 224 (|has| |#1| (|TranscendentalFunctionCategory|))) (($ $ (|Integer|)) 115 (|has| |#1| (|Field|)))) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 38) (($ |#1| $) 37) (($ (|Fraction| (|Integer|)) $) 117 (|has| |#1| (|Field|))) (($ $ (|Fraction| (|Integer|))) 116 (|has| |#1| (|Field|))))) 
(((|ComplexCategory| |#1|) (|Category|) (|CommutativeRing|)) (T |ComplexCategory|)) 
((|norm| (*1 *2 *1) (AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imaginary| (*1 *1) (AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|conjugate| (*1 *1 *1) (AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|complex| (*1 *1 *2 *2) (AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imag| (*1 *2 *1) (AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|real| (*1 *2 *1) (AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|exquo| (*1 *1 *1 *2) (|partial| AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|IntegralDomain|)))) (|abs| (*1 *1 *1) (AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|RealNumberSystem|)))) (|argument| (*1 *2 *1) (AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|polarCoordinates| (*1 *2 *1) (AND (|ofCategory| *1 (|ComplexCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|RealNumberSystem|)) (|ofCategory| *3 (|TranscendentalFunctionCategory|)) (|isDomain| *2 (|Record| (|:| |r| *3) (|:| |phi| *3))))) (|rational?| (*1 *2 *1) (AND (|ofCategory| *1 (|ComplexCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|)))) (|rational| (*1 *2 *1) (AND (|ofCategory| *1 (|ComplexCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|rationalIfCan| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|ComplexCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Fraction| (|Integer|)))))) 
(|Join| (|MonogenicAlgebra| |t#1| (|SparseUnivariatePolynomial| |t#1|)) (|FullyRetractableTo| |t#1|) (|DifferentialExtension| |t#1|) (|FullyEvalableOver| |t#1|) (|FullyPatternMatchable| |t#1|) (|Patternable| |t#1|) (|FullyLinearlyExplicitRingOver| |t#1|) (|CommutativeRing|) (CATEGORY |domain| (ATTRIBUTE |complex|) (SIGNATURE |imaginary| ($)) (SIGNATURE |conjugate| ($ $)) (SIGNATURE |complex| ($ |t#1| |t#1|)) (SIGNATURE |imag| (|t#1| $)) (SIGNATURE |real| (|t#1| $)) (SIGNATURE |norm| (|t#1| $)) (IF (|has| |t#1| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (ATTRIBUTE (|IntegralDomain|)) (SIGNATURE |exquo| ((|Union| $ "failed") $ |t#1|))) |noBranch|) (IF (|has| |t#1| (|EuclideanDomain|)) (ATTRIBUTE (|EuclideanDomain|)) |noBranch|) (IF (|has| |t#1| (ATTRIBUTE |multiplicativeValuation|)) (ATTRIBUTE |multiplicativeValuation|) |noBranch|) (IF (|has| |t#1| (ATTRIBUTE |additiveValuation|)) (ATTRIBUTE |additiveValuation|) |noBranch|) (IF (|has| |t#1| (|Field|)) (ATTRIBUTE (|Field|)) |noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |noBranch|) (IF (|has| |t#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |noBranch|) (IF (|has| |t#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |noBranch|) (IF (|has| |t#1| (|RealConstant|)) (PROGN (ATTRIBUTE (|ConvertibleTo| (|Complex| (|DoubleFloat|)))) (ATTRIBUTE (|ConvertibleTo| (|Complex| (|Float|))))) |noBranch|) (IF (|has| |t#1| (|RealNumberSystem|)) (SIGNATURE |abs| ($ $)) |noBranch|) (IF (|has| |t#1| (|TranscendentalFunctionCategory|)) (PROGN (ATTRIBUTE (|TranscendentalFunctionCategory|)) (SIGNATURE |argument| (|t#1| $)) (IF (|has| |t#1| (|RadicalCategory|)) (ATTRIBUTE (|RadicalCategory|)) |noBranch|) (IF (|has| |t#1| (|RealNumberSystem|)) (SIGNATURE |polarCoordinates| ((|Record| (|:| |r| |t#1|) (|:| |phi| |t#1|)) $)) |noBranch|)) |noBranch|) (IF (|has| |t#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") $))) |noBranch|) (IF (|has| |t#1| (|PolynomialFactorizationExplicit|)) (IF (|has| |t#1| (|EuclideanDomain|)) (ATTRIBUTE (|PolynomialFactorizationExplicit|)) |noBranch|) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|Algebra| |#1|) . T) ((|Algebra| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|CharacteristicNonZero|))) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|Complex| (|DoubleFloat|))) |has| |#1| (|RealConstant|)) ((|ConvertibleTo| (|Complex| (|Float|))) |has| |#1| (|RealConstant|)) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|ConvertibleTo| (|Pattern| (|Float|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) ((|ConvertibleTo| (|Pattern| (|Integer|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) ((|ConvertibleTo| (|SparseUnivariatePolynomial| |#1|)) . T) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|DifferentialRing|))) ((|DivisionRing|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|ElementaryFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|Eltable| |#1| $) |has| |#1| (|Eltable| |#1| |#1|)) ((|EntireRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|EuclideanDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|Evalable| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Field|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|FieldOfPrimeCharacteristic|) |has| |#1| (|FiniteFieldCategory|)) ((|Finite|) OR (|has| |#1| (|Finite|)) (|has| |#1| (|FiniteFieldCategory|))) ((|FiniteFieldCategory|) |has| |#1| (|FiniteFieldCategory|)) ((|FiniteRankAlgebra| |#1| (|SparseUnivariatePolynomial| |#1|)) . T) ((|FramedAlgebra| |#1| (|SparseUnivariatePolynomial| |#1|)) . T) ((|FullyEvalableOver| |#1|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyPatternMatchable| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|GcdDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|HyperbolicFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|InnerEvalable| (|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|IntegralDomain|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|LeftModule| (|Fraction| (|Integer|))) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|LinearlyExplicitRingOver| (|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| (|Fraction| (|Integer|))) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|Module| |#1|) . T) ((|Module| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|MonogenicAlgebra| |#1| (|SparseUnivariatePolynomial| |#1|)) . T) ((|Monoid|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PatternMatchable| (|Float|)) |has| |#1| (|PatternMatchable| (|Float|))) ((|PatternMatchable| (|Integer|)) |has| |#1| (|PatternMatchable| (|Integer|))) ((|Patternable| |#1|) . T) ((|PolynomialFactorizationExplicit|) AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) ((|PrincipalIdealDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|RadicalCategory|) AND (|has| |#1| (|RadicalCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightModule| (|Fraction| (|Integer|))) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|FiniteFieldCategory|)) ((|TranscendentalFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|TrigonometricFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))))) 
((|factor| (((|Factored| |#2|) |#2|) 63))) 
(((|ComplexFactorization| |#1| |#2|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#2|) |#2|))) (|EuclideanDomain|) (|UnivariatePolynomialCategory| (|Complex| |#1|))) (T |ComplexFactorization|)) 
((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|EuclideanDomain|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|ComplexFactorization| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4)))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#2|) |#2|))) 
((|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) 14))) 
(((|ComplexFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)))) (|CommutativeRing|) (|CommutativeRing|)) (T |ComplexFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Complex| *5)) (|ofCategory| *5 (|CommutativeRing|)) (|ofCategory| *6 (|CommutativeRing|)) (|isDomain| *2 (|Complex| *6)) (|isDomain| *1 (|ComplexFunctions2| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |map| ((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 33)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (OR (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))))) (|unitCanonical| (($ $) NIL (OR (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))))) (|unit?| (((|Boolean|) $) NIL (OR (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))))) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) NIL) (((|Matrix| |#1|)) NIL)) (|trace| ((|#1| $) NIL)) (|tanh| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|tan| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))))) (|squareFreePart| (($ $) NIL (OR (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|Field|))))) (|squareFree| (((|Factored| $) $) NIL (OR (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|Field|))))) (|sqrt| (($ $) NIL (AND (|has| |#1| (|RadicalCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))))) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))))) (|sizeLess?| (((|Boolean|) $ $) NIL (|has| |#1| (|EuclideanDomain|)))) (|size| (((|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (|sinh| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|sin| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|sech| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|sec| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) NIL)) (|retract| (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) NIL)) (|represents| (($ (|Vector| |#1|) (|Vector| $)) NIL) (($ (|Vector| |#1|)) NIL)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|rem| (($ $ $) NIL (|has| |#1| (|EuclideanDomain|)))) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) NIL) (((|Matrix| |#1|) $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| |#1|) (|Matrix| $)) NIL)) (|reduce| (($ (|SparseUnivariatePolynomial| |#1|)) NIL) (((|Union| $ "failed") (|Fraction| (|SparseUnivariatePolynomial| |#1|))) NIL (|has| |#1| (|Field|)))) (|recip| (((|Union| $ "failed") $) NIL)) (|real| ((|#1| $) 13)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|IntegerNumberSystem|)))) (|rational?| (((|Boolean|) $) NIL (|has| |#1| (|IntegerNumberSystem|)))) (|rational| (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|IntegerNumberSystem|)))) (|rank| (((|PositiveInteger|)) NIL)) (|random| (($) NIL (|has| |#1| (|Finite|)))) (|quo| (($ $ $) NIL (|has| |#1| (|EuclideanDomain|)))) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL (|has| |#1| (|EuclideanDomain|)))) (|primitiveElement| (($) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|primitive?| (((|Boolean|) $) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|FiniteFieldCategory|))) (($ $) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|prime?| (((|Boolean|) $) NIL (OR (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|Field|))))) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) NIL (AND (|has| |#1| (|RealNumberSystem|)) (|has| |#1| (|TranscendentalFunctionCategory|))))) (|pi| (($) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|patternMatch| (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (|has| |#1| (|PatternMatchable| (|Integer|)))) (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (|has| |#1| (|PatternMatchable| (|Float|))))) (|order| (((|PositiveInteger|) $) NIL (|has| |#1| (|FiniteFieldCategory|))) (((|OnePointCompletion| (|PositiveInteger|)) $) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|one?| (((|Boolean|) $) 35)) (|nthRoot| (($ $ (|Integer|)) NIL (AND (|has| |#1| (|RadicalCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))))) (|norm| ((|#1| $) 46)) (|nextItem| (((|Union| $ "failed") $) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|EuclideanDomain|)))) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) NIL (|has| |#1| (|Field|)))) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|lookup| (((|PositiveInteger|) $) NIL (|has| |#1| (|Finite|)))) (|log| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|lift| (((|SparseUnivariatePolynomial| |#1|) $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| |#1| (|EuclideanDomain|)))) (|lcm| (($ (|List| $)) NIL (|has| |#1| (|EuclideanDomain|))) (($ $ $) NIL (|has| |#1| (|EuclideanDomain|)))) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL (|has| |#1| (|Field|)))) (|init| (($) NIL (|has| |#1| (|FiniteFieldCategory|)) CONST)) (|index| (($ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|imaginary| (($) NIL)) (|imag| ((|#1| $) 15)) (|hash| (((|SingleInteger|) $) NIL)) (|generator| (($) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|EuclideanDomain|)))) (|gcd| (($ (|List| $)) NIL (|has| |#1| (|EuclideanDomain|))) (($ $ $) NIL (|has| |#1| (|EuclideanDomain|)))) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))))) (|factor| (((|Factored| $) $) NIL (OR (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|Field|))))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL (|has| |#1| (|EuclideanDomain|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|EuclideanDomain|)))) (|exquo| (((|Union| $ "failed") $ |#1|) 44 (|has| |#1| (|IntegralDomain|))) (((|Union| $ "failed") $ $) 47 (OR (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|EuclideanDomain|)))) (|exp| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ |#1| |#1|) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ (|Equation| |#1|)) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ (|List| (|Equation| |#1|))) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ (|List| (|Symbol|)) (|List| |#1|)) NIL (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|))) (($ $ (|Symbol|) |#1|) NIL (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|)))) (|euclideanSize| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|EuclideanDomain|)))) (|enumerate| (((|List| $)) NIL (|has| |#1| (|Finite|)))) (|elt| (($ $ |#1|) NIL (|has| |#1| (|Eltable| |#1| |#1|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|EuclideanDomain|)))) (|discriminant| ((|#1| (|Vector| $)) NIL) ((|#1|) NIL)) (|discreteLog| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|FiniteFieldCategory|))) (((|Union| (|NonNegativeInteger|) "failed") $ $) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#1| |#1|)) NIL) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|DifferentialRing|))) (($ $) NIL (|has| |#1| (|DifferentialRing|)))) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) NIL (|has| |#1| (|Field|)))) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) NIL)) (|csch| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|csc| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|createPrimitiveElement| (($) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|coth| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|cot| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|cosh| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|cos| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|coordinates| (((|Vector| |#1|) $ (|Vector| $)) NIL) (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) NIL) (((|Vector| |#1|) $) NIL) (((|Matrix| |#1|) (|Vector| $)) NIL)) (|convert| (((|Vector| |#1|) $) NIL) (($ (|Vector| |#1|)) NIL) (((|SparseUnivariatePolynomial| |#1|) $) NIL) (($ (|SparseUnivariatePolynomial| |#1|)) NIL) (((|Pattern| (|Integer|)) $) NIL (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|))))) (((|Pattern| (|Float|)) $) NIL (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|))))) (((|Complex| (|Float|)) $) NIL (|has| |#1| (|RealConstant|))) (((|Complex| (|DoubleFloat|)) $) NIL (|has| |#1| (|RealConstant|))) (((|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|conjugate| (($ $) 45)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|FiniteFieldCategory|))))) (|complex| (($ |#1| |#1|) 37)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ |#1|) 36) (($ (|Fraction| (|Integer|))) NIL (OR (|has| |#1| (|Field|)) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))))) (($ $) NIL (OR (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))))) (|charthRoot| (($ $) NIL (|has| |#1| (|FiniteFieldCategory|))) (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|CharacteristicNonZero|))))) (|characteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|basis| (((|Vector| $)) NIL)) (|atanh| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|atan| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|associates?| (((|Boolean|) $ $) NIL (OR (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))))) (|asinh| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|asin| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|asech| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|asec| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|argument| ((|#1| $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|acsch| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|acsc| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|acoth| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|acot| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|acosh| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|acos| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|abs| (($ $) NIL (|has| |#1| (|RealNumberSystem|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| |#1| (|Field|)))) (|Zero| (($) 28 T CONST)) (|One| (($) 30 T CONST)) (|OMwrite| (((|String|) $) 23 (|has| |#1| (|OpenMath|))) (((|String|) $ (|Boolean|)) 25 (|has| |#1| (|OpenMath|))) (((|Void|) (|OpenMathDevice|) $) 26 (|has| |#1| (|OpenMath|))) (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) 27 (|has| |#1| (|OpenMath|)))) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#1| |#1|)) NIL) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|DifferentialRing|))) (($ $) NIL (|has| |#1| (|DifferentialRing|)))) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (/ (($ $ $) NIL (|has| |#1| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) 39)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Fraction| (|Integer|))) NIL (AND (|has| |#1| (|RadicalCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|)))) (($ $ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|))) (($ $ (|Integer|)) NIL (|has| |#1| (|Field|)))) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 42) (($ $ |#1|) NIL) (($ |#1| $) NIL) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Field|))) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Field|))))) 
(((|Complex| |#1|) (|Join| (|ComplexCategory| |#1|) (CATEGORY |package| (IF (|has| |#1| (|OpenMath|)) (ATTRIBUTE (|OpenMath|)) |noBranch|))) (|CommutativeRing|)) (T |Complex|)) 
NIL 
(|Join| (|ComplexCategory| |#1|) (CATEGORY |package| (IF (|has| |#1| (|OpenMath|)) (ATTRIBUTE (|OpenMath|)) |noBranch|))) 
((|convert| (((|Pattern| |#1|) |#3|) 22))) 
(((|ComplexPattern| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |convert| ((|Pattern| |#1|) |#3|))) (|SetCategory|) (|Join| (|ConvertibleTo| (|Pattern| |#1|)) (|CommutativeRing|)) (|ComplexCategory| |#2|)) (T |ComplexPattern|)) 
((|convert| (*1 *2 *3) (AND (|ofCategory| *5 (|Join| (|ConvertibleTo| *2) (|CommutativeRing|))) (|isDomain| *2 (|Pattern| *4)) (|isDomain| *1 (|ComplexPattern| *4 *5 *3)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *3 (|ComplexCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |convert| ((|Pattern| |#1|) |#3|))) 
((~= (((|Boolean|) $ $) NIL)) (|solid?| (((|Boolean|) $) 9)) (|solid| (((|Boolean|) $ (|Boolean|)) 11)) (|new| (($) 12)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|copy| (($ $) 13)) (|coerce| (((|OutputForm|) $) 17)) (|closed?| (((|Boolean|) $) 8)) (|close| (((|Boolean|) $ (|Boolean|)) 10)) (= (((|Boolean|) $ $) NIL))) 
(((|SubSpaceComponentProperty|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |new| ($)) (SIGNATURE |closed?| ((|Boolean|) $)) (SIGNATURE |solid?| ((|Boolean|) $)) (SIGNATURE |close| ((|Boolean|) $ (|Boolean|))) (SIGNATURE |solid| ((|Boolean|) $ (|Boolean|))) (SIGNATURE |copy| ($ $))))) (T |SubSpaceComponentProperty|)) 
((|new| (*1 *1) (|isDomain| *1 (|SubSpaceComponentProperty|))) (|closed?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SubSpaceComponentProperty|)))) (|solid?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SubSpaceComponentProperty|)))) (|close| (*1 *2 *1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SubSpaceComponentProperty|)))) (|solid| (*1 *2 *1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SubSpaceComponentProperty|)))) (|copy| (*1 *1 *1) (|isDomain| *1 (|SubSpaceComponentProperty|)))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |new| ($)) (SIGNATURE |closed?| ((|Boolean|) $)) (SIGNATURE |solid?| ((|Boolean|) $)) (SIGNATURE |close| ((|Boolean|) $ (|Boolean|))) (SIGNATURE |solid| ((|Boolean|) $ (|Boolean|))) (SIGNATURE |copy| ($ $)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|CommutativeRing|) (|Category|)) (T |CommutativeRing|)) 
NIL 
(|Join| (|Ring|) (|BiModule| $ $) (CATEGORY |package| (ATTRIBUTE (|commutative| "*")))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|wholePart| ((|#1| $) 74)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sample| (($) NIL T CONST)) (|rem| (($ $ $) NIL)) (|reducedForm| (($ $) 19)) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) 47)) (|recip| (((|Union| $ "failed") $) 116)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|partialQuotients| (((|Stream| |#1|) $) 81)) (|partialNumerators| (((|Stream| |#1|) $) 78)) (|partialDenominators| (((|Stream| |#1|) $) 79)) (|one?| (((|Boolean|) $) NIL)) (|numerators| (((|Stream| |#1|) $) 87)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ (|List| $)) NIL) (($ $ $) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ (|List| $)) NIL) (($ $ $) NIL)) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL)) (|extend| (($ $ (|Integer|)) 90)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|denominators| (((|Stream| |#1|) $) 88)) (|convergents| (((|Stream| (|Fraction| |#1|)) $) 13)) (|continuedFraction| (($ (|Fraction| |#1|)) 17) (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) 37)) (|complete| (($ $) 92)) (|coerce| (((|OutputForm|) $) 126) (($ (|Integer|)) 50) (($ |#1|) 51) (($ (|Fraction| |#1|)) 35) (($ (|Fraction| (|Integer|))) NIL) (($ $) NIL)) (|characteristic| (((|NonNegativeInteger|)) 63)) (|associates?| (((|Boolean|) $ $) NIL)) (|approximants| (((|Stream| (|Fraction| |#1|)) $) 18)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) 25 T CONST)) (|One| (($) 28 T CONST)) (= (((|Boolean|) $ $) 34)) (/ (($ $ $) 114)) (- (($ $) 105) (($ $ $) 102)) (+ (($ $ $) 100)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 112) (($ $ $) 107) (($ $ |#1|) NIL) (($ |#1| $) 109) (($ (|Fraction| |#1|) $) 110) (($ $ (|Fraction| |#1|)) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ $ (|Fraction| (|Integer|))) NIL))) 
(((|ContinuedFraction| |#1|) (|Join| (|Algebra| |#1|) (|Algebra| (|Fraction| |#1|)) (|Field|) (CATEGORY |domain| (SIGNATURE |continuedFraction| ($ (|Fraction| |#1|))) (SIGNATURE |continuedFraction| ($ |#1| (|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |reducedContinuedFraction| ($ |#1| (|Stream| |#1|))) (SIGNATURE |partialNumerators| ((|Stream| |#1|) $)) (SIGNATURE |partialDenominators| ((|Stream| |#1|) $)) (SIGNATURE |partialQuotients| ((|Stream| |#1|) $)) (SIGNATURE |wholePart| (|#1| $)) (SIGNATURE |reducedForm| ($ $)) (SIGNATURE |approximants| ((|Stream| (|Fraction| |#1|)) $)) (SIGNATURE |convergents| ((|Stream| (|Fraction| |#1|)) $)) (SIGNATURE |numerators| ((|Stream| |#1|) $)) (SIGNATURE |denominators| ((|Stream| |#1|) $)) (SIGNATURE |extend| ($ $ (|Integer|))) (SIGNATURE |complete| ($ $)))) (|EuclideanDomain|)) (T |ContinuedFraction|)) 
((|continuedFraction| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| *3)) (|ofCategory| *3 (|EuclideanDomain|)) (|isDomain| *1 (|ContinuedFraction| *3)))) (|continuedFraction| (*1 *1 *2 *3 *3) (AND (|isDomain| *3 (|Stream| *2)) (|ofCategory| *2 (|EuclideanDomain|)) (|isDomain| *1 (|ContinuedFraction| *2)))) (|reducedContinuedFraction| (*1 *1 *2 *3) (AND (|isDomain| *3 (|Stream| *2)) (|ofCategory| *2 (|EuclideanDomain|)) (|isDomain| *1 (|ContinuedFraction| *2)))) (|partialNumerators| (*1 *2 *1) (AND (|isDomain| *2 (|Stream| *3)) (|isDomain| *1 (|ContinuedFraction| *3)) (|ofCategory| *3 (|EuclideanDomain|)))) (|partialDenominators| (*1 *2 *1) (AND (|isDomain| *2 (|Stream| *3)) (|isDomain| *1 (|ContinuedFraction| *3)) (|ofCategory| *3 (|EuclideanDomain|)))) (|partialQuotients| (*1 *2 *1) (AND (|isDomain| *2 (|Stream| *3)) (|isDomain| *1 (|ContinuedFraction| *3)) (|ofCategory| *3 (|EuclideanDomain|)))) (|wholePart| (*1 *2 *1) (AND (|isDomain| *1 (|ContinuedFraction| *2)) (|ofCategory| *2 (|EuclideanDomain|)))) (|reducedForm| (*1 *1 *1) (AND (|isDomain| *1 (|ContinuedFraction| *2)) (|ofCategory| *2 (|EuclideanDomain|)))) (|approximants| (*1 *2 *1) (AND (|isDomain| *2 (|Stream| (|Fraction| *3))) (|isDomain| *1 (|ContinuedFraction| *3)) (|ofCategory| *3 (|EuclideanDomain|)))) (|convergents| (*1 *2 *1) (AND (|isDomain| *2 (|Stream| (|Fraction| *3))) (|isDomain| *1 (|ContinuedFraction| *3)) (|ofCategory| *3 (|EuclideanDomain|)))) (|numerators| (*1 *2 *1) (AND (|isDomain| *2 (|Stream| *3)) (|isDomain| *1 (|ContinuedFraction| *3)) (|ofCategory| *3 (|EuclideanDomain|)))) (|denominators| (*1 *2 *1) (AND (|isDomain| *2 (|Stream| *3)) (|isDomain| *1 (|ContinuedFraction| *3)) (|ofCategory| *3 (|EuclideanDomain|)))) (|extend| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|ContinuedFraction| *3)) (|ofCategory| *3 (|EuclideanDomain|)))) (|complete| (*1 *1 *1) (AND (|isDomain| *1 (|ContinuedFraction| *2)) (|ofCategory| *2 (|EuclideanDomain|))))) 
(|Join| (|Algebra| |#1|) (|Algebra| (|Fraction| |#1|)) (|Field|) (CATEGORY |domain| (SIGNATURE |continuedFraction| ($ (|Fraction| |#1|))) (SIGNATURE |continuedFraction| ($ |#1| (|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |reducedContinuedFraction| ($ |#1| (|Stream| |#1|))) (SIGNATURE |partialNumerators| ((|Stream| |#1|) $)) (SIGNATURE |partialDenominators| ((|Stream| |#1|) $)) (SIGNATURE |partialQuotients| ((|Stream| |#1|) $)) (SIGNATURE |wholePart| (|#1| $)) (SIGNATURE |reducedForm| ($ $)) (SIGNATURE |approximants| ((|Stream| (|Fraction| |#1|)) $)) (SIGNATURE |convergents| ((|Stream| (|Fraction| |#1|)) $)) (SIGNATURE |numerators| ((|Stream| |#1|) $)) (SIGNATURE |denominators| ((|Stream| |#1|) $)) (SIGNATURE |extend| ($ $ (|Integer|))) (SIGNATURE |complete| ($ $)))) 
((|toroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) 40)) (|spherical| (((|Point| |#1|) (|Point| |#1|)) 19)) (|prolateSpheroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) 36)) (|polar| (((|Point| |#1|) (|Point| |#1|)) 17)) (|paraboloidal| (((|Point| |#1|) (|Point| |#1|)) 25)) (|parabolicCylindrical| (((|Point| |#1|) (|Point| |#1|)) 24)) (|parabolic| (((|Point| |#1|) (|Point| |#1|)) 23)) (|oblateSpheroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) 37)) (|ellipticCylindrical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) 35)) (|elliptic| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) 34)) (|cylindrical| (((|Point| |#1|) (|Point| |#1|)) 18)) (|conical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1| |#1|) 43)) (|cartesian| (((|Point| |#1|) (|Point| |#1|)) 8)) (|bipolarCylindrical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) 39)) (|bipolar| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) 38))) 
(((|CoordinateSystems| |#1|) (CATEGORY |package| (SIGNATURE |cartesian| ((|Point| |#1|) (|Point| |#1|))) (SIGNATURE |polar| ((|Point| |#1|) (|Point| |#1|))) (SIGNATURE |cylindrical| ((|Point| |#1|) (|Point| |#1|))) (SIGNATURE |spherical| ((|Point| |#1|) (|Point| |#1|))) (SIGNATURE |parabolic| ((|Point| |#1|) (|Point| |#1|))) (SIGNATURE |parabolicCylindrical| ((|Point| |#1|) (|Point| |#1|))) (SIGNATURE |paraboloidal| ((|Point| |#1|) (|Point| |#1|))) (SIGNATURE |elliptic| ((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|)) (SIGNATURE |ellipticCylindrical| ((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|)) (SIGNATURE |prolateSpheroidal| ((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|)) (SIGNATURE |oblateSpheroidal| ((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|)) (SIGNATURE |bipolar| ((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|)) (SIGNATURE |bipolarCylindrical| ((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|)) (SIGNATURE |toroidal| ((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|)) (SIGNATURE |conical| ((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1| |#1|))) (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))) (T |CoordinateSystems|)) 
((|conical| (*1 *2 *3 *3) (AND (|isDomain| *2 (|Mapping| (|Point| *3) (|Point| *3))) (|isDomain| *1 (|CoordinateSystems| *3)) (|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))))) (|toroidal| (*1 *2 *3) (AND (|isDomain| *2 (|Mapping| (|Point| *3) (|Point| *3))) (|isDomain| *1 (|CoordinateSystems| *3)) (|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))))) (|bipolarCylindrical| (*1 *2 *3) (AND (|isDomain| *2 (|Mapping| (|Point| *3) (|Point| *3))) (|isDomain| *1 (|CoordinateSystems| *3)) (|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))))) (|bipolar| (*1 *2 *3) (AND (|isDomain| *2 (|Mapping| (|Point| *3) (|Point| *3))) (|isDomain| *1 (|CoordinateSystems| *3)) (|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))))) (|oblateSpheroidal| (*1 *2 *3) (AND (|isDomain| *2 (|Mapping| (|Point| *3) (|Point| *3))) (|isDomain| *1 (|CoordinateSystems| *3)) (|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))))) (|prolateSpheroidal| (*1 *2 *3) (AND (|isDomain| *2 (|Mapping| (|Point| *3) (|Point| *3))) (|isDomain| *1 (|CoordinateSystems| *3)) (|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))))) (|ellipticCylindrical| (*1 *2 *3) (AND (|isDomain| *2 (|Mapping| (|Point| *3) (|Point| *3))) (|isDomain| *1 (|CoordinateSystems| *3)) (|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))))) (|elliptic| (*1 *2 *3) (AND (|isDomain| *2 (|Mapping| (|Point| *3) (|Point| *3))) (|isDomain| *1 (|CoordinateSystems| *3)) (|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))))) (|paraboloidal| (*1 *2 *2) (AND (|isDomain| *2 (|Point| *3)) (|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))) (|isDomain| *1 (|CoordinateSystems| *3)))) (|parabolicCylindrical| (*1 *2 *2) (AND (|isDomain| *2 (|Point| *3)) (|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))) (|isDomain| *1 (|CoordinateSystems| *3)))) (|parabolic| (*1 *2 *2) (AND (|isDomain| *2 (|Point| *3)) (|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))) (|isDomain| *1 (|CoordinateSystems| *3)))) (|spherical| (*1 *2 *2) (AND (|isDomain| *2 (|Point| *3)) (|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))) (|isDomain| *1 (|CoordinateSystems| *3)))) (|cylindrical| (*1 *2 *2) (AND (|isDomain| *2 (|Point| *3)) (|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))) (|isDomain| *1 (|CoordinateSystems| *3)))) (|polar| (*1 *2 *2) (AND (|isDomain| *2 (|Point| *3)) (|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))) (|isDomain| *1 (|CoordinateSystems| *3)))) (|cartesian| (*1 *2 *2) (AND (|isDomain| *2 (|Point| *3)) (|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))) (|isDomain| *1 (|CoordinateSystems| *3))))) 
(CATEGORY |package| (SIGNATURE |cartesian| ((|Point| |#1|) (|Point| |#1|))) (SIGNATURE |polar| ((|Point| |#1|) (|Point| |#1|))) (SIGNATURE |cylindrical| ((|Point| |#1|) (|Point| |#1|))) (SIGNATURE |spherical| ((|Point| |#1|) (|Point| |#1|))) (SIGNATURE |parabolic| ((|Point| |#1|) (|Point| |#1|))) (SIGNATURE |parabolicCylindrical| ((|Point| |#1|) (|Point| |#1|))) (SIGNATURE |paraboloidal| ((|Point| |#1|) (|Point| |#1|))) (SIGNATURE |elliptic| ((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|)) (SIGNATURE |ellipticCylindrical| ((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|)) (SIGNATURE |prolateSpheroidal| ((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|)) (SIGNATURE |oblateSpheroidal| ((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|)) (SIGNATURE |bipolar| ((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|)) (SIGNATURE |bipolarCylindrical| ((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|)) (SIGNATURE |toroidal| ((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|)) (SIGNATURE |conical| ((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1| |#1|))) 
((|characteristicPolynomial| ((|#2| |#3|) 27))) 
(((|CharacteristicPolynomialInMonogenicalAlgebra| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |characteristicPolynomial| (|#2| |#3|))) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#1|) (|MonogenicAlgebra| |#1| |#2|)) (T |CharacteristicPolynomialInMonogenicalAlgebra|)) 
((|characteristicPolynomial| (*1 *2 *3) (AND (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|CharacteristicPolynomialInMonogenicalAlgebra| *4 *2 *3)) (|ofCategory| *3 (|MonogenicAlgebra| *4 *2))))) 
(CATEGORY |package| (SIGNATURE |characteristicPolynomial| (|#2| |#3|))) 
((|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) 47 (|has| (|Polynomial| |#2|) (|PatternMatchable| |#1|))))) 
(((|ComplexPatternMatch| |#1| |#2| |#3|) (CATEGORY |package| (IF (|has| (|Polynomial| |#2|) (|PatternMatchable| |#1|)) (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) |noBranch|)) (|SetCategory|) (|Join| (|PatternMatchable| |#1|) (|CommutativeRing|)) (|ComplexCategory| |#2|)) (T |ComplexPatternMatch|)) 
((|patternMatch| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|PatternMatchResult| *5 *3)) (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *3 (|ComplexCategory| *6)) (|ofCategory| (|Polynomial| *6) (|PatternMatchable| *5)) (|ofCategory| *6 (|Join| (|PatternMatchable| *5) (|CommutativeRing|))) (|isDomain| *1 (|ComplexPatternMatch| *5 *6 *3))))) 
(CATEGORY |package| (IF (|has| (|Polynomial| |#2|) (|PatternMatchable| |#1|)) (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) |noBranch|)) 
((|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) 36)) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) 19)) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) 31) ((|#1| (|List| |#1|) (|List| |#1|)) 29))) 
(((|CRApackage| |#1|) (CATEGORY |package| (SIGNATURE |modTree| ((|List| |#1|) |#1| (|List| |#1|))) (SIGNATURE |chineseRemainder| (|#1| (|List| |#1|) (|List| |#1|))) (SIGNATURE |chineseRemainder| ((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|))) (SIGNATURE |multiEuclideanTree| ((|List| |#1|) (|List| |#1|) |#1|))) (|EuclideanDomain|)) (T |CRApackage|)) 
((|multiEuclideanTree| (*1 *2 *2 *3) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|EuclideanDomain|)) (|isDomain| *1 (|CRApackage| *3)))) (|chineseRemainder| (*1 *2 *3 *2) (AND (|isDomain| *3 (|List| (|List| *4))) (|isDomain| *2 (|List| *4)) (|ofCategory| *4 (|EuclideanDomain|)) (|isDomain| *1 (|CRApackage| *4)))) (|chineseRemainder| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| *2)) (|isDomain| *1 (|CRApackage| *2)) (|ofCategory| *2 (|EuclideanDomain|)))) (|modTree| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|EuclideanDomain|)) (|isDomain| *1 (|CRApackage| *3))))) 
(CATEGORY |package| (SIGNATURE |modTree| ((|List| |#1|) |#1| (|List| |#1|))) (SIGNATURE |chineseRemainder| (|#1| (|List| |#1|) (|List| |#1|))) (SIGNATURE |chineseRemainder| ((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|))) (SIGNATURE |multiEuclideanTree| ((|List| |#1|) (|List| |#1|) |#1|))) 
((|startPolynomial| (((|Record| (|:| |start| |#2|) (|:| |factors| (|Factored| |#2|))) |#2|) 61)) (|setErrorBound| ((|#1| |#1|) 54)) (|schwerpunkt| (((|Complex| |#1|) |#2|) 82)) (|rootRadius| ((|#1| |#2|) 122) ((|#1| |#2| |#1|) 80)) (|reciprocalPolynomial| ((|#2| |#2|) 81)) (|pleskenSplit| (((|Factored| |#2|) |#2| |#1|) 112) (((|Factored| |#2|) |#2| |#1| (|Boolean|)) 79)) (|norm| ((|#1| |#2|) 111)) (|graeffe| ((|#2| |#2|) 118)) (|factor| (((|Factored| |#2|) |#2|) 133) (((|Factored| |#2|) |#2| |#1|) 32) (((|Factored| |#2|) |#2| |#1| (|Boolean|)) 132)) (|divisorCascade| (((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2|) 131) (((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2| (|Boolean|)) 75)) (|complexZeros| (((|List| (|Complex| |#1|)) |#2| |#1|) 40) (((|List| (|Complex| |#1|)) |#2|) 41))) 
(((|ComplexRootFindingPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |complexZeros| ((|List| (|Complex| |#1|)) |#2|)) (SIGNATURE |complexZeros| ((|List| (|Complex| |#1|)) |#2| |#1|)) (SIGNATURE |divisorCascade| ((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2| (|Boolean|))) (SIGNATURE |divisorCascade| ((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2|)) (SIGNATURE |factor| ((|Factored| |#2|) |#2| |#1| (|Boolean|))) (SIGNATURE |factor| ((|Factored| |#2|) |#2| |#1|)) (SIGNATURE |factor| ((|Factored| |#2|) |#2|)) (SIGNATURE |graeffe| (|#2| |#2|)) (SIGNATURE |norm| (|#1| |#2|)) (SIGNATURE |pleskenSplit| ((|Factored| |#2|) |#2| |#1| (|Boolean|))) (SIGNATURE |pleskenSplit| ((|Factored| |#2|) |#2| |#1|)) (SIGNATURE |reciprocalPolynomial| (|#2| |#2|)) (SIGNATURE |rootRadius| (|#1| |#2| |#1|)) (SIGNATURE |rootRadius| (|#1| |#2|)) (SIGNATURE |schwerpunkt| ((|Complex| |#1|) |#2|)) (SIGNATURE |setErrorBound| (|#1| |#1|)) (SIGNATURE |startPolynomial| ((|Record| (|:| |start| |#2|) (|:| |factors| (|Factored| |#2|))) |#2|))) (|Join| (|Field|) (|OrderedRing|)) (|UnivariatePolynomialCategory| (|Complex| |#1|))) (T |ComplexRootFindingPackage|)) 
((|startPolynomial| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|))) (|isDomain| *2 (|Record| (|:| |start| *3) (|:| |factors| (|Factored| *3)))) (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4))))) (|setErrorBound| (*1 *2 *2) (AND (|ofCategory| *2 (|Join| (|Field|) (|OrderedRing|))) (|isDomain| *1 (|ComplexRootFindingPackage| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *2))))) (|schwerpunkt| (*1 *2 *3) (AND (|isDomain| *2 (|Complex| *4)) (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3)) (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|))) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|rootRadius| (*1 *2 *3) (AND (|ofCategory| *2 (|Join| (|Field|) (|OrderedRing|))) (|isDomain| *1 (|ComplexRootFindingPackage| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *2))))) (|rootRadius| (*1 *2 *3 *2) (AND (|ofCategory| *2 (|Join| (|Field|) (|OrderedRing|))) (|isDomain| *1 (|ComplexRootFindingPackage| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *2))))) (|reciprocalPolynomial| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|Field|) (|OrderedRing|))) (|isDomain| *1 (|ComplexRootFindingPackage| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Complex| *3))))) (|pleskenSplit| (*1 *2 *3 *4) (AND (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4))))) (|pleskenSplit| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|Boolean|)) (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4))))) (|norm| (*1 *2 *3) (AND (|ofCategory| *2 (|Join| (|Field|) (|OrderedRing|))) (|isDomain| *1 (|ComplexRootFindingPackage| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *2))))) (|graeffe| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|Field|) (|OrderedRing|))) (|isDomain| *1 (|ComplexRootFindingPackage| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Complex| *3))))) (|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4))))) (|factor| (*1 *2 *3 *4) (AND (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4))))) (|factor| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|Boolean|)) (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4))))) (|divisorCascade| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|))) (|isDomain| *2 (|List| (|Record| (|:| |factors| (|List| *3)) (|:| |error| *4)))) (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4))))) (|divisorCascade| (*1 *2 *3 *3 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|Field|) (|OrderedRing|))) (|isDomain| *2 (|List| (|Record| (|:| |factors| (|List| *3)) (|:| |error| *5)))) (|isDomain| *1 (|ComplexRootFindingPackage| *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *5))))) (|complexZeros| (*1 *2 *3 *4) (AND (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|))) (|isDomain| *2 (|List| (|Complex| *4))) (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4))))) (|complexZeros| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|))) (|isDomain| *2 (|List| (|Complex| *4))) (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4)))))) 
(CATEGORY |package| (SIGNATURE |complexZeros| ((|List| (|Complex| |#1|)) |#2|)) (SIGNATURE |complexZeros| ((|List| (|Complex| |#1|)) |#2| |#1|)) (SIGNATURE |divisorCascade| ((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2| (|Boolean|))) (SIGNATURE |divisorCascade| ((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2|)) (SIGNATURE |factor| ((|Factored| |#2|) |#2| |#1| (|Boolean|))) (SIGNATURE |factor| ((|Factored| |#2|) |#2| |#1|)) (SIGNATURE |factor| ((|Factored| |#2|) |#2|)) (SIGNATURE |graeffe| (|#2| |#2|)) (SIGNATURE |norm| (|#1| |#2|)) (SIGNATURE |pleskenSplit| ((|Factored| |#2|) |#2| |#1| (|Boolean|))) (SIGNATURE |pleskenSplit| ((|Factored| |#2|) |#2| |#1|)) (SIGNATURE |reciprocalPolynomial| (|#2| |#2|)) (SIGNATURE |rootRadius| (|#1| |#2| |#1|)) (SIGNATURE |rootRadius| (|#1| |#2|)) (SIGNATURE |schwerpunkt| ((|Complex| |#1|) |#2|)) (SIGNATURE |setErrorBound| (|#1| |#1|)) (SIGNATURE |startPolynomial| ((|Record| (|:| |start| |#2|) (|:| |factors| (|Factored| |#2|))) |#2|))) 
((|cycleElt| (((|Union| |#2| "failed") |#2|) 14)) (|computeCycleLength| (((|NonNegativeInteger|) |#2|) 16)) (|computeCycleEntry| ((|#2| |#2| |#2|) 18))) 
(((|CyclicStreamTools| |#1| |#2|) (CATEGORY |package| (SIGNATURE |cycleElt| ((|Union| |#2| "failed") |#2|)) (SIGNATURE |computeCycleLength| ((|NonNegativeInteger|) |#2|)) (SIGNATURE |computeCycleEntry| (|#2| |#2| |#2|))) (|Type|) (|LazyStreamAggregate| |#1|)) (T |CyclicStreamTools|)) 
((|computeCycleEntry| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|CyclicStreamTools| *3 *2)) (|ofCategory| *2 (|LazyStreamAggregate| *3)))) (|computeCycleLength| (*1 *2 *3) (AND (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|CyclicStreamTools| *4 *3)) (|ofCategory| *3 (|LazyStreamAggregate| *4)))) (|cycleElt| (*1 *2 *2) (|partial| AND (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|CyclicStreamTools| *3 *2)) (|ofCategory| *2 (|LazyStreamAggregate| *3))))) 
(CATEGORY |package| (SIGNATURE |cycleElt| ((|Union| |#2| "failed") |#2|)) (SIGNATURE |computeCycleLength| ((|NonNegativeInteger|) |#2|)) (SIGNATURE |computeCycleEntry| (|#2| |#2| |#2|))) 
((|trigs| ((|#2| |#2|) 28)) (|real?| (((|Boolean|) |#2|) 19)) (|real| (((|Expression| |#1|) |#2|) 12)) (|imag| (((|Expression| |#1|) |#2|) 14)) (|complexNormalize| ((|#2| |#2| (|Symbol|)) 68) ((|#2| |#2|) 69)) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) 9)) (|complexElementary| ((|#2| |#2| (|Symbol|)) 65) ((|#2| |#2|) 58))) 
(((|ComplexTrigonometricManipulations| |#1| |#2|) (CATEGORY |package| (SIGNATURE |complexNormalize| (|#2| |#2|)) (SIGNATURE |complexNormalize| (|#2| |#2| (|Symbol|))) (SIGNATURE |complexElementary| (|#2| |#2|)) (SIGNATURE |complexElementary| (|#2| |#2| (|Symbol|))) (SIGNATURE |real| ((|Expression| |#1|) |#2|)) (SIGNATURE |imag| ((|Expression| |#1|) |#2|)) (SIGNATURE |real?| ((|Boolean|) |#2|)) (SIGNATURE |trigs| (|#2| |#2|)) (SIGNATURE |complexForm| ((|Complex| (|Expression| |#1|)) |#2|))) (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|))) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| (|Complex| |#1|)))) (T |ComplexTrigonometricManipulations|)) 
((|complexForm| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Complex| (|Expression| *4))) (|isDomain| *1 (|ComplexTrigonometricManipulations| *4 *3)) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| (|Complex| *4)))))) (|trigs| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|isDomain| *1 (|ComplexTrigonometricManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| (|Complex| *3)))))) (|real?| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ComplexTrigonometricManipulations| *4 *3)) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| (|Complex| *4)))))) (|imag| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Expression| *4)) (|isDomain| *1 (|ComplexTrigonometricManipulations| *4 *3)) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| (|Complex| *4)))))) (|real| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Expression| *4)) (|isDomain| *1 (|ComplexTrigonometricManipulations| *4 *3)) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| (|Complex| *4)))))) (|complexElementary| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|isDomain| *1 (|ComplexTrigonometricManipulations| *4 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| (|Complex| *4)))))) (|complexElementary| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|isDomain| *1 (|ComplexTrigonometricManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| (|Complex| *3)))))) (|complexNormalize| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|isDomain| *1 (|ComplexTrigonometricManipulations| *4 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| (|Complex| *4)))))) (|complexNormalize| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|isDomain| *1 (|ComplexTrigonometricManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| (|Complex| *3))))))) 
(CATEGORY |package| (SIGNATURE |complexNormalize| (|#2| |#2|)) (SIGNATURE |complexNormalize| (|#2| |#2| (|Symbol|))) (SIGNATURE |complexElementary| (|#2| |#2|)) (SIGNATURE |complexElementary| (|#2| |#2| (|Symbol|))) (SIGNATURE |real| ((|Expression| |#1|) |#2|)) (SIGNATURE |imag| ((|Expression| |#1|) |#2|)) (SIGNATURE |real?| ((|Boolean|) |#2|)) (SIGNATURE |trigs| (|#2| |#2|)) (SIGNATURE |complexForm| ((|Complex| (|Expression| |#1|)) |#2|))) 
((|coerceP| (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|Vector| (|Matrix| |#1|))) 22)) (|coerce| (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Vector| (|Matrix| |#1|))) 30))) 
(((|CoerceVectorMatrixPackage| |#1|) (CATEGORY |package| (SIGNATURE |coerceP| ((|Vector| (|Matrix| (|Polynomial| |#1|))) (|Vector| (|Matrix| |#1|)))) (SIGNATURE |coerce| ((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Vector| (|Matrix| |#1|))))) (|CommutativeRing|)) (T |CoerceVectorMatrixPackage|)) 
((|coerce| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| (|Matrix| *4))) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Vector| (|Matrix| (|Fraction| (|Polynomial| *4))))) (|isDomain| *1 (|CoerceVectorMatrixPackage| *4)))) (|coerceP| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| (|Matrix| *4))) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Vector| (|Matrix| (|Polynomial| *4)))) (|isDomain| *1 (|CoerceVectorMatrixPackage| *4))))) 
(CATEGORY |package| (SIGNATURE |coerceP| ((|Vector| (|Matrix| (|Polynomial| |#1|))) (|Vector| (|Matrix| |#1|)))) (SIGNATURE |coerce| ((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Vector| (|Matrix| |#1|))))) 
((|wreath| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) 66)) (|skewSFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) 74)) (|powerSum| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) 40)) (|graphs| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) 52)) (|eval| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) 62)) (|elementary| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) 32)) (|dihedral| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) 48)) (|cyclic| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) 46)) (|cup| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) 60)) (|complete| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) 25)) (|cap| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) 64)) (|alternating| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) 30)) (|SFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|))) 71))) 
(((|CycleIndicators|) (CATEGORY |package| (SIGNATURE |complete| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |powerSum| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |elementary| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |alternating| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |cyclic| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |dihedral| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |graphs| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |cap| ((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))))) (SIGNATURE |cup| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))))) (SIGNATURE |eval| ((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|))))) (SIGNATURE |wreath| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))))) (SIGNATURE |SFunction| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|)))) (SIGNATURE |skewSFunction| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|)))))) (T |CycleIndicators|)) 
((|skewSFunction| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|CycleIndicators|)))) (|SFunction| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|CycleIndicators|)))) (|wreath| (*1 *2 *2 *2) (AND (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|CycleIndicators|)))) (|eval| (*1 *2 *3) (AND (|isDomain| *3 (|SymmetricPolynomial| (|Fraction| (|Integer|)))) (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|CycleIndicators|)))) (|cup| (*1 *2 *2 *2) (AND (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|CycleIndicators|)))) (|cap| (*1 *2 *3 *3) (AND (|isDomain| *3 (|SymmetricPolynomial| (|Fraction| (|Integer|)))) (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|CycleIndicators|)))) (|graphs| (*1 *2 *3) (AND (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|CycleIndicators|)) (|isDomain| *3 (|Integer|)))) (|dihedral| (*1 *2 *3) (AND (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|CycleIndicators|)) (|isDomain| *3 (|Integer|)))) (|cyclic| (*1 *2 *3) (AND (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|CycleIndicators|)) (|isDomain| *3 (|Integer|)))) (|alternating| (*1 *2 *3) (AND (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|CycleIndicators|)) (|isDomain| *3 (|Integer|)))) (|elementary| (*1 *2 *3) (AND (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|CycleIndicators|)) (|isDomain| *3 (|Integer|)))) (|powerSum| (*1 *2 *3) (AND (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|CycleIndicators|)) (|isDomain| *3 (|Integer|)))) (|complete| (*1 *2 *3) (AND (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|CycleIndicators|)) (|isDomain| *3 (|Integer|))))) 
(CATEGORY |package| (SIGNATURE |complete| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |powerSum| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |elementary| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |alternating| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |cyclic| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |dihedral| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |graphs| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |cap| ((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))))) (SIGNATURE |cup| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))))) (SIGNATURE |eval| ((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|))))) (SIGNATURE |wreath| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))))) (SIGNATURE |SFunction| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|)))) (SIGNATURE |skewSFunction| ((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))))) 
((|cyclotomicFactorization| (((|Factored| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|)) 28)) (|cyclotomicDecomposition| (((|List| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|)) 23)) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) 21))) 
(((|CyclotomicPolynomialPackage|) (CATEGORY |package| (SIGNATURE |cyclotomicDecomposition| ((|List| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|))) (SIGNATURE |cyclotomic| ((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|))) (SIGNATURE |cyclotomicFactorization| ((|Factored| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|))))) (T |CyclotomicPolynomialPackage|)) 
((|cyclotomicFactorization| (*1 *2 *3) (AND (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| (|Integer|)))) (|isDomain| *1 (|CyclotomicPolynomialPackage|)) (|isDomain| *3 (|Integer|)))) (|cyclotomic| (*1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *1 (|CyclotomicPolynomialPackage|)) (|isDomain| *3 (|Integer|)))) (|cyclotomicDecomposition| (*1 *2 *3) (AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| (|Integer|)))) (|isDomain| *1 (|CyclotomicPolynomialPackage|)) (|isDomain| *3 (|Integer|))))) 
(CATEGORY |package| (SIGNATURE |cyclotomicDecomposition| ((|List| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|))) (SIGNATURE |cyclotomic| ((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|))) (SIGNATURE |cyclotomicFactorization| ((|Factored| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|)))) 
((|singularitiesOf| (((|Stream| (|DoubleFloat|)) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 101)) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) NIL)) (|rangeIsFinite| (((|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 77)) (|problemPoints| (((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) NIL)) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) NIL)) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) 22)) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) 23)) (|functionIsOscillatory| (((|Float|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 93)) (|functionIsContinuousAtEndPoints| (((|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 40)) (|df2st| (((|String|) (|DoubleFloat|)) NIL)) (|commaSeparate| (((|String|) (|List| (|String|))) 19)) (|changeName| (((|Result|) (|Symbol|) (|Symbol|) (|Result|)) 12))) 
(((|d01AgentsPackage|) (CATEGORY |package| (SIGNATURE |rangeIsFinite| ((|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |functionIsContinuousAtEndPoints| ((|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |getlo| ((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (SIGNATURE |gethi| ((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (SIGNATURE |functionIsOscillatory| ((|Float|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |problemPoints| ((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (SIGNATURE |singularitiesOf| ((|Stream| (|DoubleFloat|)) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |df2st| ((|String|) (|DoubleFloat|))) (SIGNATURE |ldf2lst| ((|List| (|String|)) (|List| (|DoubleFloat|)))) (SIGNATURE |sdf2lst| ((|List| (|String|)) (|Stream| (|DoubleFloat|)))) (SIGNATURE |commaSeparate| ((|String|) (|List| (|String|)))) (SIGNATURE |changeName| ((|Result|) (|Symbol|) (|Symbol|) (|Result|))))) (T |d01AgentsPackage|)) 
((|changeName| (*1 *2 *3 *3 *2) (AND (|isDomain| *2 (|Result|)) (|isDomain| *3 (|Symbol|)) (|isDomain| *1 (|d01AgentsPackage|)))) (|commaSeparate| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|String|))) (|isDomain| *2 (|String|)) (|isDomain| *1 (|d01AgentsPackage|)))) (|sdf2lst| (*1 *2 *3) (AND (|isDomain| *3 (|Stream| (|DoubleFloat|))) (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|d01AgentsPackage|)))) (|ldf2lst| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|DoubleFloat|))) (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|d01AgentsPackage|)))) (|df2st| (*1 *2 *3) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *2 (|String|)) (|isDomain| *1 (|d01AgentsPackage|)))) (|singularitiesOf| (*1 *2 *3) (AND (|isDomain| *3 (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|isDomain| *2 (|Stream| (|DoubleFloat|))) (|isDomain| *1 (|d01AgentsPackage|)))) (|problemPoints| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Expression| (|DoubleFloat|))) (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|isDomain| *2 (|List| (|DoubleFloat|))) (|isDomain| *1 (|d01AgentsPackage|)))) (|functionIsOscillatory| (*1 *2 *3) (AND (|isDomain| *3 (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|isDomain| *2 (|Float|)) (|isDomain| *1 (|d01AgentsPackage|)))) (|gethi| (*1 *2 *3) (AND (|isDomain| *3 (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|d01AgentsPackage|)))) (|getlo| (*1 *2 *3) (AND (|isDomain| *3 (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|d01AgentsPackage|)))) (|functionIsContinuousAtEndPoints| (*1 *2 *3) (AND (|isDomain| *3 (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|isDomain| *2 (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|isDomain| *1 (|d01AgentsPackage|)))) (|rangeIsFinite| (*1 *2 *3) (AND (|isDomain| *3 (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|isDomain| *2 (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))) (|isDomain| *1 (|d01AgentsPackage|))))) 
(CATEGORY |package| (SIGNATURE |rangeIsFinite| ((|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |functionIsContinuousAtEndPoints| ((|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |getlo| ((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (SIGNATURE |gethi| ((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (SIGNATURE |functionIsOscillatory| ((|Float|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |problemPoints| ((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (SIGNATURE |singularitiesOf| ((|Stream| (|DoubleFloat|)) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |df2st| ((|String|) (|DoubleFloat|))) (SIGNATURE |ldf2lst| ((|List| (|String|)) (|List| (|DoubleFloat|)))) (SIGNATURE |sdf2lst| ((|List| (|String|)) (|Stream| (|DoubleFloat|)))) (SIGNATURE |commaSeparate| ((|String|) (|List| (|String|)))) (SIGNATURE |changeName| ((|Result|) (|Symbol|) (|Symbol|) (|Result|)))) 
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(((|d01ajfAnnaType|) (|NumericalIntegrationCategory|)) (T |d01ajfAnnaType|)) 
NIL 
(|NumericalIntegrationCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|numericalIntegration| (((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) 58) (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) NIL)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 37) (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|d01akfAnnaType|) (|NumericalIntegrationCategory|)) (T |d01akfAnnaType|)) 
NIL 
(|NumericalIntegrationCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|numericalIntegration| (((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) 67) (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) NIL)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 36) (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|d01alfAnnaType|) (|NumericalIntegrationCategory|)) (T |d01alfAnnaType|)) 
NIL 
(|NumericalIntegrationCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|numericalIntegration| (((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) 54) (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) NIL)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 30) (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|d01amfAnnaType|) (|NumericalIntegrationCategory|)) (T |d01amfAnnaType|)) 
NIL 
(|NumericalIntegrationCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|numericalIntegration| (((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) 65) (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) NIL)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 35) (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|d01anfAnnaType|) (|NumericalIntegrationCategory|)) (T |d01anfAnnaType|)) 
NIL 
(|NumericalIntegrationCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|numericalIntegration| (((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) 71) (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) NIL)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 33) (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|d01apfAnnaType|) (|NumericalIntegrationCategory|)) (T |d01apfAnnaType|)) 
NIL 
(|NumericalIntegrationCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|numericalIntegration| (((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) 78) (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) NIL)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 43) (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|d01aqfAnnaType|) (|NumericalIntegrationCategory|)) (T |d01aqfAnnaType|)) 
NIL 
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NIL 
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NIL 
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NIL 
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(((|d02bbfAnnaType|) (|OrdinaryDifferentialEquationsSolverCategory|)) (T |d02bbfAnnaType|)) 
NIL 
(|OrdinaryDifferentialEquationsSolverCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 37)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 60)) (= (((|Boolean|) $ $) NIL))) 
(((|d02bhfAnnaType|) (|OrdinaryDifferentialEquationsSolverCategory|)) (T |d02bhfAnnaType|)) 
NIL 
(|OrdinaryDifferentialEquationsSolverCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 36)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 64)) (= (((|Boolean|) $ $) NIL))) 
(((|d02cjfAnnaType|) (|OrdinaryDifferentialEquationsSolverCategory|)) (T |d02cjfAnnaType|)) 
NIL 
(|OrdinaryDifferentialEquationsSolverCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 42)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 73)) (= (((|Boolean|) $ $) NIL))) 
(((|d02ejfAnnaType|) (|OrdinaryDifferentialEquationsSolverCategory|)) (T |d02ejfAnnaType|)) 
NIL 
(|OrdinaryDifferentialEquationsSolverCategory|) 
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((|elliptic?| (*1 *2 *3) (AND (|isDomain| *3 (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|d03AgentsPackage|)))) (|central?| (*1 *2 *3 *3 *4) (AND (|isDomain| *4 (|List| (|Expression| (|DoubleFloat|)))) (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|d03AgentsPackage|)))) (|subscriptedVariables| (*1 *2 *2) (AND (|isDomain| *2 (|Expression| (|DoubleFloat|))) (|isDomain| *1 (|d03AgentsPackage|)))) (|varList| (*1 *2 *3 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *1 (|d03AgentsPackage|)) (|isDomain| *3 (|Symbol|))))) 
(CATEGORY |package| (SIGNATURE |varList| ((|List| (|Symbol|)) (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |subscriptedVariables| ((|Expression| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)))) (SIGNATURE |central?| ((|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|List| (|Expression| (|DoubleFloat|))))) (SIGNATURE |elliptic?| ((|Boolean|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))))) 
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(((|d03eefAnnaType|) (|PartialDifferentialEquationsSolverCategory|)) (T |d03eefAnnaType|)) 
NIL 
(|PartialDifferentialEquationsSolverCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) 12)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|d03fafAnnaType|) (|PartialDifferentialEquationsSolverCategory|)) (T |d03fafAnnaType|)) 
NIL 
(|PartialDifferentialEquationsSolverCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|fullDisplay| (((|Void|) $) 36) (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) 38)) (|elt| (($ $ (|QueryEquation|)) 19) (((|DataList| (|String|)) $ (|Symbol|)) 15)) (|display| (((|Void|) $) 34)) (|coerce| (((|OutputForm|) $) 31) (($ (|List| |#1|)) 8)) (= (((|Boolean|) $ $) NIL)) (- (($ $ $) 27)) (+ (($ $ $) 22))) 
(((|Database| |#1|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |elt| ($ $ (|QueryEquation|))) (SIGNATURE |elt| ((|DataList| (|String|)) $ (|Symbol|))) (SIGNATURE + ($ $ $)) (SIGNATURE - ($ $ $)) (SIGNATURE |coerce| ($ (|List| |#1|))) (SIGNATURE |display| ((|Void|) $)) (SIGNATURE |fullDisplay| ((|Void|) $)) (SIGNATURE |fullDisplay| ((|Void|) $ (|PositiveInteger|) (|PositiveInteger|))))) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |elt| ((|String|) $ (|Symbol|))) (SIGNATURE |display| ((|Void|) $)) (SIGNATURE |fullDisplay| ((|Void|) $))))) (T |Database|)) 
((|elt| (*1 *1 *1 *2) (AND (|isDomain| *2 (|QueryEquation|)) (|isDomain| *1 (|Database| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |elt| ((|String|) $ (|Symbol|))) (SIGNATURE |display| ((|Void|) $)) (SIGNATURE |fullDisplay| ((|Void|) $))))))) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|DataList| (|String|))) (|isDomain| *1 (|Database| *4)) (|ofCategory| *4 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |elt| ((|String|) $ *3)) (SIGNATURE |display| ((|Void|) $)) (SIGNATURE |fullDisplay| ((|Void|) $))))))) (+ (*1 *1 *1 *1) (AND (|isDomain| *1 (|Database| *2)) (|ofCategory| *2 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |elt| ((|String|) $ (|Symbol|))) (SIGNATURE |display| ((|Void|) $)) (SIGNATURE |fullDisplay| ((|Void|) $))))))) (- (*1 *1 *1 *1) (AND (|isDomain| *1 (|Database| *2)) (|ofCategory| *2 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |elt| ((|String|) $ (|Symbol|))) (SIGNATURE |display| ((|Void|) $)) (SIGNATURE |fullDisplay| ((|Void|) $))))))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |elt| ((|String|) $ (|Symbol|))) (SIGNATURE |display| ((|Void|) $)) (SIGNATURE |fullDisplay| ((|Void|) $))))) (|isDomain| *1 (|Database| *3)))) (|display| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Database| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |elt| ((|String|) $ (|Symbol|))) (SIGNATURE |display| (*2 $)) (SIGNATURE |fullDisplay| (*2 $))))))) (|fullDisplay| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Database| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |elt| ((|String|) $ (|Symbol|))) (SIGNATURE |display| (*2 $)) (SIGNATURE |fullDisplay| (*2 $))))))) (|fullDisplay| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Database| *4)) (|ofCategory| *4 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |elt| ((|String|) $ (|Symbol|))) (SIGNATURE |display| (*2 $)) (SIGNATURE |fullDisplay| (*2 $)))))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |elt| ($ $ (|QueryEquation|))) (SIGNATURE |elt| ((|DataList| (|String|)) $ (|Symbol|))) (SIGNATURE + ($ $ $)) (SIGNATURE - ($ $ $)) (SIGNATURE |coerce| ($ (|List| |#1|))) (SIGNATURE |display| ((|Void|) $)) (SIGNATURE |fullDisplay| ((|Void|) $)) (SIGNATURE |fullDisplay| ((|Void|) $ (|PositiveInteger|) (|PositiveInteger|))))) 
((|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) 46))) 
(((|DoubleResultantPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |doubleResultant| (|#2| |#4| (|Mapping| |#2| |#2|)))) (|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|)) (T |DoubleResultantPackage|)) 
((|doubleResultant| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| *2 *2)) (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *2))) (|ofCategory| *2 (|UnivariatePolynomialCategory| *5)) (|isDomain| *1 (|DoubleResultantPackage| *5 *2 *6 *3)) (|ofCategory| *3 (|FunctionFieldCategory| *5 *2 *6))))) 
(CATEGORY |package| (SIGNATURE |doubleResultant| (|#2| |#4| (|Mapping| |#2| |#2|)))) 
((|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) 41)) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) 37)) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) 55)) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) 51)) (|irreducible?| (((|Boolean|) |#2|) 48)) (|factorSquareFree| (((|Factored| |#2|) |#2|) 74)) (|factor| (((|Factored| |#2|) |#2|) 73)) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) 35)) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) 66))) 
(((|DistinctDegreeFactorize| |#1| |#2|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#2|) |#2|)) (SIGNATURE |factorSquareFree| ((|Factored| |#2|) |#2|)) (SIGNATURE |distdfact| ((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|))) (SIGNATURE |separateDegrees| ((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|)) (SIGNATURE |separateFactors| ((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))))) (SIGNATURE |exptMod| (|#2| |#2| (|NonNegativeInteger|) |#2|)) (SIGNATURE |trace2PowMod| (|#2| |#2| (|NonNegativeInteger|) |#2|)) (SIGNATURE |tracePowMod| (|#2| |#2| (|NonNegativeInteger|) |#2|)) (SIGNATURE |irreducible?| ((|Boolean|) |#2|))) (|FiniteFieldCategory|) (|UnivariatePolynomialCategory| |#1|)) (T |DistinctDegreeFactorize|)) 
((|irreducible?| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|DistinctDegreeFactorize| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|tracePowMod| (*1 *2 *2 *3 *2) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *1 (|DistinctDegreeFactorize| *4 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)))) (|trace2PowMod| (*1 *2 *2 *3 *2) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *1 (|DistinctDegreeFactorize| *4 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)))) (|exptMod| (*1 *2 *2 *3 *2) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *1 (|DistinctDegreeFactorize| *4 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)))) (|separateFactors| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| *5)))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|DistinctDegreeFactorize| *4 *5)))) (|separateDegrees| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| *3)))) (|isDomain| *1 (|DistinctDegreeFactorize| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|distdfact| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|FiniteFieldCategory|)) (|isDomain| *2 (|Record| (|:| |cont| *5) (|:| |factors| (|List| (|Record| (|:| |irr| *3) (|:| |pow| (|Integer|))))))) (|isDomain| *1 (|DistinctDegreeFactorize| *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|factorSquareFree| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|DistinctDegreeFactorize| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|DistinctDegreeFactorize| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#2|) |#2|)) (SIGNATURE |factorSquareFree| ((|Factored| |#2|) |#2|)) (SIGNATURE |distdfact| ((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|))) (SIGNATURE |separateDegrees| ((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|)) (SIGNATURE |separateFactors| ((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))))) (SIGNATURE |exptMod| (|#2| |#2| (|NonNegativeInteger|) |#2|)) (SIGNATURE |trace2PowMod| (|#2| |#2| (|NonNegativeInteger|) |#2|)) (SIGNATURE |tracePowMod| (|#2| |#2| (|NonNegativeInteger|) |#2|)) (SIGNATURE |irreducible?| ((|Boolean|) |#2|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|wholePart| (((|Integer|) $) NIL (|has| (|Integer|) (|EuclideanDomain|)))) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Integer|) (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Integer|) (|PolynomialFactorizationExplicit|)))) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sign| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedIntegralDomain|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL) (((|Union| (|Symbol|) "failed") $) NIL (|has| (|Integer|) (|RetractableTo| (|Symbol|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| (|Integer|) (|RetractableTo| (|Integer|)))) (((|Union| (|Integer|) "failed") $) NIL (|has| (|Integer|) (|RetractableTo| (|Integer|))))) (|retract| (((|Integer|) $) NIL) (((|Symbol|) $) NIL (|has| (|Integer|) (|RetractableTo| (|Symbol|)))) (((|Fraction| (|Integer|)) $) NIL (|has| (|Integer|) (|RetractableTo| (|Integer|)))) (((|Integer|) $) NIL (|has| (|Integer|) (|RetractableTo| (|Integer|))))) (|rem| (($ $ $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| (|Integer|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| (|Integer|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| (|Integer|)) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) NIL (|has| (|Integer|) (|IntegerNumberSystem|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|positive?| (((|Boolean|) $) NIL (|has| (|Integer|) (|OrderedIntegralDomain|)))) (|patternMatch| (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (|has| (|Integer|) (|PatternMatchable| (|Integer|)))) (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (|has| (|Integer|) (|PatternMatchable| (|Float|))))) (|one?| (((|Boolean|) $) NIL)) (|numerator| (($ $) NIL)) (|numer| (((|Integer|) $) NIL)) (|nextItem| (((|Union| $ "failed") $) NIL (|has| (|Integer|) (|StepThrough|)))) (|negative?| (((|Boolean|) $) NIL (|has| (|Integer|) (|OrderedIntegralDomain|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|min| (($ $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|map| (($ (|Mapping| (|Integer|) (|Integer|)) $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|init| (($) NIL (|has| (|Integer|) (|StepThrough|)) CONST)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|fractionPart| (($ $) NIL (|has| (|Integer|) (|EuclideanDomain|))) (((|Fraction| (|Integer|)) $) NIL)) (|floor| (((|Integer|) $) NIL (|has| (|Integer|) (|IntegerNumberSystem|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Integer|) (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Integer|) (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|eval| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) NIL (|has| (|Integer|) (|Evalable| (|Integer|)))) (($ $ (|Integer|) (|Integer|)) NIL (|has| (|Integer|) (|Evalable| (|Integer|)))) (($ $ (|Equation| (|Integer|))) NIL (|has| (|Integer|) (|Evalable| (|Integer|)))) (($ $ (|List| (|Equation| (|Integer|)))) NIL (|has| (|Integer|) (|Evalable| (|Integer|)))) (($ $ (|List| (|Symbol|)) (|List| (|Integer|))) NIL (|has| (|Integer|) (|InnerEvalable| (|Symbol|) (|Integer|)))) (($ $ (|Symbol|) (|Integer|)) NIL (|has| (|Integer|) (|InnerEvalable| (|Symbol|) (|Integer|))))) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|elt| (($ $ (|Integer|)) NIL (|has| (|Integer|) (|Eltable| (|Integer|) (|Integer|))))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|differentiate| (($ $) NIL (|has| (|Integer|) (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|Integer|) (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| (|Integer|) (|Integer|)) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| (|Integer|) (|Integer|))) NIL)) (|denominator| (($ $) NIL)) (|denom| (((|Integer|) $) NIL)) (|decimal| (($ (|Fraction| (|Integer|))) 8)) (|convert| (((|Pattern| (|Integer|)) $) NIL (|has| (|Integer|) (|ConvertibleTo| (|Pattern| (|Integer|))))) (((|Pattern| (|Float|)) $) NIL (|has| (|Integer|) (|ConvertibleTo| (|Pattern| (|Float|))))) (((|InputForm|) $) NIL (|has| (|Integer|) (|ConvertibleTo| (|InputForm|)))) (((|Float|) $) NIL (|has| (|Integer|) (|RealConstant|))) (((|DoubleFloat|) $) NIL (|has| (|Integer|) (|RealConstant|)))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| (|Integer|) (|PolynomialFactorizationExplicit|))))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) 7) (($ (|Integer|)) NIL) (($ (|Symbol|)) NIL (|has| (|Integer|) (|RetractableTo| (|Symbol|)))) (((|Fraction| (|Integer|)) $) NIL) (((|RadixExpansion| 10) $) 9)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| (|Integer|) (|PolynomialFactorizationExplicit|))) (|has| (|Integer|) (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|ceiling| (((|Integer|) $) NIL (|has| (|Integer|) (|IntegerNumberSystem|)))) (|associates?| (((|Boolean|) $ $) NIL)) (|abs| (($ $) NIL (|has| (|Integer|) (|OrderedIntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($ $) NIL (|has| (|Integer|) (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|Integer|) (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| (|Integer|) (|Integer|)) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| (|Integer|) (|Integer|))) NIL)) (>= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (/ (($ $ $) NIL) (($ (|Integer|) (|Integer|)) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ (|Integer|) $) NIL) (($ $ (|Integer|)) NIL))) 
(((|DecimalExpansion|) (|Join| (|QuotientFieldCategory| (|Integer|)) (CATEGORY |domain| (SIGNATURE |coerce| ((|Fraction| (|Integer|)) $)) (SIGNATURE |coerce| ((|RadixExpansion| 10) $)) (SIGNATURE |fractionPart| ((|Fraction| (|Integer|)) $)) (SIGNATURE |decimal| ($ (|Fraction| (|Integer|))))))) (T |DecimalExpansion|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|DecimalExpansion|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|RadixExpansion| 10)) (|isDomain| *1 (|DecimalExpansion|)))) (|fractionPart| (*1 *2 *1) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|DecimalExpansion|)))) (|decimal| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|DecimalExpansion|))))) 
(|Join| (|QuotientFieldCategory| (|Integer|)) (CATEGORY |domain| (SIGNATURE |coerce| ((|Fraction| (|Integer|)) $)) (SIGNATURE |coerce| ((|RadixExpansion| 10) $)) (SIGNATURE |fractionPart| ((|Fraction| (|Integer|)) $)) (SIGNATURE |decimal| ($ (|Fraction| (|Integer|)))))) 
((|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) 27) (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) 23)) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) 16))) 
(((|ElementaryFunctionDefiniteIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |integrate| ((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)))) (SIGNATURE |integrate| ((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|))) (SIGNATURE |innerint| ((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)))) (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|))) (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| |#1|))) (T |ElementaryFunctionDefiniteIntegration|)) 
((|innerint| (*1 *2 *3 *4 *5 *5 *6) (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *6 (|Boolean|)) (|ofCategory| *7 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|ofCategory| *3 (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *7))) (|isDomain| *2 (|Union| (|:| |f1| (|OrderedCompletion| *3)) (|:| |f2| (|List| (|OrderedCompletion| *3))) (|:| |fail| "failed") (|:| |pole| "potentialPole"))) (|isDomain| *1 (|ElementaryFunctionDefiniteIntegration| *7 *3)) (|isDomain| *5 (|OrderedCompletion| *3)))) (|integrate| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|SegmentBinding| (|OrderedCompletion| *3))) (|isDomain| *5 (|String|)) (|ofCategory| *3 (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *6))) (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Union| (|:| |f1| (|OrderedCompletion| *3)) (|:| |f2| (|List| (|OrderedCompletion| *3))) (|:| |fail| "failed") (|:| |pole| "potentialPole"))) (|isDomain| *1 (|ElementaryFunctionDefiniteIntegration| *6 *3)))) (|integrate| (*1 *2 *3 *4) (AND (|isDomain| *4 (|SegmentBinding| (|OrderedCompletion| *3))) (|ofCategory| *3 (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *5))) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Union| (|:| |f1| (|OrderedCompletion| *3)) (|:| |f2| (|List| (|OrderedCompletion| *3))) (|:| |fail| "failed") (|:| |pole| "potentialPole"))) (|isDomain| *1 (|ElementaryFunctionDefiniteIntegration| *5 *3))))) 
(CATEGORY |package| (SIGNATURE |integrate| ((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)))) (SIGNATURE |integrate| ((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|))) (SIGNATURE |innerint| ((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)))) 
((|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|String|)) 44) (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) 41) (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|String|)) 45) (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) 17))) 
(((|RationalFunctionDefiniteIntegration| |#1|) (CATEGORY |package| (SIGNATURE |integrate| ((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))))) (SIGNATURE |integrate| ((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|String|))) (SIGNATURE |integrate| ((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))))) (SIGNATURE |integrate| ((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|String|)))) (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (T |RationalFunctionDefiniteIntegration|)) 
((|integrate| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| *6))))) (|isDomain| *5 (|String|)) (|isDomain| *3 (|Fraction| (|Polynomial| *6))) (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Union| (|:| |f1| (|OrderedCompletion| (|Expression| *6))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| *6)))) (|:| |fail| "failed") (|:| |pole| "potentialPole"))) (|isDomain| *1 (|RationalFunctionDefiniteIntegration| *6)))) (|integrate| (*1 *2 *3 *4) (AND (|isDomain| *4 (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| *5))))) (|isDomain| *3 (|Fraction| (|Polynomial| *5))) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Union| (|:| |f1| (|OrderedCompletion| (|Expression| *5))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| *5)))) (|:| |fail| "failed") (|:| |pole| "potentialPole"))) (|isDomain| *1 (|RationalFunctionDefiniteIntegration| *5)))) (|integrate| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Fraction| (|Polynomial| *6))) (|isDomain| *4 (|SegmentBinding| (|OrderedCompletion| (|Expression| *6)))) (|isDomain| *5 (|String|)) (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Union| (|:| |f1| (|OrderedCompletion| (|Expression| *6))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| *6)))) (|:| |fail| "failed") (|:| |pole| "potentialPole"))) (|isDomain| *1 (|RationalFunctionDefiniteIntegration| *6)))) (|integrate| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5))) (|isDomain| *4 (|SegmentBinding| (|OrderedCompletion| (|Expression| *5)))) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Union| (|:| |f1| (|OrderedCompletion| (|Expression| *5))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| *5)))) (|:| |fail| "failed") (|:| |pole| "potentialPole"))) (|isDomain| *1 (|RationalFunctionDefiniteIntegration| *5))))) 
(CATEGORY |package| (SIGNATURE |integrate| ((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))))) (SIGNATURE |integrate| ((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|String|))) (SIGNATURE |integrate| ((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))))) (SIGNATURE |integrate| ((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|String|)))) 
((|reduce| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#1|)) (|:| |deg| (|PositiveInteger|))) (|SparseUnivariatePolynomial| |#1|)) 20)) (|expand| (((|List| (|Expression| |#2|)) (|Expression| |#2|) (|PositiveInteger|)) 42))) 
(((|DegreeReductionPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |reduce| ((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#1|)) (|:| |deg| (|PositiveInteger|))) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |expand| ((|List| (|Expression| |#2|)) (|Expression| |#2|) (|PositiveInteger|)))) (|Ring|) (|Join| (|IntegralDomain|) (|OrderedSet|))) (T |DegreeReductionPackage|)) 
((|expand| (*1 *2 *3 *4) (AND (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *6 (|Join| (|IntegralDomain|) (|OrderedSet|))) (|isDomain| *2 (|List| (|Expression| *6))) (|isDomain| *1 (|DegreeReductionPackage| *5 *6)) (|isDomain| *3 (|Expression| *6)) (|ofCategory| *5 (|Ring|)))) (|reduce| (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Record| (|:| |pol| (|SparseUnivariatePolynomial| *4)) (|:| |deg| (|PositiveInteger|)))) (|isDomain| *1 (|DegreeReductionPackage| *4 *5)) (|isDomain| *3 (|SparseUnivariatePolynomial| *4)) (|ofCategory| *5 (|Join| (|IntegralDomain|) (|OrderedSet|)))))) 
(CATEGORY |package| (SIGNATURE |reduce| ((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#1|)) (|:| |deg| (|PositiveInteger|))) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |expand| ((|List| (|Expression| |#2|)) (|Expression| |#2|) (|PositiveInteger|)))) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|top!| ((|#1| $) 25)) (|top| ((|#1| $) 26)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|sample| (($) NIL T CONST)) (|rotate!| (($ $) NIL)) (|reverse!| (($ $) 32)) (|push!| ((|#1| |#1| $) NIL)) (|pop!| ((|#1| $) NIL)) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|length| (((|NonNegativeInteger|) $) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|inspect| ((|#1| $) NIL)) (|insertTop!| ((|#1| |#1| $) 29)) (|insertBottom!| ((|#1| |#1| $) 31)) (|insert!| (($ |#1| $) NIL)) (|height| (((|NonNegativeInteger|) $) 27)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|front| ((|#1| $) NIL)) (|extractTop!| ((|#1| $) 24)) (|extractBottom!| ((|#1| $) 8)) (|extract!| ((|#1| $) NIL)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|enqueue!| ((|#1| |#1| $) NIL)) (|empty?| (((|Boolean|) $) 15)) (|empty| (($) NIL)) (|dequeue!| ((|#1| $) NIL)) (|dequeue| (($) NIL) (($ (|List| |#1|)) 13)) (|depth| (((|NonNegativeInteger|) $) 28)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|)))) (|bottom!| ((|#1| $) 9)) (|bag| (($ (|List| |#1|)) NIL)) (|back| ((|#1| $) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|Dequeue| |#1|) (|Join| (|DequeueAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |dequeue| ($ (|List| |#1|))) (SIGNATURE |dequeue!| (|#1| $)) (SIGNATURE |extract!| (|#1| $)) (SIGNATURE |enqueue!| (|#1| |#1| $)) (SIGNATURE |insert!| ($ |#1| $)) (SIGNATURE |inspect| (|#1| $)) (SIGNATURE |front| (|#1| $)) (SIGNATURE |back| (|#1| $)) (SIGNATURE |rotate!| ($ $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |less?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |size?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |bag| ($ (|List| |#1|))) (SIGNATURE |empty?| ((|Boolean|) $)) (SIGNATURE |empty| ($)) (SIGNATURE |sample| ($)) (SIGNATURE |copy| ($ $)) (SIGNATURE |eq?| ((|Boolean|) $ $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (SIGNATURE |depth| ((|NonNegativeInteger|) $)) (SIGNATURE |dequeue| ($)) (SIGNATURE |height| ((|NonNegativeInteger|) $)) (SIGNATURE |top| (|#1| $)) (SIGNATURE |bottom!| (|#1| $)) (SIGNATURE |extractBottom!| (|#1| $)) (SIGNATURE |extractTop!| (|#1| $)) (SIGNATURE |insertBottom!| (|#1| |#1| $)) (SIGNATURE |insertTop!| (|#1| |#1| $)) (SIGNATURE |pop!| (|#1| $)) (SIGNATURE |push!| (|#1| |#1| $)) (SIGNATURE |reverse!| ($ $)) (SIGNATURE |top!| (|#1| $)) (IF (|has| $ (ATTRIBUTE |shallowlyMutable|)) (SIGNATURE |map!| ($ (|Mapping| |#1| |#1|) $)) |noBranch|) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |latex| ((|String|) $)) (SIGNATURE |hash| ((|SingleInteger|) $)) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE = ((|Boolean|) $ $)) (SIGNATURE ~= ((|Boolean|) $ $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (PROGN (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |#| ((|NonNegativeInteger|) $)) (SIGNATURE |parts| ((|List| |#1|) $)) (SIGNATURE |members| ((|List| |#1|) $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |member?| ((|Boolean|) |#1| $)) (SIGNATURE |count| ((|NonNegativeInteger|) |#1| $))) |noBranch|) |noBranch|))) (|SetCategory|)) (T |Dequeue|)) 
((|eq?| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|copy| (*1 *1 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|empty| (*1 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|empty?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|less?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *4)) (|ofCategory| *4 (|SetCategory|)))) (|more?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *4)) (|ofCategory| *4 (|SetCategory|)))) (|size?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *4)) (|ofCategory| *4 (|SetCategory|)))) (|sample| (*1 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|#| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Dequeue| *3)))) (|map!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Dequeue| *3)))) (|any?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *4)))) (|every?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *4)))) (|count| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Dequeue| *4)))) (|parts| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|members| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|count| (*1 *2 *3 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|member?| (*1 *2 *3 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|latex| (*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|hash| (*1 *2 *1) (AND (|isDomain| *2 (|SingleInteger|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (= (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (~= (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|bag| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Dequeue| *3)))) (|extract!| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|insert!| (*1 *1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|inspect| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|push!| (*1 *2 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|pop!| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|top| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|depth| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|back| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|front| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|length| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|rotate!| (*1 *1 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|dequeue!| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|enqueue!| (*1 *2 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|dequeue| (*1 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|dequeue| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Dequeue| *3)))) (|height| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|top!| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|bottom!| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|insertTop!| (*1 *2 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|insertBottom!| (*1 *2 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|extractTop!| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|extractBottom!| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|reverse!| (*1 *1 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|))))) 
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((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|totalDifferential| (($ (|Expression| |#1|)) 23)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|retractable?| (((|Boolean|) $) NIL)) (|retractIfCan| (((|Union| (|Expression| |#1|) "failed") $) NIL)) (|retract| (((|Expression| |#1|) $) NIL)) (|reductum| (($ $) 31)) (|recip| (((|Union| $ "failed") $) NIL)) (|proj| (($ $ (|NonNegativeInteger|)) 92)) (|one?| (((|Boolean|) $) NIL)) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) NIL)) (|lieDerivative| (($ (|Vector| (|Expression| |#1|)) $ (|SquareMatrix| (|#| |#2|) (|Expression| |#1|))) 103)) (|leadingCoefficient| (((|Expression| |#1|) $) 90)) (|leadingBasisTerm| (($ $) 30)) (|latex| (((|String|) $) NIL)) (|interiorProduct| (($ (|Vector| (|Expression| |#1|)) $ (|SquareMatrix| (|#| |#2|) (|Expression| |#1|))) 102)) (|homogeneous?| (((|Boolean|) $) NIL)) (|hodgeStar| (($ $ (|SquareMatrix| (|#| |#2|) (|Expression| |#1|))) 91)) (|hash| (((|SingleInteger|) $) NIL)) (|generator| (($ (|NonNegativeInteger|)) 94)) (|exteriorDifferential| (($ $) 32)) (|dot| (((|Expression| |#1|) $ $ (|SquareMatrix| (|#| |#2|) (|Expression| |#1|))) 86)) (|dim| (((|NonNegativeInteger|) $) 58)) (|degree| (((|NonNegativeInteger|) $) 98)) (|coerce| (((|OutputForm|) $) 107) (($ (|Integer|)) NIL) (($ (|Expression| |#1|)) NIL)) (|coefficient| (((|Expression| |#1|) $ $) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 25 T CONST)) (|One| (($) 50 T CONST)) (= (((|Boolean|) $ $) 28)) (- (($ $) 97) (($ $ $) NIL)) (+ (($ $ $) 19)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 24) (($ (|Expression| |#1|) $) 18))) 
(((|DeRhamComplex| |#1| |#2|) (|Join| (|LeftAlgebra| (|Expression| |#1|)) (|RetractableTo| (|Expression| |#1|)) (CATEGORY |domain| (SIGNATURE |leadingCoefficient| ((|Expression| |#1|) $)) (SIGNATURE |leadingBasisTerm| ($ $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |coefficient| ((|Expression| |#1|) $ $)) (SIGNATURE |generator| ($ (|NonNegativeInteger|))) (SIGNATURE |homogeneous?| ((|Boolean|) $)) (SIGNATURE |retractable?| ((|Boolean|) $)) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |map| ($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $)) (SIGNATURE |totalDifferential| ($ (|Expression| |#1|))) (SIGNATURE |exteriorDifferential| ($ $)) (SIGNATURE |dim| ((|NonNegativeInteger|) $)) (SIGNATURE |hodgeStar| ($ $ (|SquareMatrix| (|#| |#2|) (|Expression| |#1|)))) (SIGNATURE |dot| ((|Expression| |#1|) $ $ (|SquareMatrix| (|#| |#2|) (|Expression| |#1|)))) (SIGNATURE |proj| ($ $ (|NonNegativeInteger|))) (SIGNATURE |interiorProduct| ($ (|Vector| (|Expression| |#1|)) $ (|SquareMatrix| (|#| |#2|) (|Expression| |#1|)))) (SIGNATURE |lieDerivative| ($ (|Vector| (|Expression| |#1|)) $ (|SquareMatrix| (|#| |#2|) (|Expression| |#1|)))))) (|Join| (|Ring|) (|OrderedSet|)) (|List| (|Symbol|))) (T |DeRhamComplex|)) 
((|leadingCoefficient| (*1 *2 *1) (AND (|isDomain| *2 (|Expression| *3)) (|isDomain| *1 (|DeRhamComplex| *3 *4)) (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|))) (|ofType| *4 (|List| (|Symbol|))))) (|leadingBasisTerm| (*1 *1 *1) (AND (|isDomain| *1 (|DeRhamComplex| *2 *3)) (|ofCategory| *2 (|Join| (|Ring|) (|OrderedSet|))) (|ofType| *3 (|List| (|Symbol|))))) (|reductum| (*1 *1 *1) (AND (|isDomain| *1 (|DeRhamComplex| *2 *3)) (|ofCategory| *2 (|Join| (|Ring|) (|OrderedSet|))) (|ofType| *3 (|List| (|Symbol|))))) (|coefficient| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Expression| *3)) (|isDomain| *1 (|DeRhamComplex| *3 *4)) (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|))) (|ofType| *4 (|List| (|Symbol|))))) (|generator| (*1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|DeRhamComplex| *3 *4)) (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|))) (|ofType| *4 (|List| (|Symbol|))))) (|homogeneous?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|DeRhamComplex| *3 *4)) (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|))) (|ofType| *4 (|List| (|Symbol|))))) (|retractable?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|DeRhamComplex| *3 *4)) (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|))) (|ofType| *4 (|List| (|Symbol|))))) (|degree| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|DeRhamComplex| *3 *4)) (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|))) (|ofType| *4 (|List| (|Symbol|))))) (|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Expression| *3) (|Expression| *3))) (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|))) (|isDomain| *1 (|DeRhamComplex| *3 *4)) (|ofType| *4 (|List| (|Symbol|))))) (|totalDifferential| (*1 *1 *2) (AND (|isDomain| *2 (|Expression| *3)) (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|))) (|isDomain| *1 (|DeRhamComplex| *3 *4)) (|ofType| *4 (|List| (|Symbol|))))) (|exteriorDifferential| (*1 *1 *1) (AND (|isDomain| *1 (|DeRhamComplex| *2 *3)) (|ofCategory| *2 (|Join| (|Ring|) (|OrderedSet|))) (|ofType| *3 (|List| (|Symbol|))))) (|dim| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|DeRhamComplex| *3 *4)) (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|))) (|ofType| *4 (|List| (|Symbol|))))) (|hodgeStar| (*1 *1 *1 *2) (AND (|isDomain| *2 (|SquareMatrix| (|#| *4) (|Expression| *3))) (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|))) (|ofType| *4 (|List| (|Symbol|))) (|isDomain| *1 (|DeRhamComplex| *3 *4)))) (|dot| (*1 *2 *1 *1 *3) (AND (|isDomain| *3 (|SquareMatrix| (|#| *5) (|Expression| *4))) (|ofType| *5 (|List| (|Symbol|))) (|isDomain| *2 (|Expression| *4)) (|isDomain| *1 (|DeRhamComplex| *4 *5)) (|ofCategory| *4 (|Join| (|Ring|) (|OrderedSet|))))) (|proj| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|DeRhamComplex| *3 *4)) (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|))) (|ofType| *4 (|List| (|Symbol|))))) (|interiorProduct| (*1 *1 *2 *1 *3) (AND (|isDomain| *2 (|Vector| (|Expression| *4))) (|isDomain| *3 (|SquareMatrix| (|#| *5) (|Expression| *4))) (|ofCategory| *4 (|Join| (|Ring|) (|OrderedSet|))) (|ofType| *5 (|List| (|Symbol|))) (|isDomain| *1 (|DeRhamComplex| *4 *5)))) (|lieDerivative| (*1 *1 *2 *1 *3) (AND (|isDomain| *2 (|Vector| (|Expression| *4))) (|isDomain| *3 (|SquareMatrix| (|#| *5) (|Expression| *4))) (|ofCategory| *4 (|Join| (|Ring|) (|OrderedSet|))) (|ofType| *5 (|List| (|Symbol|))) (|isDomain| *1 (|DeRhamComplex| *4 *5))))) 
(|Join| (|LeftAlgebra| (|Expression| |#1|)) (|RetractableTo| (|Expression| |#1|)) (CATEGORY |domain| (SIGNATURE |leadingCoefficient| ((|Expression| |#1|) $)) (SIGNATURE |leadingBasisTerm| ($ $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |coefficient| ((|Expression| |#1|) $ $)) (SIGNATURE |generator| ($ (|NonNegativeInteger|))) (SIGNATURE |homogeneous?| ((|Boolean|) $)) (SIGNATURE |retractable?| ((|Boolean|) $)) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |map| ($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $)) (SIGNATURE |totalDifferential| ($ (|Expression| |#1|))) (SIGNATURE |exteriorDifferential| ($ $)) (SIGNATURE |dim| ((|NonNegativeInteger|) $)) (SIGNATURE |hodgeStar| ($ $ (|SquareMatrix| (|#| |#2|) (|Expression| |#1|)))) (SIGNATURE |dot| ((|Expression| |#1|) $ $ (|SquareMatrix| (|#| |#2|) (|Expression| |#1|)))) (SIGNATURE |proj| ($ $ (|NonNegativeInteger|))) (SIGNATURE |interiorProduct| ($ (|Vector| (|Expression| |#1|)) $ (|SquareMatrix| (|#| |#2|) (|Expression| |#1|)))) (SIGNATURE |lieDerivative| ($ (|Vector| (|Expression| |#1|)) $ (|SquareMatrix| (|#| |#2|) (|Expression| |#1|)))))) 
((|ignore?| (((|Boolean|) (|String|)) 22)) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) 32)) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) 73) (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) 74))) 
(((|DefiniteIntegrationTools| |#1| |#2|) (CATEGORY |package| (SIGNATURE |ignore?| ((|Boolean|) (|String|))) (SIGNATURE |computeInt| ((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|))) (SIGNATURE |checkForZero| ((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|))) (SIGNATURE |checkForZero| ((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)))) (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|))) (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| |#1|))) (T |DefiniteIntegrationTools|)) 
((|checkForZero| (*1 *2 *3 *4 *4 *2) (|partial| AND (|isDomain| *2 (|Boolean|)) (|isDomain| *3 (|SparseUnivariatePolynomial| *6)) (|isDomain| *4 (|OrderedCompletion| *6)) (|ofCategory| *6 (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *5))) (|ofCategory| *5 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|DefiniteIntegrationTools| *5 *6)))) (|checkForZero| (*1 *2 *3 *4 *5 *5 *2) (|partial| AND (|isDomain| *2 (|Boolean|)) (|isDomain| *3 (|Polynomial| *6)) (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|OrderedCompletion| *7)) (|ofCategory| *6 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|ofCategory| *7 (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *6))) (|isDomain| *1 (|DefiniteIntegrationTools| *6 *7)))) (|computeInt| (*1 *2 *3 *4 *2 *2 *5) (|partial| AND (|isDomain| *2 (|OrderedCompletion| *4)) (|isDomain| *3 (|Kernel| *4)) (|isDomain| *5 (|Boolean|)) (|ofCategory| *4 (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *6))) (|ofCategory| *6 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|DefiniteIntegrationTools| *6 *4)))) (|ignore?| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|ofCategory| *4 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|DefiniteIntegrationTools| *4 *5)) (|ofCategory| *5 (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *4)))))) 
(CATEGORY |package| (SIGNATURE |ignore?| ((|Boolean|) (|String|))) (SIGNATURE |computeInt| ((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|))) (SIGNATURE |checkForZero| ((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|))) (SIGNATURE |checkForZero| ((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)))) 
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NIL)) (|Zero| (($) 41 T CONST)) (|One| (($) 42 T CONST)) (|OMwrite| (((|String|) $) 19) (((|String|) $ (|Boolean|)) 21) (((|Void|) (|OpenMathDevice|) $) 22) (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) 23)) (|Gamma| (($ $) 118) (($ $ $) NIL)) (D (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (|Beta| (($ $ $) 114)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 60)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 52)) (/ (($ $ $) 93) (($ $ (|Integer|)) 61)) (- (($ $) 53) (($ $ $) 55)) (+ (($ $ $) 54)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) 64) (($ $ (|Fraction| (|Integer|))) 148) (($ $ $) 65)) (* (($ (|PositiveInteger|) $) 36) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 57) (($ $ $) 56) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL))) 
(((|DoubleFloat|) (|Join| (|FloatingPointSystem|) (|DifferentialRing|) (|OpenMath|) (|TranscendentalFunctionCategory|) (|SpecialFunctionCategory|) (|ConvertibleTo| (|InputForm|)) (CATEGORY |domain| (SIGNATURE / ($ $ (|Integer|))) (SIGNATURE ** ($ $ $)) (SIGNATURE |exp1| ($)) (SIGNATURE |hash| ((|Integer|) $)) (SIGNATURE |log2| ($ $)) (SIGNATURE |log10| ($ $)) (SIGNATURE |atan| ($ $ $)) (SIGNATURE |Gamma| ($ $)) (SIGNATURE |Beta| ($ $ $)) (SIGNATURE |doubleFloatFormat| ((|String|) (|String|))) (SIGNATURE |rationalApproximation| ((|Fraction| (|Integer|)) $ (|NonNegativeInteger|))) (SIGNATURE |rationalApproximation| ((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |machineFraction| ((|Fraction| (|Integer|)) $)) (SIGNATURE |integerDecode| ((|List| (|Integer|)) $))))) (T |DoubleFloat|)) 
((** (*1 *1 *1 *1) (|isDomain| *1 (|DoubleFloat|))) (|Gamma| (*1 *1 *1) (|isDomain| *1 (|DoubleFloat|))) (|Beta| (*1 *1 *1 *1) (|isDomain| *1 (|DoubleFloat|))) (/ (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|DoubleFloat|)))) (|exp1| (*1 *1) (|isDomain| *1 (|DoubleFloat|))) (|hash| (*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|DoubleFloat|)))) (|log2| (*1 *1 *1) (|isDomain| *1 (|DoubleFloat|))) (|log10| (*1 *1 *1) (|isDomain| *1 (|DoubleFloat|))) (|atan| (*1 *1 *1 *1) (|isDomain| *1 (|DoubleFloat|))) (|doubleFloatFormat| (*1 *2 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|DoubleFloat|)))) (|rationalApproximation| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|DoubleFloat|)))) (|rationalApproximation| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|DoubleFloat|)))) (|machineFraction| (*1 *2 *1) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|DoubleFloat|)))) (|integerDecode| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|DoubleFloat|))))) 
(|Join| (|FloatingPointSystem|) (|DifferentialRing|) (|OpenMath|) (|TranscendentalFunctionCategory|) (|SpecialFunctionCategory|) (|ConvertibleTo| (|InputForm|)) (CATEGORY |domain| (SIGNATURE / ($ $ (|Integer|))) (SIGNATURE ** ($ $ $)) (SIGNATURE |exp1| ($)) (SIGNATURE |hash| ((|Integer|) $)) (SIGNATURE |log2| ($ $)) (SIGNATURE |log10| ($ $)) (SIGNATURE |atan| ($ $ $)) (SIGNATURE |Gamma| ($ $)) (SIGNATURE |Beta| ($ $ $)) (SIGNATURE |doubleFloatFormat| ((|String|) (|String|))) (SIGNATURE |rationalApproximation| ((|Fraction| (|Integer|)) $ (|NonNegativeInteger|))) (SIGNATURE |rationalApproximation| ((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |machineFraction| ((|Fraction| (|Integer|)) $)) (SIGNATURE |integerDecode| ((|List| (|Integer|)) $)))) 
((~= (((|Boolean|) $ $) NIL (|has| (|DoubleFloat|) (|SetCategory|)))) (|zero?| (((|Boolean|) $) NIL)) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) NIL)) (|vertConcat| (($ $ $) NIL)) (|transpose| (($ (|DoubleFloatVector|)) NIL) (($ $) NIL)) (|symmetric?| (((|Boolean|) $) NIL)) (|swapRows!| (($ $ (|Integer|) (|Integer|)) NIL)) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) NIL)) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) NIL)) (|squareTop| (($ $) NIL)) (|square?| (((|Boolean|) $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) NIL)) (|setelt| (((|DoubleFloat|) $ (|Integer|) (|Integer|) (|DoubleFloat|)) NIL) (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) NIL)) (|setRow!| (($ $ (|Integer|) (|DoubleFloatVector|)) NIL)) (|setColumn!| (($ $ (|Integer|) (|DoubleFloatVector|)) NIL)) (|scalarMatrix| (($ (|NonNegativeInteger|) (|DoubleFloat|)) NIL)) (|sample| (($) NIL T CONST)) (|rowEchelon| 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(|minRowIndex| (((|Integer|) $) 7)) (|minColIndex| (((|Integer|) $) 8)) (|members| (((|List| (|DoubleFloat|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|DoubleFloat|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|DoubleFloat|) (|SetCategory|))))) (|maxRowIndex| (((|Integer|) $) 12)) (|maxColIndex| (((|Integer|) $) 13)) (|matrix| (($ (|List| (|List| (|DoubleFloat|)))) NIL) (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| (|DoubleFloat|) (|Integer|) (|Integer|))) NIL)) (|map!| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) $) NIL)) (|map| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) $) NIL) (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) $ $) NIL) (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) $ $ (|DoubleFloat|)) NIL)) (|listOfLists| (((|List| (|List| (|DoubleFloat|))) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| (|DoubleFloat|) 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(|DoubleFloat|))) (|has| (|DoubleFloat|) (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) 17)) (|elt| (((|DoubleFloat|) $ (|Integer|) (|Integer|)) NIL) (((|DoubleFloat|) $ (|Integer|) (|Integer|) (|DoubleFloat|)) NIL) (($ $ (|List| (|Integer|)) (|List| (|Integer|))) NIL)) (|diagonalMatrix| (($ (|List| (|DoubleFloat|))) NIL) (($ (|List| $)) NIL)) (|diagonal?| (((|Boolean|) $) NIL)) (|determinant| (((|DoubleFloat|) $) NIL (|has| (|DoubleFloat|) (ATTRIBUTE (|commutative| "*"))))) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|DoubleFloat|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) (|DoubleFloat|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|DoubleFloat|) (|SetCategory|))))) (|copy| (($ $) NIL)) (|columnSpace| (((|List| (|DoubleFloatVector|)) $) NIL (|has| (|DoubleFloat|) (|EuclideanDomain|)))) (|column| (((|DoubleFloatVector|) $ (|Integer|)) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| (|DoubleFloat|) (|SetCategory|))) (($ (|DoubleFloatVector|)) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|DoubleFloat|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|antisymmetric?| (((|Boolean|) $) NIL)) (= (((|Boolean|) $ $) NIL (|has| (|DoubleFloat|) (|SetCategory|)))) (/ (($ $ (|DoubleFloat|)) NIL (|has| (|DoubleFloat|) (|Field|)))) (- (($ $ $) NIL) (($ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| (|DoubleFloat|) (|Field|)))) (* (($ $ $) NIL) (($ (|DoubleFloat|) $) NIL) (($ $ (|DoubleFloat|)) NIL) (($ (|Integer|) $) NIL) (((|DoubleFloatVector|) $ (|DoubleFloatVector|)) NIL) (((|DoubleFloatVector|) (|DoubleFloatVector|) $) NIL)) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|DoubleFloatMatrix|) (|Join| (|MatrixCategory| (|DoubleFloat|) (|DoubleFloatVector|) (|DoubleFloatVector|)) (CATEGORY |domain| (SIGNATURE |qnew| ($ (|Integer|) (|Integer|)))))) (T |DoubleFloatMatrix|)) 
((|qnew| (*1 *1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|DoubleFloatMatrix|))))) 
(|Join| (|MatrixCategory| (|DoubleFloat|) (|DoubleFloatVector|) (|DoubleFloatVector|)) (CATEGORY |domain| (SIGNATURE |qnew| ($ (|Integer|) (|Integer|))))) 
((|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) 61) (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) 62)) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) 63) (((|DoubleFloat|) (|DoubleFloat|)) 64)) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) 69) (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) 72)) (|fresnelS| (((|Float|) (|Float|)) 60)) (|fresnelC| (((|Float|) (|Float|)) 59)) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) 74) (((|DoubleFloat|) (|DoubleFloat|)) 73)) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) 91) (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) 83)) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) 94) (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) 92)) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) 65) (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) 66)) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) 67) (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) 68)) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) 105) (((|DoubleFloat|) (|DoubleFloat|)) 104)) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) 99) (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) 103)) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) 7) (((|DoubleFloat|) (|DoubleFloat|)) 9)) (|En| (((|OnePointCompletion| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|)) 23)) (|Ei6| (((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|))) 36)) (|Ei5| (((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|))) 35)) (|Ei4| (((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|))) 34)) (|Ei3| (((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|))) 33)) (|Ei2| (((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|))) 32)) (|Ei1| (((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|))) 31)) (|Ei| (((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|))) 37)) (E1 (((|OnePointCompletion| (|DoubleFloat|)) (|DoubleFloat|)) 22)) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) 79) (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) 75))) 
(((|DoubleFloatSpecialFunctions|) (CATEGORY |package| (SIGNATURE |Gamma| ((|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |Gamma| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE E1 ((|OnePointCompletion| (|DoubleFloat|)) (|DoubleFloat|))) (SIGNATURE |En| ((|OnePointCompletion| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|))) (SIGNATURE |Ei| ((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|)))) (SIGNATURE |Ei1| ((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|)))) (SIGNATURE |Ei2| ((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|)))) (SIGNATURE |Ei3| ((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|)))) (SIGNATURE |Ei4| ((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|)))) (SIGNATURE |Ei5| ((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|)))) (SIGNATURE |Ei6| ((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|)))) (SIGNATURE |Beta| ((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |Beta| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |logGamma| ((|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |logGamma| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |digamma| ((|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |digamma| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |polygamma| ((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|))) (SIGNATURE |polygamma| ((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|)))) (SIGNATURE |besselJ| ((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |besselJ| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |besselY| ((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |besselY| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |besselI| ((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |besselI| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |besselK| ((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |besselK| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |airyAi| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |airyAi| ((|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |airyBi| ((|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |airyBi| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |hypergeometric0F1| ((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |hypergeometric0F1| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |fresnelS| ((|Float|) (|Float|))) (SIGNATURE |fresnelC| ((|Float|) (|Float|))))) (T |DoubleFloatSpecialFunctions|)) 
((|fresnelC| (*1 *2 *2) (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|fresnelS| (*1 *2 *2) (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|hypergeometric0F1| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Complex| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|hypergeometric0F1| (*1 *2 *2 *2) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|airyBi| (*1 *2 *2) (AND (|isDomain| *2 (|Complex| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|airyBi| (*1 *2 *2) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|airyAi| (*1 *2 *2) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|airyAi| (*1 *2 *2) (AND (|isDomain| *2 (|Complex| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|besselK| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Complex| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|besselK| (*1 *2 *2 *2) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|besselI| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Complex| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|besselI| (*1 *2 *2 *2) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|besselY| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Complex| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|besselY| (*1 *2 *2 *2) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|besselJ| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Complex| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|besselJ| (*1 *2 *2 *2) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|polygamma| (*1 *2 *3 *2) (AND (|isDomain| *2 (|Complex| (|DoubleFloat|))) (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|polygamma| (*1 *2 *3 *2) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|digamma| (*1 *2 *2) (AND (|isDomain| *2 (|Complex| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|digamma| (*1 *2 *2) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|logGamma| (*1 *2 *2) (AND (|isDomain| *2 (|Complex| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|logGamma| (*1 *2 *2) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|Beta| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Complex| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|Beta| (*1 *2 *2 *2) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|Ei6| (*1 *2 *2) (AND (|isDomain| *2 (|OnePointCompletion| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|Ei5| (*1 *2 *2) (AND (|isDomain| *2 (|OnePointCompletion| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|Ei4| (*1 *2 *2) (AND (|isDomain| *2 (|OnePointCompletion| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|Ei3| (*1 *2 *2) (AND (|isDomain| *2 (|OnePointCompletion| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|Ei2| (*1 *2 *2) (AND (|isDomain| *2 (|OnePointCompletion| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|Ei1| (*1 *2 *2) (AND (|isDomain| *2 (|OnePointCompletion| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|Ei| (*1 *2 *2) (AND (|isDomain| *2 (|OnePointCompletion| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|En| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|OnePointCompletion| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)) (|isDomain| *4 (|DoubleFloat|)))) (E1 (*1 *2 *3) (AND (|isDomain| *2 (|OnePointCompletion| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)) (|isDomain| *3 (|DoubleFloat|)))) (|Gamma| (*1 *2 *2) (AND (|isDomain| *2 (|Complex| (|DoubleFloat|))) (|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|Gamma| (*1 *2 *2) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))) 
(CATEGORY |package| (SIGNATURE |Gamma| ((|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |Gamma| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE E1 ((|OnePointCompletion| (|DoubleFloat|)) (|DoubleFloat|))) (SIGNATURE |En| ((|OnePointCompletion| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|))) (SIGNATURE |Ei| ((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|)))) (SIGNATURE |Ei1| ((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|)))) (SIGNATURE |Ei2| ((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|)))) (SIGNATURE |Ei3| ((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|)))) (SIGNATURE |Ei4| ((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|)))) (SIGNATURE |Ei5| ((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|)))) (SIGNATURE |Ei6| ((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|)))) (SIGNATURE |Beta| ((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |Beta| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |logGamma| ((|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |logGamma| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |digamma| ((|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |digamma| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |polygamma| ((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|))) (SIGNATURE |polygamma| ((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|)))) (SIGNATURE |besselJ| ((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |besselJ| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |besselY| ((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |besselY| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |besselI| ((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |besselI| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |besselK| ((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |besselK| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |airyAi| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |airyAi| ((|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |airyBi| ((|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |airyBi| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |hypergeometric0F1| ((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE |hypergeometric0F1| ((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)))) (SIGNATURE |fresnelS| ((|Float|) (|Float|))) (SIGNATURE |fresnelC| ((|Float|) (|Float|)))) 
((~= (((|Boolean|) $ $) NIL (|has| (|DoubleFloat|) (|SetCategory|)))) (|zero| (($ (|NonNegativeInteger|)) NIL (|has| (|DoubleFloat|) (|AbelianMonoid|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) (|DoubleFloat|) (|DoubleFloat|)) $) NIL) (((|Boolean|) $) NIL (|has| (|DoubleFloat|) (|OrderedSet|)))) (|sort!| (($ (|Mapping| (|Boolean|) (|DoubleFloat|) (|DoubleFloat|)) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $) NIL (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|has| (|DoubleFloat|) (|OrderedSet|))))) (|sort| (($ (|Mapping| (|Boolean|) (|DoubleFloat|) (|DoubleFloat|)) $) NIL) (($ $) NIL (|has| (|DoubleFloat|) (|OrderedSet|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setelt| (((|DoubleFloat|) $ (|Integer|) (|DoubleFloat|)) 17 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|DoubleFloat|) $ (|UniversalSegment| (|Integer|)) (|DoubleFloat|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select| (($ (|Mapping| (|Boolean|) (|DoubleFloat|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) NIL T CONST)) (|reverse!| (($ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) NIL)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|DoubleFloat|) (|SetCategory|))))) (|remove| (($ (|DoubleFloat|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|DoubleFloat|) (|SetCategory|)))) (($ (|Mapping| (|Boolean|) (|DoubleFloat|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| (((|DoubleFloat|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) $ (|DoubleFloat|) (|DoubleFloat|)) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|DoubleFloat|) (|SetCategory|)))) (((|DoubleFloat|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) $ (|DoubleFloat|)) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|DoubleFloat|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| (((|DoubleFloat|) $ (|Integer|) (|DoubleFloat|)) 9 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qnew| (($ (|Integer|)) 14)) (|qelt| (((|DoubleFloat|) $ (|Integer|)) 8)) (|position| (((|Integer|) (|Mapping| (|Boolean|) (|DoubleFloat|)) $) NIL) (((|Integer|) (|DoubleFloat|) $) NIL (|has| (|DoubleFloat|) (|SetCategory|))) (((|Integer|) (|DoubleFloat|) $ (|Integer|)) NIL (|has| (|DoubleFloat|) (|SetCategory|)))) (|parts| (((|List| (|DoubleFloat|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|outerProduct| (((|Matrix| (|DoubleFloat|)) $ $) NIL (|has| (|DoubleFloat|) (|Ring|)))) (|new| (($ (|NonNegativeInteger|) (|DoubleFloat|)) 15)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) 12 (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL (|has| (|DoubleFloat|) (|OrderedSet|)))) (|merge| (($ (|Mapping| (|Boolean|) (|DoubleFloat|) (|DoubleFloat|)) $ $) NIL) (($ $ $) NIL (|has| (|DoubleFloat|) (|OrderedSet|)))) (|members| (((|List| (|DoubleFloat|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|DoubleFloat|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|DoubleFloat|) (|SetCategory|))))) (|maxIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| (|DoubleFloat|) (|OrderedSet|)))) (|map!| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) $) NIL) (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) $ $) NIL)) (|magnitude| (((|DoubleFloat|) $) NIL (AND (|has| (|DoubleFloat|) (|RadicalCategory|)) (|has| (|DoubleFloat|) (|Ring|))))) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|length| (((|DoubleFloat|) $) NIL (AND (|has| (|DoubleFloat|) (|RadicalCategory|)) (|has| (|DoubleFloat|) (|Ring|))))) (|latex| (((|String|) $) NIL (|has| (|DoubleFloat|) (|SetCategory|)))) (|insert| (($ (|DoubleFloat|) $ (|Integer|)) NIL) (($ $ $ (|Integer|)) NIL)) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL (|has| (|DoubleFloat|) (|SetCategory|)))) (|first| (((|DoubleFloat|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|find| (((|Union| (|DoubleFloat|) "failed") (|Mapping| (|Boolean|) (|DoubleFloat|)) $) NIL)) (|fill!| (($ $ (|DoubleFloat|)) 18 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) (|DoubleFloat|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| (|DoubleFloat|)))) NIL (AND (|has| (|DoubleFloat|) (|Evalable| (|DoubleFloat|))) (|has| (|DoubleFloat|) (|SetCategory|)))) (($ $ (|Equation| (|DoubleFloat|))) NIL (AND (|has| (|DoubleFloat|) (|Evalable| (|DoubleFloat|))) (|has| (|DoubleFloat|) (|SetCategory|)))) (($ $ (|DoubleFloat|) (|DoubleFloat|)) NIL (AND (|has| (|DoubleFloat|) (|Evalable| (|DoubleFloat|))) (|has| (|DoubleFloat|) (|SetCategory|)))) (($ $ (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) NIL (AND (|has| (|DoubleFloat|) (|Evalable| (|DoubleFloat|))) (|has| (|DoubleFloat|) (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|entry?| (((|Boolean|) (|DoubleFloat|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|DoubleFloat|) (|SetCategory|))))) (|entries| (((|List| (|DoubleFloat|)) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) 13)) (|elt| (((|DoubleFloat|) $ (|Integer|) (|DoubleFloat|)) NIL) (((|DoubleFloat|) $ (|Integer|)) 16) (($ $ (|UniversalSegment| (|Integer|))) NIL)) (|dot| (((|DoubleFloat|) $ $) NIL (|has| (|DoubleFloat|) (|Ring|)))) (|delete| (($ $ (|Integer|)) NIL) (($ $ (|UniversalSegment| (|Integer|))) NIL)) (|cross| (($ $ $) NIL (|has| (|DoubleFloat|) (|Ring|)))) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|DoubleFloat|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) (|DoubleFloat|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|DoubleFloat|) (|SetCategory|))))) (|copyInto!| (($ $ $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) NIL (|has| (|DoubleFloat|) (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| (|DoubleFloat|))) NIL)) (|concat| (($ $ (|DoubleFloat|)) NIL) (($ (|DoubleFloat|) $) NIL) (($ $ $) NIL) (($ (|List| $)) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| (|DoubleFloat|) (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|DoubleFloat|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (>= (((|Boolean|) $ $) NIL (|has| (|DoubleFloat|) (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| (|DoubleFloat|) (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL (|has| (|DoubleFloat|) (|SetCategory|)))) (<= (((|Boolean|) $ $) NIL (|has| (|DoubleFloat|) (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| (|DoubleFloat|) (|OrderedSet|)))) (- (($ $) NIL (|has| (|DoubleFloat|) (|AbelianGroup|))) (($ $ $) NIL (|has| (|DoubleFloat|) (|AbelianGroup|)))) (+ (($ $ $) NIL (|has| (|DoubleFloat|) (|AbelianSemiGroup|)))) (* (($ (|Integer|) $) NIL (|has| (|DoubleFloat|) (|AbelianGroup|))) (($ (|DoubleFloat|) $) NIL (|has| (|DoubleFloat|) (|Monoid|))) (($ $ (|DoubleFloat|)) NIL (|has| (|DoubleFloat|) (|Monoid|)))) (|#| (((|NonNegativeInteger|) $) 11 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|DoubleFloatVector|) (|Join| (|VectorCategory| (|DoubleFloat|)) (CATEGORY |domain| (SIGNATURE |qnew| ($ (|Integer|)))))) (T |DoubleFloatVector|)) 
((|qnew| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|DoubleFloatVector|))))) 
(|Join| (|VectorCategory| (|DoubleFloat|)) (CATEGORY |domain| (SIGNATURE |qnew| ($ (|Integer|))))) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|zero?| (((|Boolean|) $) NIL)) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) NIL)) (|vertConcat| (($ $ $) NIL)) (|transpose| (($ (|Vector| |#1|)) NIL) (($ $) NIL)) (|translate| (($ |#1| |#1| |#1|) 32)) (|symmetric?| (((|Boolean|) $) NIL)) (|swapRows!| (($ $ (|Integer|) (|Integer|)) NIL)) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) NIL)) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) NIL)) (|squareTop| (($ $) NIL)) (|square?| (((|Boolean|) $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) NIL)) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) NIL) (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) NIL)) (|setRow!| (($ $ (|Integer|) (|Vector| |#1|)) NIL)) (|setColumn!| (($ $ (|Integer|) (|Vector| |#1|)) NIL)) (|scale| (($ |#1| |#1| |#1|) 31)) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) NIL)) (|sample| (($) NIL T CONST)) (|rowEchelon| (($ $) NIL (|has| |#1| (|EuclideanDomain|)))) (|row| (((|Vector| |#1|) $ (|Integer|)) NIL)) (|rotatez| (($ |#1|) 30)) (|rotatey| (($ |#1|) 29)) (|rotatex| (($ |#1|) 28)) (|rank| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) NIL)) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) NIL)) (|pfaffian| ((|#1| $) NIL (|has| |#1| (|CommutativeRing|)))) (|parts| (((|List| |#1|) $) NIL)) (|nullity| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|nullSpace| (((|List| (|Vector| |#1|)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|nrows| (((|NonNegativeInteger|) $) NIL)) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) NIL)) (|ncols| (((|NonNegativeInteger|) $) NIL)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minordet| ((|#1| $) NIL (|has| |#1| (ATTRIBUTE (|commutative| "*"))))) (|minRowIndex| (((|Integer|) $) NIL)) (|minColIndex| (((|Integer|) $) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|maxRowIndex| (((|Integer|) $) NIL)) (|maxColIndex| (((|Integer|) $) NIL)) (|matrix| (($ (|List| (|List| |#1|))) 10) (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) NIL)) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) NIL)) (|listOfLists| (((|List| (|List| |#1|)) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|inverse| (((|Union| $ "failed") $) NIL (|has| |#1| (|Field|)))) (|identity| (($) 11)) (|horizConcat| (($ $ $) NIL)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|fill!| (($ $ |#1|) NIL)) (|exquo| (((|Union| $ "failed") $ |#1|) NIL (|has| |#1| (|IntegralDomain|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#1| $ (|Integer|) (|Integer|)) NIL) ((|#1| $ (|Integer|) (|Integer|) |#1|) NIL) (($ $ (|List| (|Integer|)) (|List| (|Integer|))) NIL)) (|diagonalMatrix| (($ (|List| |#1|)) NIL) (($ (|List| $)) NIL)) (|diagonal?| (((|Boolean|) $) NIL)) (|determinant| ((|#1| $) NIL (|has| |#1| (ATTRIBUTE (|commutative| "*"))))) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) NIL)) (|columnSpace| (((|List| (|Vector| |#1|)) $) NIL (|has| |#1| (|EuclideanDomain|)))) (|column| (((|Vector| |#1|) $ (|Integer|)) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|))) (($ (|Vector| |#1|)) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|antisymmetric?| (((|Boolean|) $) NIL)) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (/ (($ $ |#1|) NIL (|has| |#1| (|Field|)))) (- (($ $ $) NIL) (($ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| |#1| (|Field|)))) (* (($ $ $) NIL) (($ |#1| $) NIL) (($ $ |#1|) NIL) (($ (|Integer|) $) NIL) (((|Vector| |#1|) $ (|Vector| |#1|)) 14) (((|Vector| |#1|) (|Vector| |#1|) $) NIL) (((|Point| |#1|) $ (|Point| |#1|)) 20)) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|DenavitHartenbergMatrix| |#1|) (|Join| (|MatrixCategory| |#1| (|Vector| |#1|) (|Vector| |#1|)) (CATEGORY |domain| (SIGNATURE * ((|Point| |#1|) $ (|Point| |#1|))) (SIGNATURE |identity| ($)) (SIGNATURE |rotatex| ($ |#1|)) (SIGNATURE |rotatey| ($ |#1|)) (SIGNATURE |rotatez| ($ |#1|)) (SIGNATURE |scale| ($ |#1| |#1| |#1|)) (SIGNATURE |translate| ($ |#1| |#1| |#1|)))) (|Join| (|Field|) (|TranscendentalFunctionCategory|))) (T |DenavitHartenbergMatrix|)) 
((* (*1 *2 *1 *2) (AND (|isDomain| *2 (|Point| *3)) (|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|))) (|isDomain| *1 (|DenavitHartenbergMatrix| *3)))) (|identity| (*1 *1) (AND (|isDomain| *1 (|DenavitHartenbergMatrix| *2)) (|ofCategory| *2 (|Join| (|Field|) (|TranscendentalFunctionCategory|))))) (|rotatex| (*1 *1 *2) (AND (|isDomain| *1 (|DenavitHartenbergMatrix| *2)) (|ofCategory| *2 (|Join| (|Field|) (|TranscendentalFunctionCategory|))))) (|rotatey| (*1 *1 *2) (AND (|isDomain| *1 (|DenavitHartenbergMatrix| *2)) (|ofCategory| *2 (|Join| (|Field|) (|TranscendentalFunctionCategory|))))) (|rotatez| (*1 *1 *2) (AND (|isDomain| *1 (|DenavitHartenbergMatrix| *2)) (|ofCategory| *2 (|Join| (|Field|) (|TranscendentalFunctionCategory|))))) (|scale| (*1 *1 *2 *2 *2) (AND (|isDomain| *1 (|DenavitHartenbergMatrix| *2)) (|ofCategory| *2 (|Join| (|Field|) (|TranscendentalFunctionCategory|))))) (|translate| (*1 *1 *2 *2 *2) (AND (|isDomain| *1 (|DenavitHartenbergMatrix| *2)) (|ofCategory| *2 (|Join| (|Field|) (|TranscendentalFunctionCategory|)))))) 
(|Join| (|MatrixCategory| |#1| (|Vector| |#1|) (|Vector| |#1|)) (CATEGORY |domain| (SIGNATURE * ((|Point| |#1|) $ (|Point| |#1|))) (SIGNATURE |identity| ($)) (SIGNATURE |rotatex| ($ |#1|)) (SIGNATURE |rotatey| ($ |#1|)) (SIGNATURE |rotatez| ($ |#1|)) (SIGNATURE |scale| ($ |#1| |#1| |#1|)) (SIGNATURE |translate| ($ |#1| |#1| |#1|)))) 
((|select!| (($ (|Mapping| (|Boolean|) |#2|) $) 17)) (|remove!| (($ |#2| $) NIL) (($ (|Mapping| (|Boolean|) |#2|) $) 25)) (|dictionary| (($) NIL) (($ (|List| |#2|)) 11)) (= (((|Boolean|) $ $) 23))) 
(((|Dictionary&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |select!| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |remove!| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |remove!| (|#1| |#2| |#1|)) (SIGNATURE |dictionary| (|#1| (|List| |#2|))) (SIGNATURE |dictionary| (|#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|))) (|Dictionary| |#2|) (|SetCategory|)) (T |Dictionary&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |select!| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |remove!| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |remove!| (|#1| |#2| |#1|)) (SIGNATURE |dictionary| (|#1| (|List| |#2|))) (SIGNATURE |dictionary| (|#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) 42 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 52 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) 7 T CONST)) (|removeDuplicates| (($ $) 55 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove!| (($ |#1| $) 44 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) |#1|) $) 43 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remove| (($ |#1| $) 54 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#1|) $) 51 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 53 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 50 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 49 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|inspect| ((|#1| $) 36)) (|insert!| (($ |#1| $) 37)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) 48)) (|extract!| ((|#1| $) 38)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|dictionary| (($) 46) (($ (|List| |#1|)) 45)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|convert| (((|InputForm|) $) 56 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 47)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|bag| (($ (|List| |#1|)) 39)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|Dictionary| |#1|) (|Category|) (|SetCategory|)) (T |Dictionary|)) 
NIL 
(|Join| (|DictionaryOperations| |t#1|)) 
(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((|differentiate| (($ $ (|Mapping| |#2| |#2|)) NIL) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) 11) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|))) NIL) (($ $ (|Symbol|)) 19) (($ $ (|NonNegativeInteger|)) NIL) (($ $) 16)) (D (($ $ (|Mapping| |#2| |#2|)) 12) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) 14) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|))) NIL) (($ $ (|Symbol|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL))) 
(((|DifferentialExtension&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE D (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE D (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE D (|#1| |#1| (|Symbol|))) (SIGNATURE D (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE D (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE D (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE D (|#1| |#1| (|Mapping| |#2| |#2|) (|NonNegativeInteger|))) (SIGNATURE D (|#1| |#1| (|Mapping| |#2| |#2|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|)))) (|DifferentialExtension| |#2|) (|Ring|)) (T |DifferentialExtension&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE D (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE D (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE D (|#1| |#1| (|Symbol|))) (SIGNATURE D (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE D (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE D (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE D (|#1| |#1| (|Mapping| |#2| |#2|) (|NonNegativeInteger|))) (SIGNATURE D (|#1| |#1| (|Mapping| |#2| |#2|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|differentiate| (($ $ (|Mapping| |#1| |#1|)) 51) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) 50) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 43 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 42 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) 41 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|)) 40 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|NonNegativeInteger|)) 38 (|has| |#1| (|DifferentialRing|))) (($ $) 36 (|has| |#1| (|DifferentialRing|)))) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $ (|Mapping| |#1| |#1|)) 49) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) 48) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 47 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 46 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) 45 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|)) 44 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|NonNegativeInteger|)) 39 (|has| |#1| (|DifferentialRing|))) (($ $) 37 (|has| |#1| (|DifferentialRing|)))) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|DifferentialExtension| |#1|) (|Category|) (|Ring|)) (T |DifferentialExtension|)) 
((|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|DifferentialExtension| *3)) (|ofCategory| *3 (|Ring|)))) (|differentiate| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|DifferentialExtension| *4)) (|ofCategory| *4 (|Ring|)))) (D (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|DifferentialExtension| *3)) (|ofCategory| *3 (|Ring|)))) (D (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|DifferentialExtension| *4)) (|ofCategory| *4 (|Ring|))))) 
(|Join| (|Ring|) (CATEGORY |domain| (SIGNATURE |differentiate| ($ $ (|Mapping| |t#1| |t#1|))) (SIGNATURE |differentiate| ($ $ (|Mapping| |t#1| |t#1|) (|NonNegativeInteger|))) (SIGNATURE D ($ $ (|Mapping| |t#1| |t#1|))) (SIGNATURE D ($ $ (|Mapping| |t#1| |t#1|) (|NonNegativeInteger|))) (IF (|has| |t#1| (|DifferentialRing|)) (ATTRIBUTE (|DifferentialRing|)) |noBranch|) (IF (|has| |t#1| (|PartialDifferentialRing| (|Symbol|))) (ATTRIBUTE (|PartialDifferentialRing| (|Symbol|))) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|DifferentialRing|) |has| |#1| (|DifferentialRing|)) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|differentiate| (($ $) NIL) (($ $ (|NonNegativeInteger|)) 10)) (D (($ $) 8) (($ $ (|NonNegativeInteger|)) 12))) 
(((|DifferentialRing&| |#1|) (CATEGORY |domain| (SIGNATURE D (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE D (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1|))) (|DifferentialRing|)) (T |DifferentialRing&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE D (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE D (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|differentiate| (($ $) 37) (($ $ (|NonNegativeInteger|)) 35)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $) 36) (($ $ (|NonNegativeInteger|)) 34)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|DifferentialRing|) (|Category|)) (T |DifferentialRing|)) 
((|differentiate| (*1 *1 *1) (|ofCategory| *1 (|DifferentialRing|))) (D (*1 *1 *1) (|ofCategory| *1 (|DifferentialRing|))) (|differentiate| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|DifferentialRing|)) (|isDomain| *2 (|NonNegativeInteger|)))) (D (*1 *1 *1 *2) (AND (|ofCategory| *1 (|DifferentialRing|)) (|isDomain| *2 (|NonNegativeInteger|))))) 
(|Join| (|Ring|) (CATEGORY |domain| (SIGNATURE |differentiate| ($ $)) (SIGNATURE D ($ $)) (SIGNATURE |differentiate| ($ $ (|NonNegativeInteger|))) (SIGNATURE D ($ $ (|NonNegativeInteger|))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|dictionary| (($) 12) (($ (|List| |#2|)) NIL)) (|copy| (($ $) 14)) (|construct| (($ (|List| |#2|)) 10)) (|coerce| (((|OutputForm|) $) 21))) 
(((|DictionaryOperations&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |dictionary| (|#1| (|List| |#2|))) (SIGNATURE |dictionary| (|#1|)) (SIGNATURE |construct| (|#1| (|List| |#2|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |copy| (|#1| |#1|))) (|DictionaryOperations| |#2|) (|SetCategory|)) (T |DictionaryOperations&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |dictionary| (|#1| (|List| |#2|))) (SIGNATURE |dictionary| (|#1|)) (SIGNATURE |construct| (|#1| (|List| |#2|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |copy| (|#1| |#1|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) 42 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 52 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) 7 T CONST)) (|removeDuplicates| (($ $) 55 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove!| (($ |#1| $) 44 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) |#1|) $) 43 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remove| (($ |#1| $) 54 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#1|) $) 51 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 53 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 50 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 49 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|inspect| ((|#1| $) 36)) (|insert!| (($ |#1| $) 37)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) 48)) (|extract!| ((|#1| $) 38)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|dictionary| (($) 46) (($ (|List| |#1|)) 45)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|convert| (((|InputForm|) $) 56 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 47)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|bag| (($ (|List| |#1|)) 39)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|DictionaryOperations| |#1|) (|Category|) (|SetCategory|)) (T |DictionaryOperations|)) 
((|dictionary| (*1 *1) (AND (|ofCategory| *1 (|DictionaryOperations| *2)) (|ofCategory| *2 (|SetCategory|)))) (|dictionary| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *1 (|DictionaryOperations| *3)))) (|remove!| (*1 *1 *2 *1) (AND (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|DictionaryOperations| *2)) (|ofCategory| *2 (|SetCategory|)))) (|remove!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|DictionaryOperations| *3)) (|ofCategory| *3 (|SetCategory|)))) (|select!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|DictionaryOperations| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(|Join| (|BagAggregate| |t#1|) (|Collection| |t#1|) (CATEGORY |domain| (SIGNATURE |dictionary| ($)) (SIGNATURE |dictionary| ($ (|List| |t#1|))) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (PROGN (SIGNATURE |remove!| ($ |t#1| $)) (SIGNATURE |remove!| ($ (|Mapping| (|Boolean|) |t#1|) $)) (SIGNATURE |select!| ($ (|Mapping| (|Boolean|) |t#1|) $))) |noBranch|))) 
(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) 25))) 
(((|DiophantineSolutionPackage|) (CATEGORY |package| (SIGNATURE |dioSolve| ((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|))))))) (T |DiophantineSolutionPackage|)) 
((|dioSolve| (*1 *2 *3) (AND (|isDomain| *3 (|Equation| (|Polynomial| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|)))))) (|isDomain| *1 (|DiophantineSolutionPackage|))))) 
(CATEGORY |package| (SIGNATURE |dioSolve| ((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))))) 
((|size| (((|NonNegativeInteger|)) 51)) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#3|)) (|:| |vec| (|Vector| |#3|))) (|Matrix| $) (|Vector| $)) 49) (((|Matrix| |#3|) (|Matrix| $)) 41) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| (|Integer|)) (|Matrix| $)) NIL)) (|dimension| (((|CardinalNumber|)) 57)) (|differentiate| (($ $ (|Mapping| |#3| |#3|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#3| |#3|)) 18) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|))) NIL) (($ $ (|Symbol|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (|coerce| (((|Vector| |#3|) $) NIL) (($ |#3|) NIL) (((|OutputForm|) $) NIL) (($ (|Integer|)) 12) (($ (|Fraction| (|Integer|))) NIL)) (|characteristic| (((|NonNegativeInteger|)) 15)) (/ (($ $ |#3|) 54))) 
(((|DirectProductCategory&| |#1| |#2| |#3|) (CATEGORY |domain| (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |characteristic| ((|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |reducedSystem| ((|Matrix| (|Integer|)) (|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |coerce| (|#1| |#3|)) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#3| |#3|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#3| |#3|) (|NonNegativeInteger|))) (SIGNATURE |reducedSystem| ((|Matrix| |#3|) (|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| |#3|)) (|:| |vec| (|Vector| |#3|))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |size| ((|NonNegativeInteger|))) (SIGNATURE / (|#1| |#1| |#3|)) (SIGNATURE |dimension| ((|CardinalNumber|))) (SIGNATURE |coerce| ((|Vector| |#3|) |#1|))) (|DirectProductCategory| |#2| |#3|) (|NonNegativeInteger|) (|Type|)) (T |DirectProductCategory&|)) 
((|dimension| (*1 *2) (AND (|ofType| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|Type|)) (|isDomain| *2 (|CardinalNumber|)) (|isDomain| *1 (|DirectProductCategory&| *3 *4 *5)) (|ofCategory| *3 (|DirectProductCategory| *4 *5)))) (|size| (*1 *2) (AND (|ofType| *4 *2) (|ofCategory| *5 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|DirectProductCategory&| *3 *4 *5)) (|ofCategory| *3 (|DirectProductCategory| *4 *5)))) (|characteristic| (*1 *2) (AND (|ofType| *4 *2) (|ofCategory| *5 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|DirectProductCategory&| *3 *4 *5)) (|ofCategory| *3 (|DirectProductCategory| *4 *5))))) 
(CATEGORY |domain| (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |characteristic| ((|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |reducedSystem| ((|Matrix| (|Integer|)) (|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |coerce| (|#1| |#3|)) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#3| |#3|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#3| |#3|) (|NonNegativeInteger|))) (SIGNATURE |reducedSystem| ((|Matrix| |#3|) (|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| |#3|)) (|:| |vec| (|Vector| |#3|))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |size| ((|NonNegativeInteger|))) (SIGNATURE / (|#1| |#1| |#3|)) (SIGNATURE |dimension| ((|CardinalNumber|))) (SIGNATURE |coerce| ((|Vector| |#3|) |#1|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#2| (|SetCategory|)))) (|zero?| (((|Boolean|) $) 67 (|has| |#2| (|CancellationAbelianMonoid|)))) (|unitVector| (($ (|PositiveInteger|)) 123 (|has| |#2| (|Ring|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sup| (($ $ $) 119 (|has| |#2| (|OrderedAbelianMonoidSup|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) 69 (|has| |#2| (|CancellationAbelianMonoid|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|size| (((|NonNegativeInteger|)) 104 (|has| |#2| (|Finite|)))) (|sign| (((|Integer|) $) 117 (|has| |#2| (|OrderedRing|)))) (|setelt| ((|#2| $ (|Integer|) |#2|) 49 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) 7 T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 62 (|and| (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#2| (|SetCategory|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) 59 (|and| (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|)))) (((|Union| |#2| "failed") $) 56 (|has| |#2| (|SetCategory|)))) (|retract| (((|Integer|) $) 63 (|and| (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#2| (|SetCategory|)))) (((|Fraction| (|Integer|)) $) 60 (|and| (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|)))) ((|#2| $) 55 (|has| |#2| (|SetCategory|)))) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) 103 (|and| (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) 102 (|and| (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|)))) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| $) (|Vector| $)) 101 (|has| |#2| (|Ring|))) (((|Matrix| |#2|) (|Matrix| $)) 100 (|has| |#2| (|Ring|)))) (|recip| (((|Union| $ "failed") $) 75 (|has| |#2| (|Monoid|)))) (|random| (($) 107 (|has| |#2| (|Finite|)))) (|qsetelt!| ((|#2| $ (|Integer|) |#2|) 50 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#2| $ (|Integer|)) 48)) (|positive?| (((|Boolean|) $) 115 (|has| |#2| (|OrderedRing|)))) (|parts| (((|List| |#2|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|one?| (((|Boolean|) $) 78 (|has| |#2| (|Monoid|)))) (|negative?| (((|Boolean|) $) 116 (|has| |#2| (|OrderedRing|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|minIndex| (((|Integer|) $) 40 (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) 114 (OR (|has| |#2| (|OrderedRing|)) (|has| |#2| (|OrderedAbelianMonoidSup|))))) (|members| (((|List| |#2|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#2| $) 27 (AND (|has| |#2| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|maxIndex| (((|Integer|) $) 41 (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) 113 (OR (|has| |#2| (|OrderedRing|)) (|has| |#2| (|OrderedAbelianMonoidSup|))))) (|map!| (($ (|Mapping| |#2| |#2|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#2| |#2|) $) 35)) (|lookup| (((|PositiveInteger|) $) 106 (|has| |#2| (|Finite|)))) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (|has| |#2| (|SetCategory|)))) (|indices| (((|List| (|Integer|)) $) 43)) (|index?| (((|Boolean|) (|Integer|) $) 44)) (|index| (($ (|PositiveInteger|)) 105 (|has| |#2| (|Finite|)))) (|hash| (((|SingleInteger|) $) 21 (|has| |#2| (|SetCategory|)))) (|first| ((|#2| $) 39 (|has| (|Integer|) (|OrderedSet|)))) (|fill!| (($ $ |#2|) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#2|))) 26 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|Equation| |#2|)) 25 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ |#2| |#2|) 24 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|List| |#2|) (|List| |#2|)) 23 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|enumerate| (((|List| $)) 108 (|has| |#2| (|Finite|)))) (|entry?| (((|Boolean|) |#2| $) 42 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|entries| (((|List| |#2|) $) 45)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| ((|#2| $ (|Integer|) |#2|) 47) ((|#2| $ (|Integer|)) 46)) (|dot| ((|#2| $ $) 122 (|has| |#2| (|Ring|)))) (|directProduct| (($ (|Vector| |#2|)) 124)) (|dimension| (((|CardinalNumber|)) 121 (|has| |#2| (|Field|)))) (|differentiate| (($ $) 95 (|and| (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) (($ $ (|NonNegativeInteger|)) 93 (|and| (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) (($ $ (|Symbol|)) 91 (|and| (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|List| (|Symbol|))) 90 (|and| (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 89 (|and| (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 88 (|and| (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) 81 (|has| |#2| (|Ring|))) (($ $ (|Mapping| |#2| |#2|)) 80 (|has| |#2| (|Ring|)))) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#2| $) 28 (AND (|has| |#2| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|coerce| (((|Vector| |#2|) $) 125) (((|OutputForm|) $) 20 (|has| |#2| (|SetCategory|))) (($ (|Integer|)) 61 (OR (|and| (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#2| (|SetCategory|))) (|has| |#2| (|Ring|)))) (($ (|Fraction| (|Integer|))) 58 (|and| (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|)))) (($ |#2|) 57 (|has| |#2| (|SetCategory|)))) (|characteristic| (((|NonNegativeInteger|)) 99 (|has| |#2| (|Ring|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|abs| (($ $) 118 (|has| |#2| (|OrderedRing|)))) (^ (($ $ (|NonNegativeInteger|)) 76 (|has| |#2| (|Monoid|))) (($ $ (|PositiveInteger|)) 72 (|has| |#2| (|Monoid|)))) (|Zero| (($) 66 (|has| |#2| (|CancellationAbelianMonoid|)) CONST)) (|One| (($) 79 (|has| |#2| (|Monoid|)) CONST)) (D (($ $) 94 (|and| (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) (($ $ (|NonNegativeInteger|)) 92 (|and| (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) (($ $ (|Symbol|)) 87 (|and| (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|List| (|Symbol|))) 86 (|and| (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 85 (|and| (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 84 (|and| (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) 83 (|has| |#2| (|Ring|))) (($ $ (|Mapping| |#2| |#2|)) 82 (|has| |#2| (|Ring|)))) (>= (((|Boolean|) $ $) 111 (OR (|has| |#2| (|OrderedRing|)) (|has| |#2| (|OrderedAbelianMonoidSup|))))) (> (((|Boolean|) $ $) 110 (OR (|has| |#2| (|OrderedRing|)) (|has| |#2| (|OrderedAbelianMonoidSup|))))) (= (((|Boolean|) $ $) 19 (|has| |#2| (|SetCategory|)))) (<= (((|Boolean|) $ $) 112 (OR (|has| |#2| (|OrderedRing|)) (|has| |#2| (|OrderedAbelianMonoidSup|))))) (< (((|Boolean|) $ $) 109 (OR (|has| |#2| (|OrderedRing|)) (|has| |#2| (|OrderedAbelianMonoidSup|))))) (/ (($ $ |#2|) 120 (|has| |#2| (|Field|)))) (- (($ $ $) 97 (|has| |#2| (|Ring|))) (($ $) 96 (|has| |#2| (|Ring|)))) (+ (($ $ $) 64 (|has| |#2| (|AbelianSemiGroup|)))) (** (($ $ (|NonNegativeInteger|)) 77 (|has| |#2| (|Monoid|))) (($ $ (|PositiveInteger|)) 73 (|has| |#2| (|Monoid|)))) (* (($ (|Integer|) $) 98 (|has| |#2| (|Ring|))) (($ $ $) 74 (|has| |#2| (|Monoid|))) (($ $ |#2|) 71 (|has| |#2| (|Monoid|))) (($ |#2| $) 70 (|has| |#2| (|Monoid|))) (($ (|NonNegativeInteger|) $) 68 (|has| |#2| (|CancellationAbelianMonoid|))) (($ (|PositiveInteger|) $) 65 (|has| |#2| (|AbelianSemiGroup|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|DirectProductCategory| |#1| |#2|) (|Category|) (|NonNegativeInteger|) (|Type|)) (T |DirectProductCategory|)) 
((|directProduct| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *4)) (|ofCategory| *4 (|Type|)) (|ofCategory| *1 (|DirectProductCategory| *3 *4)))) (|unitVector| (*1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|DirectProductCategory| *3 *4)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *4 (|Type|)))) (|dot| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|DirectProductCategory| *3 *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|Ring|)))) (* (*1 *1 *1 *2) (AND (|ofCategory| *1 (|DirectProductCategory| *3 *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|Monoid|)))) (* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|DirectProductCategory| *3 *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|Monoid|))))) 
(|Join| (|IndexedAggregate| (|Integer|) |t#2|) (|CoercibleTo| (|Vector| |t#2|)) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (SIGNATURE |directProduct| ($ (|Vector| |t#2|))) (IF (|has| |t#2| (|SetCategory|)) (ATTRIBUTE (|FullyRetractableTo| |t#2|)) |noBranch|) (IF (|has| |t#2| (|Ring|)) (PROGN (ATTRIBUTE (|BiModule| |t#2| |t#2|)) (ATTRIBUTE (|DifferentialExtension| |t#2|)) (ATTRIBUTE (|FullyLinearlyExplicitRingOver| |t#2|)) (SIGNATURE |unitVector| ($ (|PositiveInteger|))) (SIGNATURE |dot| (|t#2| $ $))) |noBranch|) (IF (|has| |t#2| (|AbelianSemiGroup|)) (ATTRIBUTE (|AbelianSemiGroup|)) |noBranch|) (IF (|has| |t#2| (|CancellationAbelianMonoid|)) (ATTRIBUTE (|CancellationAbelianMonoid|)) |noBranch|) (IF (|has| |t#2| (|Monoid|)) (PROGN (ATTRIBUTE (|Monoid|)) (SIGNATURE * ($ |t#2| $)) (SIGNATURE * ($ $ |t#2|))) |noBranch|) (IF (|has| |t#2| (|Finite|)) (ATTRIBUTE (|Finite|)) |noBranch|) (IF (|has| |t#2| (|CommutativeRing|)) (PROGN (ATTRIBUTE (|Algebra| |t#2|)) (ATTRIBUTE (|CommutativeRing|))) |noBranch|) (IF (|has| |t#2| (ATTRIBUTE |unitsKnown|)) (ATTRIBUTE |unitsKnown|) |noBranch|) (IF (|has| |t#2| (|OrderedRing|)) (ATTRIBUTE (|OrderedRing|)) |noBranch|) (IF (|has| |t#2| (|OrderedAbelianMonoidSup|)) (ATTRIBUTE (|OrderedAbelianMonoidSup|)) |noBranch|) (IF (|has| |t#2| (|Field|)) (ATTRIBUTE (|VectorSpace| |t#2|)) |noBranch|))) 
(((|AbelianGroup|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedRing|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|AbelianMonoid|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedRing|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|))) ((|AbelianSemiGroup|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedRing|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|AbelianSemiGroup|))) ((|Aggregate|) . T) ((|Algebra| |#2|) |has| |#2| (|CommutativeRing|)) ((|BasicType|) OR (|has| |#2| (|SetCategory|)) (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedRing|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Finite|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|AbelianSemiGroup|))) ((|BiModule| |#2| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|BiModule| $ $) |has| |#2| (|CommutativeRing|)) ((|CancellationAbelianMonoid|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedRing|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#2| (|SetCategory|)) (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedRing|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Finite|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|AbelianSemiGroup|))) ((|CoercibleTo| (|Vector| |#2|)) . T) ((|CommutativeRing|) |has| |#2| (|CommutativeRing|)) ((|DifferentialExtension| |#2|) |has| |#2| (|Ring|)) ((|DifferentialRing|) AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|))) ((|Eltable| (|Integer|) |#2|) . T) ((|EltableAggregate| (|Integer|) |#2|) . T) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|Finite|) |has| |#2| (|Finite|)) ((|FullyLinearlyExplicitRingOver| |#2|) |has| |#2| (|Ring|)) ((|FullyRetractableTo| |#2|) |has| |#2| (|SetCategory|)) ((|HomogeneousAggregate| |#2|) . T) ((|IndexedAggregate| (|Integer|) |#2|) . T) ((|InnerEvalable| |#2| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|LeftModule| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|LeftModule| $) OR (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedRing|)) (|has| |#2| (|CommutativeRing|))) ((|LinearlyExplicitRingOver| (|Integer|)) AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|))) ((|LinearlyExplicitRingOver| |#2|) |has| |#2| (|Ring|)) ((|Module| |#2|) OR (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|Monoid|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedRing|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|CommutativeRing|))) ((|OrderedAbelianGroup|) |has| |#2| (|OrderedRing|)) ((|OrderedAbelianMonoid|) OR (|has| |#2| (|OrderedRing|)) (|has| |#2| (|OrderedAbelianMonoidSup|))) ((|OrderedAbelianMonoidSup|) |has| |#2| (|OrderedAbelianMonoidSup|)) ((|OrderedAbelianSemiGroup|) OR (|has| |#2| (|OrderedRing|)) (|has| |#2| (|OrderedAbelianMonoidSup|))) ((|OrderedCancellationAbelianMonoid|) OR (|has| |#2| (|OrderedRing|)) (|has| |#2| (|OrderedAbelianMonoidSup|))) ((|OrderedRing|) |has| |#2| (|OrderedRing|)) ((|OrderedSet|) OR (|has| |#2| (|OrderedRing|)) (|has| |#2| (|OrderedAbelianMonoidSup|))) ((|PartialDifferentialRing| (|Symbol|)) AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|))) ((|RetractableTo| (|Fraction| (|Integer|))) AND (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|))) ((|RetractableTo| (|Integer|)) AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#2| (|SetCategory|))) ((|RetractableTo| |#2|) |has| |#2| (|SetCategory|)) ((|RightModule| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|RightModule| $) |has| |#2| (|CommutativeRing|)) ((|Ring|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedRing|)) (|has| |#2| (|CommutativeRing|))) ((|Rng|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedRing|)) (|has| |#2| (|CommutativeRing|))) ((|SemiGroup|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedRing|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|CommutativeRing|))) ((|SetCategory|) OR (|has| |#2| (|SetCategory|)) (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedRing|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Finite|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|AbelianSemiGroup|))) ((|Type|) . T) ((|VectorSpace| |#2|) |has| |#2| (|Field|))) 
((|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) 21)) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) 23)) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) 18))) 
(((|DirectProductFunctions2| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |scan| ((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|)) (SIGNATURE |reduce| (|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|)) (SIGNATURE |map| ((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)))) (|NonNegativeInteger|) (|Type|) (|Type|)) (T |DirectProductFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *7 *6)) (|isDomain| *4 (|DirectProduct| *5 *6)) (|ofType| *5 (|NonNegativeInteger|)) (|ofCategory| *6 (|Type|)) (|ofCategory| *7 (|Type|)) (|isDomain| *2 (|DirectProduct| *5 *7)) (|isDomain| *1 (|DirectProductFunctions2| *5 *6 *7)))) (|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *6 *2)) (|isDomain| *4 (|DirectProduct| *5 *6)) (|ofType| *5 (|NonNegativeInteger|)) (|ofCategory| *6 (|Type|)) (|ofCategory| *2 (|Type|)) (|isDomain| *1 (|DirectProductFunctions2| *5 *6 *2)))) (|scan| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *5 *7 *5)) (|isDomain| *4 (|DirectProduct| *6 *7)) (|ofType| *6 (|NonNegativeInteger|)) (|ofCategory| *7 (|Type|)) (|ofCategory| *5 (|Type|)) (|isDomain| *2 (|DirectProduct| *6 *5)) (|isDomain| *1 (|DirectProductFunctions2| *6 *7 *5))))) 
(CATEGORY |package| (SIGNATURE |scan| ((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|)) (SIGNATURE |reduce| (|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|)) (SIGNATURE |map| ((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)))) 
((~= (((|Boolean|) $ $) NIL (|has| |#2| (|SetCategory|)))) (|zero?| (((|Boolean|) $) NIL (|has| |#2| (|CancellationAbelianMonoid|)))) (|unitVector| (($ (|PositiveInteger|)) 56 (|has| |#2| (|Ring|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sup| (($ $ $) 60 (|has| |#2| (|OrderedAbelianMonoidSup|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) 49 (|has| |#2| (|CancellationAbelianMonoid|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 17)) (|size| (((|NonNegativeInteger|)) NIL (|has| |#2| (|Finite|)))) (|sign| (((|Integer|) $) NIL (|has| |#2| (|OrderedRing|)))) (|setelt| ((|#2| $ (|Integer|) |#2|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#2| (|SetCategory|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (AND (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|)))) (((|Union| |#2| "failed") $) 29 (|has| |#2| (|SetCategory|)))) (|retract| (((|Integer|) $) NIL (AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#2| (|SetCategory|)))) (((|Fraction| (|Integer|)) $) NIL (AND (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|)))) ((|#2| $) 27 (|has| |#2| (|SetCategory|)))) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|)))) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| $) (|Vector| $)) NIL (|has| |#2| (|Ring|))) (((|Matrix| |#2|) (|Matrix| $)) NIL (|has| |#2| (|Ring|)))) (|recip| (((|Union| $ "failed") $) 53 (|has| |#2| (|Monoid|)))) (|random| (($) NIL (|has| |#2| (|Finite|)))) (|qsetelt!| ((|#2| $ (|Integer|) |#2|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#2| $ (|Integer|)) 51)) (|positive?| (((|Boolean|) $) NIL (|has| |#2| (|OrderedRing|)))) (|parts| (((|List| |#2|) $) 15 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|one?| (((|Boolean|) $) NIL (|has| |#2| (|Monoid|)))) (|negative?| (((|Boolean|) $) NIL (|has| |#2| (|OrderedRing|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) 20 (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL (OR (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedRing|))))) (|members| (((|List| |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|maxIndex| (((|Integer|) $) 50 (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (OR (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedRing|))))) (|map!| (($ (|Mapping| |#2| |#2|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#2| |#2|) $) 41)) (|lookup| (((|PositiveInteger|) $) NIL (|has| |#2| (|Finite|)))) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| |#2| (|SetCategory|)))) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|index| (($ (|PositiveInteger|)) NIL (|has| |#2| (|Finite|)))) (|hash| (((|SingleInteger|) $) NIL (|has| |#2| (|SetCategory|)))) (|first| ((|#2| $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|fill!| (($ $ |#2|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 24 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#2|))) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|Equation| |#2|)) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ |#2| |#2|) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|List| |#2|) (|List| |#2|)) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|enumerate| (((|List| $)) NIL (|has| |#2| (|Finite|)))) (|entry?| (((|Boolean|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|entries| (((|List| |#2|) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#2| $ (|Integer|) |#2|) NIL) ((|#2| $ (|Integer|)) 21)) (|dot| ((|#2| $ $) NIL (|has| |#2| (|Ring|)))) (|directProduct| (($ (|Vector| |#2|)) 18)) (|dimension| (((|CardinalNumber|)) NIL (|has| |#2| (|Field|)))) (|differentiate| (($ $) NIL (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) (($ $ (|NonNegativeInteger|)) NIL (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) (($ $ (|Symbol|)) NIL (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) NIL (|has| |#2| (|Ring|))) (($ $ (|Mapping| |#2| |#2|)) NIL (|has| |#2| (|Ring|)))) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|copy| (($ $) NIL)) (|coerce| (((|Vector| |#2|) $) 10) (((|OutputForm|) $) NIL (|has| |#2| (|SetCategory|))) (($ (|Integer|)) NIL (OR (AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#2| (|SetCategory|))) (|has| |#2| (|Ring|)))) (($ (|Fraction| (|Integer|))) NIL (AND (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|)))) (($ |#2|) 13 (|has| |#2| (|SetCategory|)))) (|characteristic| (((|NonNegativeInteger|)) NIL (|has| |#2| (|Ring|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|abs| (($ $) NIL (|has| |#2| (|OrderedRing|)))) (^ (($ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|Monoid|))) (($ $ (|PositiveInteger|)) NIL (|has| |#2| (|Monoid|)))) (|Zero| (($) 35 (|has| |#2| (|CancellationAbelianMonoid|)) CONST)) (|One| (($) 38 (|has| |#2| (|Monoid|)) CONST)) (D (($ $) NIL (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) (($ $ (|NonNegativeInteger|)) NIL (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) (($ $ (|Symbol|)) NIL (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) NIL (|has| |#2| (|Ring|))) (($ $ (|Mapping| |#2| |#2|)) NIL (|has| |#2| (|Ring|)))) (>= (((|Boolean|) $ $) NIL (OR (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedRing|))))) (> (((|Boolean|) $ $) NIL (OR (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedRing|))))) (= (((|Boolean|) $ $) 26 (|has| |#2| (|SetCategory|)))) (<= (((|Boolean|) $ $) NIL (OR (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedRing|))))) (< (((|Boolean|) $ $) 58 (OR (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedRing|))))) (/ (($ $ |#2|) NIL (|has| |#2| (|Field|)))) (- (($ $ $) NIL (|has| |#2| (|Ring|))) (($ $) NIL (|has| |#2| (|Ring|)))) (+ (($ $ $) 33 (|has| |#2| (|AbelianSemiGroup|)))) (** (($ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|Monoid|))) (($ $ (|PositiveInteger|)) NIL (|has| |#2| (|Monoid|)))) (* (($ (|Integer|) $) NIL (|has| |#2| (|Ring|))) (($ $ $) 44 (|has| |#2| (|Monoid|))) (($ $ |#2|) 42 (|has| |#2| (|Monoid|))) (($ |#2| $) 43 (|has| |#2| (|Monoid|))) (($ (|NonNegativeInteger|) $) NIL (|has| |#2| (|CancellationAbelianMonoid|))) (($ (|PositiveInteger|) $) NIL (|has| |#2| (|AbelianSemiGroup|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|DirectProduct| |#1| |#2|) (|DirectProductCategory| |#1| |#2|) (|NonNegativeInteger|) (|Type|)) (T |DirectProduct|)) 
NIL 
(|DirectProductCategory| |#1| |#2|) 
((~= (((|Boolean|) $ $) NIL)) (|zeta| (($) 34 T CONST)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|CommutativeRing|)))) (|unitCanonical| (($ $) NIL (|has| |#1| (|CommutativeRing|)))) (|unit?| (((|Boolean|) $) 54 (|has| |#1| (|CommutativeRing|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) 55)) (|one?| (((|Boolean|) $) NIL)) (|multiplicative?| (((|Boolean|) $ (|PositiveInteger|)) 71)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|CommutativeRing|)))) (|elt| ((|#1| $ (|PositiveInteger|)) 9)) (|coerce| (((|OutputForm|) $) 29) (($ (|Integer|)) NIL) (($ (|Mapping| |#1| (|PositiveInteger|))) 12) (((|Mapping| |#1| (|PositiveInteger|)) $) 11) (($ (|Stream| |#1|)) 26) (((|Stream| |#1|) $) 24) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|))) (($ $) NIL (|has| |#1| (|CommutativeRing|)))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|associates?| (((|Boolean|) $ $) NIL (|has| |#1| (|CommutativeRing|)))) (|additive?| (((|Boolean|) $ (|PositiveInteger|)) 72)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 33 T CONST)) (|One| (($) 13 T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) 38) (($ $ $) NIL)) (+ (($ $ $) 36)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 40) (($ $ $) 51) (($ |#1| $) 42 (|has| |#1| (|CommutativeRing|))) (($ $ |#1|) NIL (|has| |#1| (|CommutativeRing|))))) 
(((|DirichletRing| |#1|) (|Join| (|Ring|) (|Eltable| (|PositiveInteger|) |#1|) (CATEGORY |domain| (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|IntegralDomain|)) |noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |#1|)) |noBranch|) (SIGNATURE |coerce| ($ (|Mapping| |#1| (|PositiveInteger|)))) (SIGNATURE |coerce| ((|Mapping| |#1| (|PositiveInteger|)) $)) (SIGNATURE |coerce| ($ (|Stream| |#1|))) (SIGNATURE |coerce| ((|Stream| |#1|) $)) (SIGNATURE |zeta| ($) |constant|) (SIGNATURE |multiplicative?| ((|Boolean|) $ (|PositiveInteger|))) (SIGNATURE |additive?| ((|Boolean|) $ (|PositiveInteger|))))) (|Ring|)) (T |DirichletRing|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 (|PositiveInteger|))) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|DirichletRing| *3)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 (|PositiveInteger|))) (|isDomain| *1 (|DirichletRing| *3)) (|ofCategory| *3 (|Ring|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|DirichletRing| *3)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Stream| *3)) (|isDomain| *1 (|DirichletRing| *3)) (|ofCategory| *3 (|Ring|)))) (|zeta| (*1 *1) (AND (|isDomain| *1 (|DirichletRing| *2)) (|ofCategory| *2 (|Ring|)))) (|multiplicative?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|DirichletRing| *4)) (|ofCategory| *4 (|Ring|)))) (|additive?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|DirichletRing| *4)) (|ofCategory| *4 (|Ring|))))) 
(|Join| (|Ring|) (|Eltable| (|PositiveInteger|) |#1|) (CATEGORY |domain| (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|IntegralDomain|)) |noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |#1|)) |noBranch|) (SIGNATURE |coerce| ($ (|Mapping| |#1| (|PositiveInteger|)))) (SIGNATURE |coerce| ((|Mapping| |#1| (|PositiveInteger|)) $)) (SIGNATURE |coerce| ($ (|Stream| |#1|))) (SIGNATURE |coerce| ((|Stream| |#1|) $)) (SIGNATURE |zeta| ($) |constant|) (SIGNATURE |multiplicative?| ((|Boolean|) $ (|PositiveInteger|))) (SIGNATURE |additive?| ((|Boolean|) $ (|PositiveInteger|))))) 
((|sayLength| (((|Integer|) (|List| (|String|))) 24) (((|Integer|) (|String|)) 19)) (|say| (((|Void|) (|List| (|String|))) 29) (((|Void|) (|String|)) 28)) (|newLine| (((|String|)) 14)) (|copies| (((|String|) (|Integer|) (|String|)) 16)) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) 25) (((|String|) (|String|) (|Integer|) (|String|)) 23)) (|bright| (((|List| (|String|)) (|List| (|String|))) 13) (((|List| (|String|)) (|String|)) 11))) 
(((|DisplayPackage|) (CATEGORY |package| (SIGNATURE |bright| ((|List| (|String|)) (|String|))) (SIGNATURE |bright| ((|List| (|String|)) (|List| (|String|)))) (SIGNATURE |newLine| ((|String|))) (SIGNATURE |copies| ((|String|) (|Integer|) (|String|))) (SIGNATURE |center| ((|String|) (|String|) (|Integer|) (|String|))) (SIGNATURE |center| ((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|))) (SIGNATURE |say| ((|Void|) (|String|))) (SIGNATURE |say| ((|Void|) (|List| (|String|)))) (SIGNATURE |sayLength| ((|Integer|) (|String|))) (SIGNATURE |sayLength| ((|Integer|) (|List| (|String|)))))) (T |DisplayPackage|)) 
((|sayLength| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|String|))) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|DisplayPackage|)))) (|sayLength| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|DisplayPackage|)))) (|say| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|String|))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|DisplayPackage|)))) (|say| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|DisplayPackage|)))) (|center| (*1 *2 *2 *3 *4) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *3 (|Integer|)) (|isDomain| *4 (|String|)) (|isDomain| *1 (|DisplayPackage|)))) (|center| (*1 *2 *2 *3 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|DisplayPackage|)))) (|copies| (*1 *2 *3 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|DisplayPackage|)))) (|newLine| (*1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|DisplayPackage|)))) (|bright| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|DisplayPackage|)))) (|bright| (*1 *2 *3) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|DisplayPackage|)) (|isDomain| *3 (|String|))))) 
(CATEGORY |package| (SIGNATURE |bright| ((|List| (|String|)) (|String|))) (SIGNATURE |bright| ((|List| (|String|)) (|List| (|String|)))) (SIGNATURE |newLine| ((|String|))) (SIGNATURE |copies| ((|String|) (|Integer|) (|String|))) (SIGNATURE |center| ((|String|) (|String|) (|Integer|) (|String|))) (SIGNATURE |center| ((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|))) (SIGNATURE |say| ((|Void|) (|String|))) (SIGNATURE |say| ((|Void|) (|List| (|String|)))) (SIGNATURE |sayLength| ((|Integer|) (|String|))) (SIGNATURE |sayLength| ((|Integer|) (|List| (|String|))))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) 44)) (|suppOfZero| (((|List| |#1|) $) 30)) (|suppOfPole| (((|List| |#1|) $) 29)) (|supp| (((|List| |#1|) $) 31)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|split| (((|List| $) $) 36)) (|size| (((|NonNegativeInteger|) $) 43)) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 39)) (|retract| ((|#1| $) 40)) (|nthFactor| ((|#1| $ (|Integer|)) 46)) (|nthCoef| (((|Integer|) $ (|Integer|)) 45)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 49)) (|mapCoef| (($ (|Mapping| (|Integer|) (|Integer|)) $) 48)) (|latex| (((|String|) $) 9)) (|incr| (($ $) 26)) (|highCommonTerms| (($ $ $) 50 (|has| (|Integer|) (|OrderedAbelianMonoid|)))) (|hash| (((|SingleInteger|) $) 10)) (|effective?| (((|Boolean|) $) 32)) (|divOfZero| (($ $) 28)) (|divOfPole| (($ $) 27)) (|degree| (((|Integer|) $) 37)) (|concat| (($ $ $) 33)) (|collect| (($ $) 34)) (|coerce| (((|OutputForm|) $) 11) (($ |#1|) 38)) (|coefficient| (((|Integer|) |#1| $) 47)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 35)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13) (($ |#1| $) 41)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ (|Integer|)) 52) (($ (|Integer|) $) 51) (($ (|Integer|) |#1|) 42))) 
(((|DivisorCategory| |#1|) (|Category|) (|SetCategory|)) (T |DivisorCategory|)) 
((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|DivisorCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Integer|)))) (|split| (*1 *2 *1) (AND (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|DivisorCategory| *3)))) (<= (*1 *2 *1 *1) (AND (|ofCategory| *1 (|DivisorCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|collect| (*1 *1 *1) (AND (|ofCategory| *1 (|DivisorCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (|concat| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|DivisorCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (|effective?| (*1 *2 *1) (AND (|ofCategory| *1 (|DivisorCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|supp| (*1 *2 *1) (AND (|ofCategory| *1 (|DivisorCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|List| *3)))) (|suppOfZero| (*1 *2 *1) (AND (|ofCategory| *1 (|DivisorCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|List| *3)))) (|suppOfPole| (*1 *2 *1) (AND (|ofCategory| *1 (|DivisorCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|List| *3)))) (|divOfZero| (*1 *1 *1) (AND (|ofCategory| *1 (|DivisorCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (|divOfPole| (*1 *1 *1) (AND (|ofCategory| *1 (|DivisorCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (|incr| (*1 *1 *1) (AND (|ofCategory| *1 (|DivisorCategory| *2)) (|ofCategory| *2 (|SetCategory|))))) 
(|Join| (|AbelianGroup|) (|Module| (|Integer|)) (|FreeAbelianMonoidCategory| |t#1| (|Integer|)) (CATEGORY |domain| (SIGNATURE |degree| ((|Integer|) $)) (SIGNATURE |split| ((|List| $) $)) (SIGNATURE <= ((|Boolean|) $ $)) (SIGNATURE |collect| ($ $)) (SIGNATURE |concat| ($ $ $)) (SIGNATURE |effective?| ((|Boolean|) $)) (SIGNATURE |supp| ((|List| |t#1|) $)) (SIGNATURE |suppOfZero| ((|List| |t#1|) $)) (SIGNATURE |suppOfPole| ((|List| |t#1|) $)) (SIGNATURE |divOfZero| ($ $)) (SIGNATURE |divOfPole| ($ $)) (SIGNATURE |incr| ($ $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| (|Integer|) (|Integer|)) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|FreeAbelianMonoidCategory| |#1| (|Integer|)) . T) ((|LeftModule| (|Integer|)) . T) ((|Module| (|Integer|)) . T) ((|RetractableTo| |#1|) . T) ((|RightModule| (|Integer|)) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 17)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) 30)) (|suppOfZero| (((|List| |#1|) $) 36)) (|suppOfPole| (((|List| |#1|) $) 37)) (|supp| (((|List| |#1|) $) 35)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|split| (((|List| $) $) 29)) (|size| (((|NonNegativeInteger|) $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL)) (|retract| ((|#1| $) NIL)) (|reductum| (($ $) 24)) (|nthFactor| ((|#1| $ (|Integer|)) NIL)) (|nthCoef| (((|Integer|) $ (|Integer|)) NIL)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) NIL)) (|mapCoef| (($ (|Mapping| (|Integer|) (|Integer|)) $) NIL)) (|latex| (((|String|) $) NIL)) (|incr| (($ $) 8)) (|highCommonTerms| (($ $ $) NIL (|has| (|Integer|) (|OrderedAbelianMonoid|)))) (|head| (((|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|))) $) 26)) (|hash| (((|SingleInteger|) $) NIL)) (|effective?| (((|Boolean|) $) 50)) (|divOfZero| (($ $) 38)) (|divOfPole| (($ $) 39)) (|degree| (((|Integer|) $) 58)) (|concat| (($ $ $) 44)) (|collect| (($ $) 33)) (|coerce| (((|OutputForm|) $) 22) (($ |#1|) 27)) (|coefficient| (((|Integer|) |#1| $) 32)) (|Zero| (($) 23 T CONST)) (= (((|Boolean|) $ $) 40)) (<= (((|Boolean|) $ $) 51)) (- (($ $) 48) (($ $ $) 47)) (+ (($ $ $) 45) (($ |#1| $) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 49) (($ $ (|Integer|)) NIL) (($ (|Integer|) $) 49) (($ (|Integer|) |#1|) NIL))) 
(((|Divisor| |#1|) (|Join| (|DivisorCategory| |#1|) (CATEGORY |domain| (SIGNATURE |head| ((|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|))) $)) (SIGNATURE |reductum| ($ $)))) (|SetCategoryWithDegree|)) (T |Divisor|)) 
((|head| (*1 *2 *1) (AND (|isDomain| *2 (|Record| (|:| |gen| *3) (|:| |exp| (|Integer|)))) (|isDomain| *1 (|Divisor| *3)) (|ofCategory| *3 (|SetCategoryWithDegree|)))) (|reductum| (*1 *1 *1) (AND (|isDomain| *1 (|Divisor| *2)) (|ofCategory| *2 (|SetCategoryWithDegree|))))) 
(|Join| (|DivisorCategory| |#1|) (CATEGORY |domain| (SIGNATURE |head| ((|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|))) $)) (SIGNATURE |reductum| ($ $)))) 
((^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) 9)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) 18)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ (|Fraction| (|Integer|)) $) 25) (($ $ (|Fraction| (|Integer|))) NIL))) 
(((|DivisionRing&| |#1|) (CATEGORY |domain| (SIGNATURE ^ (|#1| |#1| (|Integer|))) (SIGNATURE ** (|#1| |#1| (|Integer|))) (SIGNATURE * (|#1| |#1| (|Fraction| (|Integer|)))) (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE ^ (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|))) (SIGNATURE ^ (|#1| |#1| (|PositiveInteger|))) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|DivisionRing|)) (T |DivisionRing&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE ^ (|#1| |#1| (|Integer|))) (SIGNATURE ** (|#1| |#1| (|Integer|))) (SIGNATURE * (|#1| |#1| (|Fraction| (|Integer|)))) (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE ^ (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|))) (SIGNATURE ^ (|#1| |#1| (|PositiveInteger|))) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 38)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ (|Fraction| (|Integer|))) 43)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 39)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 40)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ (|Fraction| (|Integer|)) $) 42) (($ $ (|Fraction| (|Integer|))) 41))) 
(((|DivisionRing|) (|Category|)) (T |DivisionRing|)) 
((** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|DivisionRing|)) (|isDomain| *2 (|Integer|)))) (^ (*1 *1 *1 *2) (AND (|ofCategory| *1 (|DivisionRing|)) (|isDomain| *2 (|Integer|)))) (|inv| (*1 *1 *1) (|ofCategory| *1 (|DivisionRing|)))) 
(|Join| (|EntireRing|) (|Algebra| (|Fraction| (|Integer|))) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Integer|))) (SIGNATURE ^ ($ $ (|Integer|))) (SIGNATURE |inv| ($ $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) . T) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|EntireRing|) . T) ((|LeftModule| (|Fraction| (|Integer|))) . T) ((|LeftModule| $) . T) ((|Module| (|Fraction| (|Integer|))) . T) ((|Monoid|) . T) ((|RightModule| (|Fraction| (|Integer|))) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) 45)) (|tail| (($ $) 54)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setvalue!| ((|#1| $ |#1|) 36 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setprevious!| (($ $ $) 50 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setnext!| (($ $ $) 49 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) 7 T CONST)) (|previous| (($ $) 53)) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) 47)) (|node?| (((|Boolean|) $ $) 39 (|has| |#1| (|SetCategory|)))) (|next| (($ $) 52)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|leaves| (((|List| |#1|) $) 42)) (|leaf?| (((|Boolean|) $) 46)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|last| ((|#1| $) 56)) (|head| (($ $) 55)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| ((|#1| $ "value") 44)) (|distance| (((|Integer|) $ $) 41)) (|cyclic?| (((|Boolean|) $) 43)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|concat!| (($ $ $) 51 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|children| (((|List| $) $) 48)) (|child?| (((|Boolean|) $ $) 40 (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|DoublyLinkedAggregate| |#1|) (|Category|) (|Type|)) (T |DoublyLinkedAggregate|)) 
((|last| (*1 *2 *1) (AND (|ofCategory| *1 (|DoublyLinkedAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|head| (*1 *1 *1) (AND (|ofCategory| *1 (|DoublyLinkedAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|tail| (*1 *1 *1) (AND (|ofCategory| *1 (|DoublyLinkedAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|previous| (*1 *1 *1) (AND (|ofCategory| *1 (|DoublyLinkedAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|next| (*1 *1 *1) (AND (|ofCategory| *1 (|DoublyLinkedAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|concat!| (*1 *1 *1 *1) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|DoublyLinkedAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setprevious!| (*1 *1 *1 *1) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|DoublyLinkedAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setnext!| (*1 *1 *1 *1) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|DoublyLinkedAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|RecursiveAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |last| (|t#1| $)) (SIGNATURE |head| ($ $)) (SIGNATURE |tail| ($ $)) (SIGNATURE |previous| ($ $)) (SIGNATURE |next| ($ $)) (IF (|has| $ (ATTRIBUTE |shallowlyMutable|)) (PROGN (SIGNATURE |concat!| ($ $ $)) (SIGNATURE |setprevious!| ($ $ $)) (SIGNATURE |setnext!| ($ $ $))) |noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) NIL)) (|third| ((|#1| $) NIL)) (|tail| (($ $) NIL)) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|split!| (($ $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) $) NIL (|has| |#1| (|OrderedSet|))) (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) NIL)) (|sort!| (($ $) NIL (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|has| |#1| (|OrderedSet|)))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sort| (($ $) 10 (|has| |#1| (|OrderedSet|))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setvalue!| ((|#1| $ |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setrest!| (($ $ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setlast!| ((|#1| $ |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setfirst!| ((|#1| $ |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ "first" |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "rest" $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ "last" |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|Integer|) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) NIL)) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|second| ((|#1| $) NIL)) (|sample| (($) NIL T CONST)) (|reverse!| (($ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) NIL)) (|rest| (($ $) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|removeDuplicates!| (($ $) NIL (|has| |#1| (|SetCategory|)))) (|removeDuplicates| (($ $) 7 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|remove!| (($ |#1| $) NIL (|has| |#1| (|SetCategory|))) (($ (|Mapping| (|Boolean|) |#1|) $) NIL)) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|qsetelt!| ((|#1| $ (|Integer|) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#1| $ (|Integer|)) NIL)) (|possiblyInfinite?| (((|Boolean|) $) NIL)) (|position| (((|Integer|) |#1| $ (|Integer|)) NIL (|has| |#1| (|SetCategory|))) (((|Integer|) |#1| $) NIL (|has| |#1| (|SetCategory|))) (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) NIL)) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) NIL)) (|node?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|new| (($ (|NonNegativeInteger|) |#1|) NIL)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|merge!| (($ $ $) NIL (|has| |#1| (|OrderedSet|))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) NIL)) (|merge| (($ $ $) NIL (|has| |#1| (|OrderedSet|))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|maxIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL)) (|list| (($ |#1|) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|leaves| (((|List| |#1|) $) NIL)) (|leaf?| (((|Boolean|) $) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|last| ((|#1| $) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|insert!| (($ $ $ (|Integer|)) NIL) (($ |#1| $ (|Integer|)) NIL)) (|insert| (($ $ $ (|Integer|)) NIL) (($ |#1| $ (|Integer|)) NIL)) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|first| ((|#1| $) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) NIL)) (|fill!| (($ $ |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|explicitlyFinite?| (((|Boolean|) $) NIL)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE 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(((|DataList| |#1|) (|Join| (|ListAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|List| |#1|))) (SIGNATURE |coerce| ((|List| |#1|) $)) (SIGNATURE |datalist| ($ (|List| |#1|))) (SIGNATURE |elt| ($ $ "unique")) (SIGNATURE |elt| ($ $ "sort")) (SIGNATURE |elt| ((|NonNegativeInteger|) $ "count")))) (|OrderedSet|)) (T |DataList|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|DataList| *3)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|DataList| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|datalist| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|DataList| *3)))) (|elt| (*1 *1 *1 *2) (AND (|isDomain| *2 "unique") (|isDomain| *1 (|DataList| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|elt| (*1 *1 *1 *2) (AND (|isDomain| *2 "sort") (|isDomain| *1 (|DataList| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 "count") (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|DataList| *4)) (|ofCategory| *4 (|OrderedSet|))))) 
(|Join| (|ListAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|List| |#1|))) (SIGNATURE |coerce| ((|List| |#1|) $)) (SIGNATURE |datalist| ($ (|List| |#1|))) (SIGNATURE |elt| ($ $ "unique")) (SIGNATURE |elt| ($ $ "sort")) (SIGNATURE |elt| ((|NonNegativeInteger|) $ "count")))) 
((|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) 26))) 
(((|DiscreteLogarithmPackage| |#1|) (CATEGORY |package| (SIGNATURE |shanksDiscLogAlgorithm| ((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)))) (|Join| (|Monoid|) (|Finite|) (CATEGORY |package| (SIGNATURE ** (|#1| |#1| (|Integer|)))))) (T |DiscreteLogarithmPackage|)) 
((|shanksDiscLogAlgorithm| (*1 *2 *3 *3 *2) (|partial| AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *3 (|Join| (|Monoid|) (|Finite|) (CATEGORY |package| (SIGNATURE ** (*3 *3 (|Integer|)))))) (|isDomain| *1 (|DiscreteLogarithmPackage| *3))))) 
(CATEGORY |package| (SIGNATURE |shanksDiscLogAlgorithm| ((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)))) 
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$ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (AND (|has| (|OrderedVariableList| |#1|) (|PatternMatchable| (|Integer|))) (|has| |#2| (|PatternMatchable| (|Integer|)))))) (|one?| (((|Boolean|) $) NIL)) (|numberOfMonomials| (((|NonNegativeInteger|) $) NIL)) (|multivariate| (($ (|SparseUnivariatePolynomial| |#2|) (|OrderedVariableList| |#1|)) NIL) (($ (|SparseUnivariatePolynomial| $) (|OrderedVariableList| |#1|)) NIL)) (|monomials| (((|List| $) $) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monomial| (($ |#2| (|DirectProduct| (|#| |#1|) (|NonNegativeInteger|))) NIL) (($ $ (|OrderedVariableList| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| (|NonNegativeInteger|))) NIL)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ (|OrderedVariableList| |#1|)) NIL)) (|minimumDegree| (((|DirectProduct| (|#| |#1|) (|NonNegativeInteger|)) $) NIL) (((|NonNegativeInteger|) $ (|OrderedVariableList| |#1|)) NIL) (((|List| (|NonNegativeInteger|)) $ (|List| (|OrderedVariableList| |#1|))) NIL)) (|min| (($ $ $) NIL (|has| |#2| (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#2| (|OrderedSet|)))) (|mapExponents| (($ (|Mapping| (|DirectProduct| (|#| |#1|) (|NonNegativeInteger|)) (|DirectProduct| (|#| |#1|) (|NonNegativeInteger|))) $) NIL)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL)) (|mainVariable| (((|Union| (|OrderedVariableList| |#1|) "failed") $) NIL)) (|leadingMonomial| (($ $) NIL)) (|leadingCoefficient| ((|#2| $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| |#2| (|GcdDomain|)))) (|lcm| (($ (|List| $)) NIL (|has| |#2| (|GcdDomain|))) (($ $ $) NIL (|has| |#2| (|GcdDomain|)))) (|latex| (((|String|) $) NIL)) (|isTimes| (((|Union| (|List| $) "failed") $) NIL)) (|isPlus| (((|Union| (|List| $) "failed") $) NIL)) (|isExpt| (((|Union| (|Record| (|:| |var| (|OrderedVariableList| |#1|)) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|ground?| (((|Boolean|) $) NIL)) (|ground| ((|#2| $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|GcdDomain|)))) (|gcd| (($ (|List| $)) NIL (|has| |#2| (|GcdDomain|))) (($ $ $) NIL (|has| |#2| (|GcdDomain|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|exquo| (((|Union| $ "failed") $ |#2|) NIL (|has| |#2| (|IntegralDomain|))) (((|Union| $ "failed") $ $) NIL (|has| |#2| (|IntegralDomain|)))) (|eval| (($ $ (|List| (|Equation| $))) NIL) (($ $ (|Equation| $)) NIL) (($ $ $ $) NIL) (($ $ (|List| $) (|List| $)) NIL) (($ $ (|OrderedVariableList| |#1|) |#2|) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| |#2|)) NIL) (($ $ (|OrderedVariableList| |#1|) $) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| $)) NIL)) (|discriminant| (($ $ (|OrderedVariableList| |#1|)) NIL (|has| |#2| (|CommutativeRing|)))) (|differentiate| (($ $ (|OrderedVariableList| |#1|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|))) NIL) (($ $ (|OrderedVariableList| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| (|NonNegativeInteger|))) NIL)) (|degree| (((|DirectProduct| (|#| |#1|) (|NonNegativeInteger|)) $) NIL) (((|NonNegativeInteger|) $ (|OrderedVariableList| |#1|)) NIL) (((|List| (|NonNegativeInteger|)) $ (|List| (|OrderedVariableList| |#1|))) NIL)) (|convert| (((|Pattern| (|Float|)) $) NIL (AND (|has| (|OrderedVariableList| |#1|) (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Float|)))))) (((|Pattern| (|Integer|)) $) NIL (AND (|has| (|OrderedVariableList| |#1|) (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Integer|)))))) (((|InputForm|) $) NIL (AND (|has| (|OrderedVariableList| |#1|) (|ConvertibleTo| (|InputForm|))) (|has| |#2| (|ConvertibleTo| (|InputForm|)))))) (|content| ((|#2| $) NIL (|has| |#2| (|GcdDomain|))) (($ $ (|OrderedVariableList| |#1|)) NIL (|has| |#2| (|GcdDomain|)))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#2| (|PolynomialFactorizationExplicit|))))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ |#2|) NIL) (($ (|OrderedVariableList| |#1|)) NIL) (($ (|Fraction| (|Integer|))) NIL (OR (|has| |#2| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))))) (($ $) NIL (|has| |#2| (|IntegralDomain|)))) (|coefficients| (((|List| |#2|) $) NIL)) (|coefficient| ((|#2| $ (|DirectProduct| (|#| |#1|) (|NonNegativeInteger|))) NIL) (($ $ (|OrderedVariableList| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| (|NonNegativeInteger|))) NIL)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#2| (|PolynomialFactorizationExplicit|))) (|has| |#2| (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|CommutativeRing|)))) (|associates?| (((|Boolean|) $ $) NIL (|has| |#2| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($ $ (|OrderedVariableList| |#1|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|))) NIL) (($ $ (|OrderedVariableList| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| (|NonNegativeInteger|))) NIL)) (>= (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (/ (($ $ |#2|) NIL (|has| |#2| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#2| (|Algebra| (|Fraction| (|Integer|))))) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#2| (|Algebra| (|Fraction| (|Integer|))))) (($ |#2| $) NIL) (($ $ |#2|) NIL))) 
(((|DistributedMultivariatePolynomial| |#1| |#2|) (|Join| (|PolynomialCategory| |#2| (|DirectProduct| (|#| |#1|) (|NonNegativeInteger|)) (|OrderedVariableList| |#1|)) (CATEGORY |domain| (SIGNATURE |reorder| ($ $ (|List| (|Integer|)))))) (|List| (|Symbol|)) (|Ring|)) (T |DistributedMultivariatePolynomial|)) 
((|reorder| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|DistributedMultivariatePolynomial| *3 *4)) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|Ring|))))) 
(|Join| (|PolynomialCategory| |#2| (|DirectProduct| (|#| |#1|) (|NonNegativeInteger|)) (|OrderedVariableList| |#1|)) (CATEGORY |domain| (SIGNATURE |reorder| ($ $ (|List| (|Integer|)))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitVector| (($ (|PositiveInteger|)) NIL (|has| |#4| (|Ring|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sup| (($ $ $) NIL (|has| |#4| (|OrderedAbelianMonoidSup|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|size| (((|NonNegativeInteger|)) NIL (|has| |#4| (|Finite|)))) (|sign| (((|Integer|) $) NIL (|has| |#4| (|OrderedRing|)))) (|setelt| ((|#4| $ (|Integer|) |#4|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#4| "failed") $) NIL (|has| |#4| (|SetCategory|))) (((|Union| (|Integer|) "failed") $) NIL (AND (|has| |#4| (|RetractableTo| (|Integer|))) (|has| |#4| (|SetCategory|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (AND (|has| |#4| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#4| (|SetCategory|))))) (|retract| ((|#4| $) NIL 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$) NIL)) (|coerce| (((|Vector| |#4|) $) NIL) (((|OutputForm|) $) NIL) (($ |#4|) NIL (|has| |#4| (|SetCategory|))) (($ (|Integer|)) NIL (OR (AND (|has| |#4| (|RetractableTo| (|Integer|))) (|has| |#4| (|SetCategory|))) (|has| |#4| (|Ring|)))) (($ (|Fraction| (|Integer|))) NIL (AND (|has| |#4| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#4| (|SetCategory|))))) (|characteristic| (((|NonNegativeInteger|)) NIL (|has| |#4| (|Ring|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|abs| (($ $) NIL (|has| |#4| (|OrderedRing|)))) (^ (($ $ (|NonNegativeInteger|)) NIL (OR (AND (|has| |#4| (|DifferentialRing|)) (|has| |#4| (|Ring|))) (AND (|has| |#4| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#4| (|Ring|))) (|has| |#4| (|Monoid|)) (AND (|has| |#4| (|PartialDifferentialRing| (|Symbol|))) (|has| |#4| (|Ring|))))) (($ $ (|PositiveInteger|)) NIL (OR (AND (|has| |#4| (|DifferentialRing|)) (|has| |#4| (|Ring|))) (AND (|has| |#4| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#4| (|Ring|))) (|has| |#4| (|Monoid|)) (AND (|has| |#4| (|PartialDifferentialRing| (|Symbol|))) (|has| |#4| (|Ring|)))))) (|Zero| (($) NIL T CONST)) (|One| (($) NIL (OR (AND (|has| |#4| (|DifferentialRing|)) (|has| |#4| (|Ring|))) (AND (|has| |#4| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#4| (|Ring|))) (|has| |#4| (|Monoid|)) (AND (|has| |#4| (|PartialDifferentialRing| (|Symbol|))) (|has| |#4| (|Ring|)))) CONST)) (D (($ $ (|Mapping| |#4| |#4|) (|NonNegativeInteger|)) NIL (|has| |#4| (|Ring|))) (($ $ (|Mapping| |#4| |#4|)) NIL (|has| |#4| (|Ring|))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| |#4| (|PartialDifferentialRing| (|Symbol|))) (|has| |#4| (|Ring|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| |#4| (|PartialDifferentialRing| (|Symbol|))) (|has| |#4| (|Ring|)))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#4| (|PartialDifferentialRing| (|Symbol|))) (|has| |#4| (|Ring|)))) (($ $ (|Symbol|)) NIL (AND (|has| |#4| (|PartialDifferentialRing| (|Symbol|))) (|has| |#4| (|Ring|)))) (($ $ (|NonNegativeInteger|)) NIL (AND (|has| |#4| (|DifferentialRing|)) (|has| |#4| (|Ring|)))) (($ $) NIL (AND (|has| |#4| (|DifferentialRing|)) (|has| |#4| (|Ring|))))) (>= (((|Boolean|) $ $) NIL (OR (|has| |#4| (|OrderedAbelianMonoidSup|)) (|has| |#4| (|OrderedRing|))))) (> (((|Boolean|) $ $) NIL (OR (|has| |#4| (|OrderedAbelianMonoidSup|)) (|has| |#4| (|OrderedRing|))))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (OR (|has| |#4| (|OrderedAbelianMonoidSup|)) (|has| |#4| (|OrderedRing|))))) (< (((|Boolean|) $ $) NIL (OR (|has| |#4| (|OrderedAbelianMonoidSup|)) (|has| |#4| (|OrderedRing|))))) (/ (($ $ |#4|) NIL (|has| |#4| (|Field|)))) (- (($ $ $) NIL) (($ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|NonNegativeInteger|)) NIL (OR (AND (|has| |#4| (|DifferentialRing|)) (|has| |#4| (|Ring|))) (AND (|has| |#4| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#4| (|Ring|))) (|has| |#4| (|Monoid|)) (AND (|has| |#4| (|PartialDifferentialRing| (|Symbol|))) (|has| |#4| (|Ring|))))) (($ $ (|PositiveInteger|)) NIL (OR (AND (|has| |#4| (|DifferentialRing|)) (|has| |#4| (|Ring|))) (AND (|has| |#4| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#4| (|Ring|))) (|has| |#4| (|Monoid|)) (AND (|has| |#4| (|PartialDifferentialRing| (|Symbol|))) (|has| |#4| (|Ring|)))))) (* (($ |#2| $) 14) (($ (|Integer|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|PositiveInteger|) $) NIL) (($ |#3| $) 18) (($ $ |#4|) NIL (|has| |#4| (|Monoid|))) (($ |#4| $) NIL (|has| |#4| (|Monoid|))) (($ $ $) NIL (OR (AND (|has| |#4| (|DifferentialRing|)) (|has| |#4| (|Ring|))) (AND (|has| |#4| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#4| (|Ring|))) (|has| |#4| (|Monoid|)) (AND (|has| |#4| (|PartialDifferentialRing| (|Symbol|))) (|has| |#4| (|Ring|)))))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|DirectProductMatrixModule| |#1| |#2| |#3| |#4|) (|Join| (|DirectProductCategory| |#1| |#4|) (|LeftModule| |#2|) (|LeftModule| |#3|)) (|PositiveInteger|) (|Ring|) (|SquareMatrixCategory| |#1| |#2| (|DirectProduct| |#1| |#2|) (|DirectProduct| |#1| |#2|)) (|LeftModule| |#2|)) (T |DirectProductMatrixModule|)) 
NIL 
(|Join| (|DirectProductCategory| |#1| |#4|) (|LeftModule| |#2|) (|LeftModule| |#3|)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitVector| (($ (|PositiveInteger|)) NIL (|has| |#3| (|Ring|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sup| (($ $ $) NIL (|has| |#3| (|OrderedAbelianMonoidSup|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|size| (((|NonNegativeInteger|)) NIL (|has| |#3| (|Finite|)))) (|sign| (((|Integer|) $) NIL (|has| |#3| (|OrderedRing|)))) (|setelt| ((|#3| $ (|Integer|) |#3|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#3| "failed") $) NIL (|has| |#3| (|SetCategory|))) (((|Union| (|Integer|) "failed") $) NIL (AND (|has| |#3| (|RetractableTo| (|Integer|))) (|has| |#3| (|SetCategory|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (AND (|has| |#3| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#3| (|SetCategory|))))) (|retract| ((|#3| $) NIL (|has| |#3| (|SetCategory|))) (((|Integer|) $) NIL (AND (|has| |#3| (|RetractableTo| (|Integer|))) (|has| |#3| (|SetCategory|)))) (((|Fraction| (|Integer|)) $) NIL (AND (|has| |#3| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#3| (|SetCategory|))))) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#3|)) (|:| |vec| (|Vector| |#3|))) (|Matrix| $) (|Vector| $)) NIL (|has| |#3| (|Ring|))) (((|Matrix| |#3|) (|Matrix| $)) NIL (|has| |#3| (|Ring|))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (AND (|has| |#3| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#3| (|Ring|)))) (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (AND (|has| |#3| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#3| (|Ring|))))) (|recip| (((|Union| $ "failed") $) NIL (OR (AND (|has| |#3| (|DifferentialRing|)) (|has| |#3| (|Ring|))) (AND (|has| |#3| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#3| (|Ring|))) (|has| |#3| (|Monoid|)) (AND (|has| |#3| (|PartialDifferentialRing| (|Symbol|))) (|has| |#3| (|Ring|)))))) (|random| (($) NIL (|has| |#3| (|Finite|)))) (|qsetelt!| ((|#3| $ (|Integer|) |#3|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#3| $ (|Integer|)) NIL)) (|positive?| (((|Boolean|) $) NIL (|has| |#3| (|OrderedRing|)))) (|parts| (((|List| |#3|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|one?| (((|Boolean|) $) NIL (OR (AND (|has| |#3| (|DifferentialRing|)) (|has| |#3| (|Ring|))) (AND (|has| |#3| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#3| (|Ring|))) (|has| |#3| (|Monoid|)) (AND (|has| |#3| (|PartialDifferentialRing| (|Symbol|))) (|has| |#3| (|Ring|)))))) (|negative?| (((|Boolean|) $) NIL (|has| |#3| (|OrderedRing|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL (OR (|has| |#3| (|OrderedAbelianMonoidSup|)) (|has| |#3| (|OrderedRing|))))) (|members| (((|List| |#3|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#3| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#3| (|SetCategory|))))) (|maxIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (OR (|has| |#3| (|OrderedAbelianMonoidSup|)) (|has| |#3| (|OrderedRing|))))) (|map!| (($ (|Mapping| |#3| |#3|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#3| |#3|) $) NIL)) (|lookup| (((|PositiveInteger|) $) NIL (|has| |#3| (|Finite|)))) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL)) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|index| (($ (|PositiveInteger|)) NIL (|has| |#3| (|Finite|)))) (|hash| (((|SingleInteger|) $) NIL)) (|first| ((|#3| $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|fill!| (($ $ |#3|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#3|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#3|))) NIL (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|)))) (($ $ (|Equation| |#3|)) NIL (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|)))) (($ $ |#3| |#3|) NIL (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|)))) (($ $ (|List| |#3|) (|List| |#3|)) NIL (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|enumerate| (((|List| $)) NIL (|has| |#3| (|Finite|)))) (|entry?| (((|Boolean|) |#3| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#3| (|SetCategory|))))) (|entries| (((|List| |#3|) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#3| $ (|Integer|) |#3|) NIL) ((|#3| $ (|Integer|)) 11)) (|dot| ((|#3| $ $) NIL (|has| |#3| (|Ring|)))) (|directProduct| (($ (|Vector| |#3|)) NIL)) (|dimension| (((|CardinalNumber|)) NIL (|has| |#3| (|Field|)))) (|differentiate| (($ $ (|Mapping| |#3| |#3|) 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NIL 
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NIL 
(CATEGORY |domain| (SIGNATURE |coerce| (|#1| |#1|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |eval| (|#1| |#1| (|List| |#3|) (|List| |#2|))) (SIGNATURE |eval| (|#1| |#1| |#3| |#2|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#3|) (|List| |#1|))) (SIGNATURE |eval| (|#1| |#1| |#3| |#1|)) (SIGNATURE |makeVariable| ((|Mapping| |#1| (|NonNegativeInteger|)) |#1|)) (SIGNATURE |separant| (|#1| |#1|)) (SIGNATURE |initial| (|#1| |#1|)) (SIGNATURE |leader| (|#4| |#1|)) (SIGNATURE |isobaric?| ((|Boolean|) |#1|)) (SIGNATURE |weight| ((|NonNegativeInteger|) |#1| |#3|)) (SIGNATURE |weights| ((|List| (|NonNegativeInteger|)) |#1| |#3|)) (SIGNATURE |weight| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |weights| ((|List| (|NonNegativeInteger|)) |#1|)) (SIGNATURE |degree| ((|NonNegativeInteger|) |#1| |#3|)) (SIGNATURE |order| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |order| ((|NonNegativeInteger|) |#1| |#3|)) (SIGNATURE |differentialVariables| ((|List| |#3|) |#1|)) (SIGNATURE |makeVariable| ((|Mapping| |#1| (|NonNegativeInteger|)) |#3|)) (SIGNATURE |retractIfCan| ((|Union| |#3| "failed") |#1|)) (SIGNATURE |coerce| (|#1| |#3|)) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |degree| ((|List| (|NonNegativeInteger|)) |#1| (|List| |#4|))) (SIGNATURE |degree| ((|NonNegativeInteger|) |#1| |#4|)) (SIGNATURE |retractIfCan| ((|Union| |#4| "failed") |#1|)) (SIGNATURE |coerce| (|#1| |#4|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#4|) (|List| |#1|))) (SIGNATURE |eval| (|#1| |#1| |#4| |#1|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#4|) (|List| |#2|))) (SIGNATURE |eval| (|#1| |#1| |#4| |#2|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#1|) (|List| |#1|))) (SIGNATURE |eval| (|#1| |#1| |#1| |#1|)) (SIGNATURE |eval| (|#1| |#1| (|Equation| |#1|))) (SIGNATURE |eval| (|#1| |#1| (|List| (|Equation| |#1|)))) (SIGNATURE |degree| (|#5| |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|List| |#4|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |differentiate| (|#1| |#1| |#4| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| |#4|))) (SIGNATURE |differentiate| (|#1| |#1| |#4|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) 
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(|Join| (|PolynomialCategory| |t#1| |t#4| |t#3|) (|DifferentialExtension| |t#1|) (|RetractableTo| |t#2|) (CATEGORY |domain| (SIGNATURE |makeVariable| ((|Mapping| $ (|NonNegativeInteger|)) |t#2|)) (SIGNATURE |differentialVariables| ((|List| |t#2|) $)) (SIGNATURE |order| ((|NonNegativeInteger|) $ |t#2|)) (SIGNATURE |order| ((|NonNegativeInteger|) $)) (SIGNATURE |degree| ((|NonNegativeInteger|) $ |t#2|)) (SIGNATURE |weights| ((|List| (|NonNegativeInteger|)) $)) (SIGNATURE |weight| ((|NonNegativeInteger|) $)) (SIGNATURE |weights| ((|List| (|NonNegativeInteger|)) $ |t#2|)) (SIGNATURE |weight| ((|NonNegativeInteger|) $ |t#2|)) (SIGNATURE |isobaric?| ((|Boolean|) $)) (SIGNATURE |leader| (|t#3| $)) (SIGNATURE |initial| ($ $)) (SIGNATURE |separant| ($ $)) (IF (|has| |t#1| (|DifferentialRing|)) (PROGN (ATTRIBUTE (|InnerEvalable| |t#2| |t#1|)) (ATTRIBUTE (|InnerEvalable| |t#2| $)) (ATTRIBUTE (|Evalable| $)) (SIGNATURE |makeVariable| ((|Mapping| $ (|NonNegativeInteger|)) $))) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| |#4|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|ConvertibleTo| (|InputForm|)) AND (|has| |#1| (|ConvertibleTo| (|InputForm|))) (|has| |#3| (|ConvertibleTo| (|InputForm|)))) ((|ConvertibleTo| (|Pattern| (|Float|))) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#3| (|ConvertibleTo| (|Pattern| (|Float|))))) ((|ConvertibleTo| (|Pattern| (|Integer|))) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Pattern| (|Integer|))))) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) |has| |#1| (|DifferentialRing|)) ((|EntireRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|Evalable| $) . T) ((|FiniteAbelianMonoidRing| |#1| |#4|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|GcdDomain|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|GcdDomain|))) ((|InnerEvalable| |#2| |#1|) |has| |#1| (|DifferentialRing|)) ((|InnerEvalable| |#2| $) |has| |#1| (|DifferentialRing|)) ((|InnerEvalable| |#3| |#1|) . T) ((|InnerEvalable| |#3| $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|LeftModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|GcdDomain|))) ((|LinearlyExplicitRingOver| (|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|Monoid|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialRing| |#3|) . T) ((|PatternMatchable| (|Float|)) AND (|has| |#1| (|PatternMatchable| (|Float|))) (|has| |#3| (|PatternMatchable| (|Float|)))) ((|PatternMatchable| (|Integer|)) AND (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#3| (|PatternMatchable| (|Integer|)))) ((|PolynomialCategory| |#1| |#4| |#3|) . T) ((|PolynomialFactorizationExplicit|) |has| |#1| (|PolynomialFactorizationExplicit|)) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RetractableTo| |#2|) . T) ((|RetractableTo| |#3|) . T) ((|RightModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|PolynomialFactorizationExplicit|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|top!| ((|#1| $) 51)) (|top| ((|#1| $) 41)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|sample| (($) 7 T CONST)) (|rotate!| (($ $) 57)) (|reverse!| (($ $) 45)) (|push!| ((|#1| |#1| $) 43)) (|pop!| ((|#1| $) 42)) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|length| (((|NonNegativeInteger|) $) 58)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|inspect| ((|#1| $) 36)) (|insertTop!| ((|#1| |#1| $) 49)) (|insertBottom!| ((|#1| |#1| $) 48)) (|insert!| (($ |#1| $) 37)) (|height| (((|NonNegativeInteger|) $) 52)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|front| ((|#1| $) 59)) (|extractTop!| ((|#1| $) 47)) (|extractBottom!| ((|#1| $) 46)) (|extract!| ((|#1| $) 38)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|enqueue!| ((|#1| |#1| $) 55)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|dequeue!| ((|#1| $) 56)) (|dequeue| (($) 54) (($ (|List| |#1|)) 53)) (|depth| (((|NonNegativeInteger|) $) 40)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|bottom!| ((|#1| $) 50)) (|bag| (($ (|List| |#1|)) 39)) (|back| ((|#1| $) 60)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|DequeueAggregate| |#1|) (|Category|) (|Type|)) (T |DequeueAggregate|)) 
((|dequeue| (*1 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|dequeue| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *1 (|DequeueAggregate| *3)))) (|height| (*1 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|top!| (*1 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|bottom!| (*1 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|insertTop!| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|insertBottom!| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|extractTop!| (*1 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|extractBottom!| (*1 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|reverse!| (*1 *1 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|StackAggregate| |t#1|) (|QueueAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |dequeue| ($)) (SIGNATURE |dequeue| ($ (|List| |t#1|))) (SIGNATURE |height| ((|NonNegativeInteger|) $)) (SIGNATURE |top!| (|t#1| $)) (SIGNATURE |bottom!| (|t#1| $)) (SIGNATURE |insertTop!| (|t#1| |t#1| $)) (SIGNATURE |insertBottom!| (|t#1| |t#1| $)) (SIGNATURE |extractTop!| (|t#1| $)) (SIGNATURE |extractBottom!| (|t#1| $)) (SIGNATURE |reverse!| ($ $)))) 
(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|QueueAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|StackAggregate| |#1|) . T) ((|Type|) . T)) 
((|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) 139)) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) 160) (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) 158) (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) 163) (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) 159) (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) 150) (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) 149) (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) 129) (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) 127) (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) 128) (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) 125)) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) 162) (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) 161) (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) 165) (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) 164) (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) 152) (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) 151) (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) 135) (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) 134) (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) 133) (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) 132) (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) 99) (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) 98) (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) 95) (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) 94))) 
(((|TopLevelDrawFunctionsForCompiledFunctions|) (CATEGORY |package| (SIGNATURE |draw| ((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|)))) (SIGNATURE |draw| ((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)))) (SIGNATURE |draw| ((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|)))) (SIGNATURE |draw| ((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)))) (SIGNATURE |draw| ((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|)))) (SIGNATURE |draw| ((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)))) (SIGNATURE |draw| ((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|)))) (SIGNATURE |draw| ((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)))) (SIGNATURE |makeObject| ((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|)))) (SIGNATURE |makeObject| ((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)))) (SIGNATURE |makeObject| ((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|)))) (SIGNATURE |makeObject| ((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)))) (SIGNATURE |draw| ((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|)))) (SIGNATURE |draw| ((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)))) (SIGNATURE |makeObject| ((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|)))) (SIGNATURE |makeObject| ((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)))) (SIGNATURE |draw| ((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|)))) (SIGNATURE |draw| ((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)))) (SIGNATURE |makeObject| ((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|)))) (SIGNATURE |makeObject| ((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)))) (SIGNATURE |draw| ((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|)))) (SIGNATURE |draw| ((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)))) (SIGNATURE |makeObject| ((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|)))) (SIGNATURE |makeObject| ((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)))) (SIGNATURE |recolor| ((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)))))) (T |TopLevelDrawFunctionsForCompiledFunctions|)) 
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(((|TopLevelDrawFunctionsForPoints|) (CATEGORY |package| (SIGNATURE |draw| ((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)))) (SIGNATURE |draw| ((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|)))) (SIGNATURE |draw| ((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|))))) (SIGNATURE |draw| ((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|))) (|List| (|DrawOption|)))) (SIGNATURE |draw| ((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)))) (SIGNATURE |draw| ((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|)))))) (T |TopLevelDrawFunctionsForPoints|)) 
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(|GcdDomain|)))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ |#1|) 23) (($ |#3|) 22) (($ |#2|) NIL) (($ (|SparseMultivariatePolynomial| |#1| |#2|)) 28) (($ (|Fraction| (|Integer|))) NIL (OR (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))))) (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|coefficients| (((|List| |#1|) $) NIL)) (|coefficient| ((|#1| $ (|IndexedExponents| |#3|)) NIL) (($ $ |#3| (|NonNegativeInteger|)) NIL) (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) NIL)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) NIL 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(((|DifferentialSparseMultivariatePolynomial| |#1| |#2| |#3|) (|Join| (|DifferentialPolynomialCategory| |#1| |#2| |#3| (|IndexedExponents| |#3|)) (|RetractableTo| (|SparseMultivariatePolynomial| |#1| |#2|))) (|Ring|) (|OrderedSet|) (|DifferentialVariableCategory| |#2|)) (T |DifferentialSparseMultivariatePolynomial|)) 
NIL 
(|Join| (|DifferentialPolynomialCategory| |#1| |#2| |#3| (|IndexedExponents| |#3|)) (|RetractableTo| (|SparseMultivariatePolynomial| |#1| |#2|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) 45)) (|tree| (($ |#1| (|List| $)) 51) (($ |#1|) 50) (($ (|List| |#1|)) 49)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setvalue!| ((|#1| $ |#1|) 36 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) 7 T CONST)) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) 47)) (|node?| (((|Boolean|) $ $) 39 (|has| |#1| (|SetCategory|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|leaves| (((|List| |#1|) $) 42)) (|leaf?| (((|Boolean|) $) 46)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| ((|#1| $ "value") 44)) (|distance| (((|Integer|) $ $) 41)) (|cyclic?| (((|Boolean|) $) 43)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|children| (((|List| $) $) 48)) (|child?| (((|Boolean|) $ $) 40 (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|DesingTreeCategory| |#1|) (|Category|) (|SetCategory|)) (T |DesingTreeCategory|)) 
((|tree| (*1 *1 *2 *3) (AND (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|DesingTreeCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (|tree| (*1 *1 *2) (AND (|ofCategory| *1 (|DesingTreeCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (|tree| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *1 (|DesingTreeCategory| *3))))) 
(|Join| (|RecursiveAggregate| |t#1|) (CATEGORY |domain| (ATTRIBUTE |shallowlyMutable|) (ATTRIBUTE |finiteAggregate|) (SIGNATURE |tree| ($ |t#1| (|List| $))) (SIGNATURE |tree| ($ |t#1|)) (SIGNATURE |tree| ($ (|List| |t#1|))))) 
(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) 12)) (|tree| (($ |#1| (|List| $)) 31) (($ |#1|) 32) (($ (|List| |#1|)) 33)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setvalue!| ((|#1| $ |#1|) 35 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) NIL T CONST)) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) NIL)) (|node?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|leaves| (((|List| |#1|) $) 22)) (|leaf?| (((|Boolean|) $) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|fullOutput| (((|Boolean|) (|Boolean|)) 18) (((|Boolean|)) 19)) (|fullOut| (((|OutputForm|) $) 15)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|encode| (((|String|) $) 28)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#1| $ "value") NIL)) (|distance| (((|Integer|) $ $) NIL)) (|cyclic?| (((|Boolean|) $) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) NIL)) (|coerce| (((|OutputForm|) $) 30 (|has| |#1| (|SetCategory|)))) (|children| (((|List| $) $) 8)) (|child?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 26 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|DesingTree| |#1|) (|Join| (|DesingTreeCategory| |#1|) (CATEGORY |domain| (SIGNATURE |encode| ((|String|) $)) (SIGNATURE |fullOut| ((|OutputForm|) $)) (SIGNATURE |fullOutput| ((|Boolean|) (|Boolean|))) (SIGNATURE |fullOutput| ((|Boolean|))))) (|SetCategory|)) (T |DesingTree|)) 
((|encode| (*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|DesingTree| *3)) (|ofCategory| *3 (|SetCategory|)))) (|fullOut| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|DesingTree| *3)) (|ofCategory| *3 (|SetCategory|)))) (|fullOutput| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|DesingTree| *3)) (|ofCategory| *3 (|SetCategory|)))) (|fullOutput| (*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|DesingTree| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(|Join| (|DesingTreeCategory| |#1|) (CATEGORY |domain| (SIGNATURE |encode| ((|String|) $)) (SIGNATURE |fullOut| ((|OutputForm|) $)) (SIGNATURE |fullOutput| ((|Boolean|) (|Boolean|))) (SIGNATURE |fullOutput| ((|Boolean|))))) 
((|initializeParamOfPlaces| (((|Void|) |#10| (|List| |#3|)) 133) (((|Void|) |#10|) 135)) (|initParLocLeaves| (((|Void|) |#10|) NIL)) (|inBetweenExcpDiv| ((|#8| |#10|) 28)) (|genusTreeNeg| (((|Integer|) (|NonNegativeInteger|) (|List| |#10|)) 147)) (|genusTree| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|List| |#10|)) 145)) (|genusNeg| (((|Integer|) |#3|) 148)) (|genus| (((|NonNegativeInteger|) |#3|) 146)) (|fullParamInit| (((|Void|) |#10|) 136)) (|divisorAtDesingTree| ((|#8| |#3| |#10|) 111)) (|desingTreeAtPoint| ((|#10| |#5| |#3|) 138)) (|desingTree| (((|List| |#10|) |#3|) 144)) (|blowUpWithExcpDiv| (((|Void|) |#10|) 134)) (|blowUp| (((|List| |#9|) |#9|) 87)) (|adjunctionDivisor| ((|#8| |#10|) 110))) 
(((|DesingTreePackage| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8| |#9| |#10| |#11|) (CATEGORY |package| (SIGNATURE |blowUp| ((|List| |#9|) |#9|)) (SIGNATURE |divisorAtDesingTree| (|#8| |#3| |#10|)) (SIGNATURE |adjunctionDivisor| (|#8| |#10|)) (SIGNATURE |blowUpWithExcpDiv| ((|Void|) |#10|)) (SIGNATURE |desingTreeAtPoint| (|#10| |#5| |#3|)) (SIGNATURE |desingTree| ((|List| |#10|) |#3|)) (SIGNATURE |fullParamInit| ((|Void|) |#10|)) (SIGNATURE |initParLocLeaves| ((|Void|) |#10|)) (SIGNATURE |initializeParamOfPlaces| ((|Void|) |#10|)) (SIGNATURE |initializeParamOfPlaces| ((|Void|) |#10| (|List| |#3|))) (SIGNATURE |genus| ((|NonNegativeInteger|) |#3|)) (SIGNATURE |genusNeg| ((|Integer|) |#3|)) (SIGNATURE |genusTree| ((|NonNegativeInteger|) (|NonNegativeInteger|) (|List| |#10|))) (SIGNATURE |inBetweenExcpDiv| (|#8| |#10|)) (SIGNATURE |genusTreeNeg| ((|Integer|) (|NonNegativeInteger|) (|List| |#10|)))) (|Field|) (|List| (|Symbol|)) (|PolynomialCategory| |#1| |#4| (|OrderedVariableList| |#2|)) (|DirectProductCategory| (|#| |#2|) (|NonNegativeInteger|)) (|ProjectiveSpaceCategory| |#1|) (|LocalPowerSeriesCategory| |#1|) (|PlacesCategory| |#1| |#6|) (|DivisorCategory| |#7|) (|InfinitlyClosePointCategory| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8| |#11|) (|DesingTreeCategory| |#9|) (|BlowUpMethodCategory|)) (T |DesingTreePackage|)) 
((|genusTreeNeg| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *14)) (|ofCategory| *14 (|DesingTreeCategory| *13)) (|ofCategory| *13 (|InfinitlyClosePointCategory| *5 *6 *7 *8 *9 *10 *11 *12 *15)) (|ofCategory| *15 (|BlowUpMethodCategory|)) (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|PolynomialCategory| *5 *8 (|OrderedVariableList| *6))) (|ofCategory| *8 (|DirectProductCategory| (|#| *6) *3)) (|ofCategory| *9 (|ProjectiveSpaceCategory| *5)) (|ofCategory| *10 (|LocalPowerSeriesCategory| *5)) (|ofCategory| *11 (|PlacesCategory| *5 *10)) (|ofCategory| *12 (|DivisorCategory| *11)) (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|DesingTreePackage| *5 *6 *7 *8 *9 *10 *11 *12 *13 *14 *15)))) (|inBetweenExcpDiv| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *8 *9 *10 *2 *12)) (|ofCategory| *12 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|DivisorCategory| *10)) (|isDomain| *1 (|DesingTreePackage| *4 *5 *6 *7 *8 *9 *10 *2 *11 *3 *12)) (|ofCategory| *3 (|DesingTreeCategory| *11)))) (|genusTree| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| *13)) (|ofCategory| *13 (|DesingTreeCategory| *12)) (|ofCategory| *12 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *8 *9 *10 *11 *14)) (|ofCategory| *14 (|BlowUpMethodCategory|)) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) *2)) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|ofCategory| *11 (|DivisorCategory| *10)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|DesingTreePackage| *4 *5 *6 *7 *8 *9 *10 *11 *12 *13 *14)))) (|genusNeg| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *3 (|PolynomialCategory| *4 *6 (|OrderedVariableList| *5))) (|ofCategory| *6 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *9 (|PlacesCategory| *4 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *4 *5 *3 *6 *7 *8 *9 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|DesingTreePackage| *4 *5 *3 *6 *7 *8 *9 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|genus| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *3 (|PolynomialCategory| *4 *6 (|OrderedVariableList| *5))) (|ofCategory| *6 (|DirectProductCategory| (|#| *5) *2)) (|ofCategory| *7 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *9 (|PlacesCategory| *4 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *4 *5 *3 *6 *7 *8 *9 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|DesingTreePackage| *4 *5 *3 *6 *7 *8 *9 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|initializeParamOfPlaces| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *7)) (|ofCategory| *7 (|PolynomialCategory| *5 *8 (|OrderedVariableList| *6))) (|ofCategory| *8 (|DirectProductCategory| (|#| *6) (|NonNegativeInteger|))) (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *9 (|ProjectiveSpaceCategory| *5)) (|ofCategory| *10 (|LocalPowerSeriesCategory| *5)) (|ofCategory| *11 (|PlacesCategory| *5 *10)) (|ofCategory| *12 (|DivisorCategory| *11)) (|ofCategory| *13 (|InfinitlyClosePointCategory| *5 *6 *7 *8 *9 *10 *11 *12 *14)) (|ofCategory| *14 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|DesingTreePackage| *5 *6 *7 *8 *9 *10 *11 *12 *13 *3 *14)) (|ofCategory| *3 (|DesingTreeCategory| *13)))) (|initializeParamOfPlaces| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|ofCategory| *11 (|DivisorCategory| *10)) (|ofCategory| *12 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *8 *9 *10 *11 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|DesingTreePackage| *4 *5 *6 *7 *8 *9 *10 *11 *12 *3 *13)) (|ofCategory| *3 (|DesingTreeCategory| *12)))) (|initParLocLeaves| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|ofCategory| *11 (|DivisorCategory| *10)) (|ofCategory| *12 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *8 *9 *10 *11 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|DesingTreePackage| *4 *5 *6 *7 *8 *9 *10 *11 *12 *3 *13)) (|ofCategory| *3 (|DesingTreeCategory| *12)))) (|fullParamInit| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|ofCategory| *11 (|DivisorCategory| *10)) (|ofCategory| *12 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *8 *9 *10 *11 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|DesingTreePackage| *4 *5 *6 *7 *8 *9 *10 *11 *12 *3 *13)) (|ofCategory| *3 (|DesingTreeCategory| *12)))) (|desingTree| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *3 (|PolynomialCategory| *4 *6 (|OrderedVariableList| *5))) (|ofCategory| *6 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *9 (|PlacesCategory| *4 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *4 *5 *3 *6 *7 *8 *9 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|List| *12)) (|isDomain| *1 (|DesingTreePackage| *4 *5 *3 *6 *7 *8 *9 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|desingTreeAtPoint| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *4 (|PolynomialCategory| *5 *7 (|OrderedVariableList| *6))) (|ofCategory| *7 (|DirectProductCategory| (|#| *6) (|NonNegativeInteger|))) (|ofCategory| *3 (|ProjectiveSpaceCategory| *5)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *5)) (|ofCategory| *9 (|PlacesCategory| *5 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *12 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|DesingTreeCategory| *11)) (|isDomain| *1 (|DesingTreePackage| *5 *6 *4 *7 *3 *8 *9 *10 *11 *2 *12)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *5 *6 *4 *7 *3 *8 *9 *10 *12)))) (|blowUpWithExcpDiv| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|ofCategory| *11 (|DivisorCategory| *10)) (|ofCategory| *12 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *8 *9 *10 *11 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|DesingTreePackage| *4 *5 *6 *7 *8 *9 *10 *11 *12 *3 *13)) (|ofCategory| *3 (|DesingTreeCategory| *12)))) (|adjunctionDivisor| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *8 *9 *10 *2 *12)) (|ofCategory| *12 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|DivisorCategory| *10)) (|isDomain| *1 (|DesingTreePackage| *4 *5 *6 *7 *8 *9 *10 *2 *11 *3 *12)) (|ofCategory| *3 (|DesingTreeCategory| *11)))) (|divisorAtDesingTree| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *3 (|PolynomialCategory| *5 *7 (|OrderedVariableList| *6))) (|ofCategory| *7 (|DirectProductCategory| (|#| *6) (|NonNegativeInteger|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *5)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *5)) (|ofCategory| *10 (|PlacesCategory| *5 *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *5 *6 *3 *7 *8 *9 *10 *2 *12)) (|ofCategory| *12 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|DivisorCategory| *10)) (|isDomain| *1 (|DesingTreePackage| *5 *6 *3 *7 *8 *9 *10 *2 *11 *4 *12)) (|ofCategory| *4 (|DesingTreeCategory| *11)))) (|blowUp| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|ofCategory| *11 (|DivisorCategory| *10)) (|ofCategory| *3 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *8 *9 *10 *11 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|DesingTreePackage| *4 *5 *6 *7 *8 *9 *10 *11 *3 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *3))))) 
(CATEGORY |package| (SIGNATURE |blowUp| ((|List| |#9|) |#9|)) (SIGNATURE |divisorAtDesingTree| (|#8| |#3| |#10|)) (SIGNATURE |adjunctionDivisor| (|#8| |#10|)) (SIGNATURE |blowUpWithExcpDiv| ((|Void|) |#10|)) (SIGNATURE |desingTreeAtPoint| (|#10| |#5| |#3|)) (SIGNATURE |desingTree| ((|List| |#10|) |#3|)) (SIGNATURE |fullParamInit| ((|Void|) |#10|)) (SIGNATURE |initParLocLeaves| ((|Void|) |#10|)) (SIGNATURE |initializeParamOfPlaces| ((|Void|) |#10|)) (SIGNATURE |initializeParamOfPlaces| ((|Void|) |#10| (|List| |#3|))) (SIGNATURE |genus| ((|NonNegativeInteger|) |#3|)) (SIGNATURE |genusNeg| ((|Integer|) |#3|)) (SIGNATURE |genusTree| ((|NonNegativeInteger|) (|NonNegativeInteger|) (|List| |#10|))) (SIGNATURE |inBetweenExcpDiv| (|#8| |#10|)) (SIGNATURE |genusTreeNeg| ((|Integer|) (|NonNegativeInteger|) (|List| |#10|)))) 
((|weight| (((|NonNegativeInteger|) $) 30)) (|retractIfCan| (((|Union| |#2| "failed") $) 17)) (|retract| ((|#2| $) 27)) (|differentiate| (($ $) 12) (($ $ (|NonNegativeInteger|)) 15)) (|coerce| (((|OutputForm|) $) 26) (($ |#2|) 10)) (= (((|Boolean|) $ $) 20)) (< (((|Boolean|) $ $) 29))) 
(((|DifferentialVariableCategory&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |weight| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|))) (|DifferentialVariableCategory| |#2|) (|OrderedSet|)) (T |DifferentialVariableCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |weight| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|weight| (((|NonNegativeInteger|) $) 21)) (|variable| ((|#1| $) 22)) (|retractIfCan| (((|Union| |#1| "failed") $) 26)) (|retract| ((|#1| $) 25)) (|order| (((|NonNegativeInteger|) $) 23)) (|min| (($ $ $) 12)) (|max| (($ $ $) 13)) (|makeVariable| (($ |#1| (|NonNegativeInteger|)) 24)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|differentiate| (($ $) 20) (($ $ (|NonNegativeInteger|)) 19)) (|coerce| (((|OutputForm|) $) 11) (($ |#1|) 27)) (>= (((|Boolean|) $ $) 15)) (> (((|Boolean|) $ $) 16)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 14)) (< (((|Boolean|) $ $) 17))) 
(((|DifferentialVariableCategory| |#1|) (|Category|) (|OrderedSet|)) (T |DifferentialVariableCategory|)) 
((|coerce| (*1 *1 *2) (AND (|ofCategory| *1 (|DifferentialVariableCategory| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|makeVariable| (*1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|DifferentialVariableCategory| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|order| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialVariableCategory| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|variable| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialVariableCategory| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|weight| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialVariableCategory| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|differentiate| (*1 *1 *1) (AND (|ofCategory| *1 (|DifferentialVariableCategory| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|DifferentialVariableCategory| *3)) (|ofCategory| *3 (|OrderedSet|))))) 
(|Join| (|OrderedSet|) (|RetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE |makeVariable| ($ |t#1| (|NonNegativeInteger|))) (SIGNATURE |order| ((|NonNegativeInteger|) $)) (SIGNATURE |variable| (|t#1| $)) (SIGNATURE |weight| ((|NonNegativeInteger|) $)) (SIGNATURE |differentiate| ($ $)) (SIGNATURE |differentiate| ($ $ (|NonNegativeInteger|))) (SIGNATURE |coerce| ($ |t#1|)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|OrderedSet|) . T) ((|RetractableTo| |#1|) . T) ((|SetCategory|) . T)) 
((|variables| (((|List| (|Symbol|)) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) 40)) (|varList| (((|List| (|Symbol|)) (|Expression| (|DoubleFloat|)) (|NonNegativeInteger|)) 79)) (|sumOfSquares| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) 50)) (|splitLinear| (((|Expression| (|DoubleFloat|)) (|Expression| (|DoubleFloat|))) 65)) (|sortConstraints| (((|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|))))) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) 26)) (|simpleBounds?| (((|Boolean|) (|List| (|Expression| (|DoubleFloat|)))) 83)) (|quadratic?| (((|Boolean|) (|Expression| (|DoubleFloat|))) 24)) (|optAttributes| (((|List| (|String|)) (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) 104)) (|nonLinearPart| (((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|)))) 86)) (|linearPart| (((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|)))) 85)) (|linearMatrix| (((|Matrix| (|DoubleFloat|)) (|List| (|Expression| (|DoubleFloat|))) (|NonNegativeInteger|)) 93)) (|linear?| (((|Boolean|) (|Expression| (|DoubleFloat|))) 20) (((|Boolean|) (|List| (|Expression| (|DoubleFloat|)))) 84)) (|finiteBound| (((|List| (|DoubleFloat|)) (|List| (|OrderedCompletion| (|DoubleFloat|))) (|DoubleFloat|)) 14)) (|expenseOfEvaluation| (((|Float|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) 99)) (|changeNameToObjf| (((|Result|) (|Symbol|) (|Result|)) 33))) 
(((|e04AgentsPackage|) (CATEGORY |package| (SIGNATURE |finiteBound| ((|List| (|DoubleFloat|)) (|List| (|OrderedCompletion| (|DoubleFloat|))) (|DoubleFloat|))) (SIGNATURE |sortConstraints| ((|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|))))) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|))))))) (SIGNATURE |sumOfSquares| ((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|)))) (SIGNATURE |splitLinear| ((|Expression| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)))) (SIGNATURE |simpleBounds?| ((|Boolean|) (|List| (|Expression| (|DoubleFloat|))))) (SIGNATURE |linear?| ((|Boolean|) (|List| (|Expression| (|DoubleFloat|))))) (SIGNATURE |linear?| ((|Boolean|) (|Expression| (|DoubleFloat|)))) (SIGNATURE |linearMatrix| ((|Matrix| (|DoubleFloat|)) (|List| (|Expression| (|DoubleFloat|))) (|NonNegativeInteger|))) (SIGNATURE |linearPart| ((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|))))) (SIGNATURE |nonLinearPart| ((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|))))) (SIGNATURE |quadratic?| ((|Boolean|) (|Expression| (|DoubleFloat|)))) (SIGNATURE |variables| ((|List| (|Symbol|)) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) (SIGNATURE |varList| ((|List| (|Symbol|)) (|Expression| (|DoubleFloat|)) (|NonNegativeInteger|))) (SIGNATURE |changeNameToObjf| ((|Result|) (|Symbol|) (|Result|))) (SIGNATURE |expenseOfEvaluation| ((|Float|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) (SIGNATURE |optAttributes| ((|List| (|String|)) (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))))))) (T |e04AgentsPackage|)) 
((|optAttributes| (*1 *2 *3) (AND (|isDomain| *3 (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|e04AgentsPackage|)))) (|expenseOfEvaluation| (*1 *2 *3) (AND (|isDomain| *3 (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) (|isDomain| *2 (|Float|)) (|isDomain| *1 (|e04AgentsPackage|)))) (|changeNameToObjf| (*1 *2 *3 *2) (AND (|isDomain| *2 (|Result|)) (|isDomain| *3 (|Symbol|)) (|isDomain| *1 (|e04AgentsPackage|)))) (|varList| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Expression| (|DoubleFloat|))) (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *1 (|e04AgentsPackage|)))) (|variables| (*1 *2 *3) (AND (|isDomain| *3 (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *1 (|e04AgentsPackage|)))) (|quadratic?| (*1 *2 *3) (AND (|isDomain| *3 (|Expression| (|DoubleFloat|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|e04AgentsPackage|)))) (|nonLinearPart| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|Expression| (|DoubleFloat|)))) (|isDomain| *1 (|e04AgentsPackage|)))) (|linearPart| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|Expression| (|DoubleFloat|)))) (|isDomain| *1 (|e04AgentsPackage|)))) (|linearMatrix| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Expression| (|DoubleFloat|)))) (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *2 (|Matrix| (|DoubleFloat|))) (|isDomain| *1 (|e04AgentsPackage|)))) (|linear?| (*1 *2 *3) (AND (|isDomain| *3 (|Expression| (|DoubleFloat|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|e04AgentsPackage|)))) (|linear?| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Expression| (|DoubleFloat|)))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|e04AgentsPackage|)))) (|simpleBounds?| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Expression| (|DoubleFloat|)))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|e04AgentsPackage|)))) (|splitLinear| (*1 *2 *2) (AND (|isDomain| *2 (|Expression| (|DoubleFloat|))) (|isDomain| *1 (|e04AgentsPackage|)))) (|sumOfSquares| (*1 *2 *2) (|partial| AND (|isDomain| *2 (|Expression| (|DoubleFloat|))) (|isDomain| *1 (|e04AgentsPackage|)))) (|sortConstraints| (*1 *2 *2) (AND (|isDomain| *2 (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|isDomain| *1 (|e04AgentsPackage|)))) (|finiteBound| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|isDomain| *4 (|DoubleFloat|)) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|e04AgentsPackage|))))) 
(CATEGORY |package| (SIGNATURE |finiteBound| ((|List| (|DoubleFloat|)) (|List| (|OrderedCompletion| (|DoubleFloat|))) (|DoubleFloat|))) (SIGNATURE |sortConstraints| ((|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|))))) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|))))))) (SIGNATURE |sumOfSquares| ((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|)))) (SIGNATURE |splitLinear| ((|Expression| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)))) (SIGNATURE |simpleBounds?| ((|Boolean|) (|List| (|Expression| (|DoubleFloat|))))) (SIGNATURE |linear?| ((|Boolean|) (|List| (|Expression| (|DoubleFloat|))))) (SIGNATURE |linear?| ((|Boolean|) (|Expression| (|DoubleFloat|)))) (SIGNATURE |linearMatrix| ((|Matrix| (|DoubleFloat|)) (|List| (|Expression| (|DoubleFloat|))) (|NonNegativeInteger|))) (SIGNATURE |linearPart| ((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|))))) (SIGNATURE |nonLinearPart| ((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|))))) (SIGNATURE |quadratic?| ((|Boolean|) (|Expression| (|DoubleFloat|)))) (SIGNATURE |variables| ((|List| (|Symbol|)) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) (SIGNATURE |varList| ((|List| (|Symbol|)) (|Expression| (|DoubleFloat|)) (|NonNegativeInteger|))) (SIGNATURE |changeNameToObjf| ((|Result|) (|Symbol|) (|Result|))) (SIGNATURE |expenseOfEvaluation| ((|Float|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) (SIGNATURE |optAttributes| ((|List| (|String|)) (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))))) 
((~= (((|Boolean|) $ $) NIL)) (|numericalOptimization| (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) NIL) (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) 39)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) 20) (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|e04dgfAnnaType|) (|NumericalOptimizationCategory|)) (T |e04dgfAnnaType|)) 
NIL 
(|NumericalOptimizationCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|numericalOptimization| (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) 54) (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) 49)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) 29) (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) 31)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|e04fdfAnnaType|) (|NumericalOptimizationCategory|)) (T |e04fdfAnnaType|)) 
NIL 
(|NumericalOptimizationCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|numericalOptimization| (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) 73) (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) 69)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) 40) (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) 51)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|e04gcfAnnaType|) (|NumericalOptimizationCategory|)) (T |e04gcfAnnaType|)) 
NIL 
(|NumericalOptimizationCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|numericalOptimization| (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) NIL) (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) 48)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) 27) (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|e04jafAnnaType|) (|NumericalOptimizationCategory|)) (T |e04jafAnnaType|)) 
NIL 
(|NumericalOptimizationCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|numericalOptimization| (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) NIL) (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) 48)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) 23) (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|e04mbfAnnaType|) (|NumericalOptimizationCategory|)) (T |e04mbfAnnaType|)) 
NIL 
(|NumericalOptimizationCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|numericalOptimization| (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) NIL) (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) 69)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) 23) (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|e04nafAnnaType|) (|NumericalOptimizationCategory|)) (T |e04nafAnnaType|)) 
NIL 
(|NumericalOptimizationCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|numericalOptimization| (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) NIL) (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) 73)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) 19) (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|e04ucfAnnaType|) (|NumericalOptimizationCategory|)) (T |e04ucfAnnaType|)) 
NIL 
(|NumericalOptimizationCategory|) 
((~= (((|Boolean|) $ $) NIL)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|exponents| (((|List| (|Integer|)) $) 16)) (|degree| (((|NonNegativeInteger|) $) 14)) (|coerce| (((|OutputForm|) $) 20) (($ (|List| (|Integer|))) 12)) (|Nul| (($ (|NonNegativeInteger|)) 17)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 9)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 10))) 
(((|ExtAlgBasis|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|List| (|Integer|)))) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |exponents| ((|List| (|Integer|)) $)) (SIGNATURE |Nul| ($ (|NonNegativeInteger|)))))) (T |ExtAlgBasis|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|ExtAlgBasis|)))) (|degree| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ExtAlgBasis|)))) (|exponents| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|ExtAlgBasis|)))) (|Nul| (*1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ExtAlgBasis|))))) 
(|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|List| (|Integer|)))) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |exponents| ((|List| (|Integer|)) $)) (SIGNATURE |Nul| ($ (|NonNegativeInteger|))))) 
((|tanh| ((|#2| |#2|) 77)) (|tan| ((|#2| |#2|) 65)) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) 116)) (|sinh| ((|#2| |#2|) 75)) (|sin| ((|#2| |#2|) 63)) (|sech| ((|#2| |#2|) 79)) (|sec| ((|#2| |#2|) 67)) (|pi| ((|#2|) 46)) (|operator| (((|BasicOperator|) (|BasicOperator|)) 95)) (|log| ((|#2| |#2|) 61)) (|localReal?| (((|Boolean|) |#2|) 134)) (|iitanh| ((|#2| |#2|) 180)) (|iitan| ((|#2| |#2|) 156)) (|iisqrt3| ((|#2|) 59)) (|iisqrt2| ((|#2|) 58)) (|iisinh| ((|#2| |#2|) 176)) (|iisin| ((|#2| |#2|) 152)) (|iisech| ((|#2| |#2|) 184)) (|iisec| ((|#2| |#2|) 160)) (|iilog| ((|#2| |#2|) 148)) (|iiexp| ((|#2| |#2|) 150)) (|iicsch| ((|#2| |#2|) 186)) (|iicsc| ((|#2| |#2|) 162)) (|iicoth| ((|#2| |#2|) 182)) (|iicot| ((|#2| |#2|) 158)) (|iicosh| ((|#2| |#2|) 178)) (|iicos| ((|#2| |#2|) 154)) (|iiatanh| ((|#2| |#2|) 192)) (|iiatan| ((|#2| |#2|) 168)) (|iiasinh| ((|#2| |#2|) 188)) (|iiasin| ((|#2| |#2|) 164)) (|iiasech| ((|#2| |#2|) 196)) (|iiasec| ((|#2| |#2|) 172)) (|iiacsch| ((|#2| |#2|) 198)) (|iiacsc| ((|#2| |#2|) 174)) (|iiacoth| ((|#2| |#2|) 194)) (|iiacot| ((|#2| |#2|) 170)) (|iiacosh| ((|#2| |#2|) 190)) (|iiacos| ((|#2| |#2|) 166)) (|exp| ((|#2| |#2|) 62)) (|csch| ((|#2| |#2|) 80)) (|csc| ((|#2| |#2|) 68)) (|coth| ((|#2| |#2|) 78)) (|cot| ((|#2| |#2|) 66)) (|cosh| ((|#2| |#2|) 76)) (|cos| ((|#2| |#2|) 64)) (|belong?| (((|Boolean|) (|BasicOperator|)) 93)) (|atanh| ((|#2| |#2|) 83)) (|atan| ((|#2| |#2|) 71)) (|asinh| ((|#2| |#2|) 81)) (|asin| ((|#2| |#2|) 69)) (|asech| ((|#2| |#2|) 85)) (|asec| ((|#2| |#2|) 73)) (|acsch| ((|#2| |#2|) 86)) (|acsc| ((|#2| |#2|) 74)) (|acoth| ((|#2| |#2|) 84)) (|acot| ((|#2| |#2|) 72)) (|acosh| ((|#2| |#2|) 82)) (|acos| ((|#2| |#2|) 70))) 
(((|ElementaryFunction| |#1| |#2|) (CATEGORY |package| (SIGNATURE |exp| (|#2| |#2|)) (SIGNATURE |log| (|#2| |#2|)) (SIGNATURE |sin| (|#2| |#2|)) (SIGNATURE |cos| (|#2| |#2|)) (SIGNATURE |tan| (|#2| |#2|)) (SIGNATURE |cot| (|#2| |#2|)) (SIGNATURE |sec| (|#2| |#2|)) (SIGNATURE |csc| (|#2| |#2|)) (SIGNATURE |asin| (|#2| |#2|)) (SIGNATURE |acos| (|#2| |#2|)) (SIGNATURE |atan| (|#2| |#2|)) (SIGNATURE |acot| (|#2| |#2|)) (SIGNATURE |asec| (|#2| |#2|)) (SIGNATURE |acsc| (|#2| |#2|)) (SIGNATURE |sinh| (|#2| |#2|)) (SIGNATURE |cosh| (|#2| |#2|)) (SIGNATURE |tanh| (|#2| |#2|)) (SIGNATURE |coth| (|#2| |#2|)) (SIGNATURE |sech| (|#2| |#2|)) (SIGNATURE |csch| (|#2| |#2|)) (SIGNATURE |asinh| (|#2| |#2|)) (SIGNATURE |acosh| (|#2| |#2|)) (SIGNATURE |atanh| (|#2| |#2|)) (SIGNATURE |acoth| (|#2| |#2|)) (SIGNATURE |asech| (|#2| |#2|)) (SIGNATURE |acsch| (|#2| |#2|)) (SIGNATURE |pi| (|#2|)) (SIGNATURE |belong?| ((|Boolean|) (|BasicOperator|))) (SIGNATURE |operator| ((|BasicOperator|) (|BasicOperator|))) (SIGNATURE |iisqrt2| (|#2|)) (SIGNATURE |iisqrt3| (|#2|)) (SIGNATURE |iiexp| (|#2| |#2|)) (SIGNATURE |iilog| (|#2| |#2|)) (SIGNATURE |iisin| (|#2| |#2|)) (SIGNATURE |iicos| (|#2| |#2|)) (SIGNATURE |iitan| (|#2| |#2|)) (SIGNATURE |iicot| (|#2| |#2|)) (SIGNATURE |iisec| (|#2| |#2|)) (SIGNATURE |iicsc| (|#2| |#2|)) (SIGNATURE |iiasin| (|#2| |#2|)) (SIGNATURE |iiacos| (|#2| |#2|)) (SIGNATURE |iiatan| (|#2| |#2|)) (SIGNATURE |iiacot| (|#2| |#2|)) (SIGNATURE |iiasec| (|#2| |#2|)) (SIGNATURE |iiacsc| (|#2| |#2|)) (SIGNATURE |iisinh| (|#2| |#2|)) (SIGNATURE |iicosh| (|#2| |#2|)) (SIGNATURE |iitanh| (|#2| |#2|)) (SIGNATURE |iicoth| (|#2| |#2|)) (SIGNATURE |iisech| (|#2| |#2|)) (SIGNATURE |iicsch| (|#2| |#2|)) (SIGNATURE |iiasinh| (|#2| |#2|)) (SIGNATURE |iiacosh| (|#2| |#2|)) (SIGNATURE |iiatanh| (|#2| |#2|)) (SIGNATURE |iiacoth| (|#2| |#2|)) (SIGNATURE |iiasech| (|#2| |#2|)) (SIGNATURE |iiacsch| (|#2| |#2|)) (SIGNATURE |specialTrigs| ((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|)))))) (SIGNATURE |localReal?| ((|Boolean|) |#2|))) (|Join| (|OrderedSet|) (|IntegralDomain|)) (|Join| (|FunctionSpace| |#1|) (|RadicalCategory|))) (T |ElementaryFunction|)) 
((|localReal?| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ElementaryFunction| *4 *3)) (|ofCategory| *3 (|Join| (|FunctionSpace| *4) (|RadicalCategory|))))) (|specialTrigs| (*1 *2 *2 *3) (|partial| AND (|isDomain| *3 (|List| (|Record| (|:| |func| *2) (|:| |pole| (|Boolean|))))) (|ofCategory| *2 (|Join| (|FunctionSpace| *4) (|RadicalCategory|))) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *4 *2)))) (|iiacsch| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iiasech| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iiacoth| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iiatanh| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iiacosh| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iiasinh| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iicsch| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iisech| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iicoth| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iitanh| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iicosh| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iisinh| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iiacsc| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iiasec| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iiacot| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iiatan| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iiacos| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iiasin| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iicsc| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iisec| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iicot| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iitan| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iicos| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iisin| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iilog| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iiexp| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|iisqrt3| (*1 *2) (AND (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|iisqrt2| (*1 *2) (AND (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|operator| (*1 *2 *2) (AND (|isDomain| *2 (|BasicOperator|)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *4)) (|ofCategory| *4 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|belong?| (*1 *2 *3) (AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ElementaryFunction| *4 *5)) (|ofCategory| *5 (|Join| (|FunctionSpace| *4) (|RadicalCategory|))))) (|pi| (*1 *2) (AND (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|acsch| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|asech| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|acoth| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|atanh| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|acosh| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|asinh| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|csch| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|sech| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|coth| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|tanh| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|cosh| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|sinh| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|acsc| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|asec| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|acot| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|atan| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|acos| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|asin| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|csc| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|sec| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|cot| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|tan| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|cos| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|sin| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|log| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|))))) (|exp| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|ElementaryFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(CATEGORY |package| (SIGNATURE |exp| (|#2| |#2|)) (SIGNATURE |log| (|#2| |#2|)) (SIGNATURE |sin| (|#2| |#2|)) (SIGNATURE |cos| (|#2| |#2|)) (SIGNATURE |tan| (|#2| |#2|)) (SIGNATURE |cot| (|#2| |#2|)) (SIGNATURE |sec| (|#2| |#2|)) (SIGNATURE |csc| (|#2| |#2|)) (SIGNATURE |asin| (|#2| |#2|)) (SIGNATURE |acos| (|#2| |#2|)) (SIGNATURE |atan| (|#2| |#2|)) (SIGNATURE |acot| (|#2| |#2|)) (SIGNATURE |asec| (|#2| |#2|)) (SIGNATURE |acsc| (|#2| |#2|)) (SIGNATURE |sinh| (|#2| |#2|)) (SIGNATURE |cosh| (|#2| |#2|)) (SIGNATURE |tanh| (|#2| |#2|)) (SIGNATURE |coth| (|#2| |#2|)) (SIGNATURE |sech| (|#2| |#2|)) (SIGNATURE |csch| (|#2| |#2|)) (SIGNATURE |asinh| (|#2| |#2|)) (SIGNATURE |acosh| (|#2| |#2|)) (SIGNATURE |atanh| (|#2| |#2|)) (SIGNATURE |acoth| (|#2| |#2|)) (SIGNATURE |asech| (|#2| |#2|)) (SIGNATURE |acsch| (|#2| |#2|)) (SIGNATURE |pi| (|#2|)) (SIGNATURE |belong?| ((|Boolean|) (|BasicOperator|))) (SIGNATURE |operator| ((|BasicOperator|) (|BasicOperator|))) (SIGNATURE |iisqrt2| (|#2|)) (SIGNATURE |iisqrt3| (|#2|)) (SIGNATURE |iiexp| (|#2| |#2|)) (SIGNATURE |iilog| (|#2| |#2|)) (SIGNATURE |iisin| (|#2| |#2|)) (SIGNATURE |iicos| (|#2| |#2|)) (SIGNATURE |iitan| (|#2| |#2|)) (SIGNATURE |iicot| (|#2| |#2|)) (SIGNATURE |iisec| (|#2| |#2|)) (SIGNATURE |iicsc| (|#2| |#2|)) (SIGNATURE |iiasin| (|#2| |#2|)) (SIGNATURE |iiacos| (|#2| |#2|)) (SIGNATURE |iiatan| (|#2| |#2|)) (SIGNATURE |iiacot| (|#2| |#2|)) (SIGNATURE |iiasec| (|#2| |#2|)) (SIGNATURE |iiacsc| (|#2| |#2|)) (SIGNATURE |iisinh| (|#2| |#2|)) (SIGNATURE |iicosh| (|#2| |#2|)) (SIGNATURE |iitanh| (|#2| |#2|)) (SIGNATURE |iicoth| (|#2| |#2|)) (SIGNATURE |iisech| (|#2| |#2|)) (SIGNATURE |iicsch| (|#2| |#2|)) (SIGNATURE |iiasinh| (|#2| |#2|)) (SIGNATURE |iiacosh| (|#2| |#2|)) (SIGNATURE |iiatanh| (|#2| |#2|)) (SIGNATURE |iiacoth| (|#2| |#2|)) (SIGNATURE |iiasech| (|#2| |#2|)) (SIGNATURE |iiacsch| (|#2| |#2|)) (SIGNATURE |specialTrigs| ((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|)))))) (SIGNATURE |localReal?| ((|Boolean|) |#2|))) 
((|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) 133)) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) 50)) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) 126)) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) 125)) (|realElementary| ((|#2| |#2| (|Symbol|)) 19) ((|#2| |#2|) 22)) (|normalize| ((|#2| |#2| (|Symbol|)) 139) ((|#2| |#2|) 137))) 
(((|ElementaryFunctionStructurePackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |normalize| (|#2| |#2|)) (SIGNATURE |normalize| (|#2| |#2| (|Symbol|))) (SIGNATURE |rischNormalize| ((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|))) (SIGNATURE |realElementary| (|#2| |#2|)) (SIGNATURE |realElementary| (|#2| |#2| (|Symbol|))) (SIGNATURE |validExponential| ((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|))) (SIGNATURE |rootNormalize| (|#2| |#2| (|Kernel| |#2|))) (SIGNATURE |tanQ| (|#2| (|Fraction| (|Integer|)) |#2|))) (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|))) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |ElementaryFunctionStructurePackage|)) 
((|tanQ| (*1 *2 *3 *2) (AND (|isDomain| *3 (|Fraction| (|Integer|))) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|ElementaryFunctionStructurePackage| *4 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *4))))) (|rootNormalize| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Kernel| *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *4))) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|ElementaryFunctionStructurePackage| *4 *2)))) (|validExponential| (*1 *2 *3 *2 *4) (|partial| AND (|isDomain| *3 (|List| (|Kernel| *2))) (|isDomain| *4 (|Symbol|)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *5))) (|ofCategory| *5 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|ElementaryFunctionStructurePackage| *5 *2)))) (|realElementary| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|ElementaryFunctionStructurePackage| *4 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *4))))) (|realElementary| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|ElementaryFunctionStructurePackage| *3 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *3))))) (|rischNormalize| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |func| *3) (|:| |kers| (|List| (|Kernel| *3))) (|:| |vals| (|List| *3)))) (|isDomain| *1 (|ElementaryFunctionStructurePackage| *5 *3)) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *5))))) (|normalize| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|ElementaryFunctionStructurePackage| *4 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *4))))) (|normalize| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|ElementaryFunctionStructurePackage| *3 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *3)))))) 
(CATEGORY |package| (SIGNATURE |normalize| (|#2| |#2|)) (SIGNATURE |normalize| (|#2| |#2| (|Symbol|))) (SIGNATURE |rischNormalize| ((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|))) (SIGNATURE |realElementary| (|#2| |#2|)) (SIGNATURE |realElementary| (|#2| |#2| (|Symbol|))) (SIGNATURE |validExponential| ((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|))) (SIGNATURE |rootNormalize| (|#2| |#2| (|Kernel| |#2|))) (SIGNATURE |tanQ| (|#2| (|Fraction| (|Integer|)) |#2|))) 
((|tanhIfCan| (((|Union| |#3| "failed") |#3|) 110)) (|tanh| ((|#3| |#3|) 131)) (|tanIfCan| (((|Union| |#3| "failed") |#3|) 82)) (|tan| ((|#3| |#3|) 121)) (|sinhIfCan| (((|Union| |#3| "failed") |#3|) 58)) (|sinh| ((|#3| |#3|) 129)) (|sinIfCan| (((|Union| |#3| "failed") |#3|) 46)) (|sin| ((|#3| |#3|) 119)) (|sechIfCan| (((|Union| |#3| "failed") |#3|) 112)) (|sech| ((|#3| |#3|) 133)) (|secIfCan| (((|Union| |#3| "failed") |#3|) 84)) (|sec| ((|#3| |#3|) 123)) (|nthRootIfCan| (((|Union| |#3| "failed") |#3| (|NonNegativeInteger|)) 36)) (|logIfCan| (((|Union| |#3| "failed") |#3|) 74)) (|log| ((|#3| |#3|) 118)) (|expIfCan| (((|Union| |#3| "failed") |#3|) 44)) (|exp| ((|#3| |#3|) 117)) (|cschIfCan| (((|Union| |#3| "failed") |#3|) 113)) (|csch| ((|#3| |#3|) 134)) (|cscIfCan| (((|Union| |#3| "failed") |#3|) 85)) (|csc| ((|#3| |#3|) 124)) (|cothIfCan| (((|Union| |#3| "failed") |#3|) 111)) (|coth| ((|#3| |#3|) 132)) (|cotIfCan| (((|Union| |#3| "failed") |#3|) 83)) (|cot| ((|#3| |#3|) 122)) (|coshIfCan| (((|Union| |#3| "failed") |#3|) 60)) (|cosh| ((|#3| |#3|) 130)) (|cosIfCan| (((|Union| |#3| "failed") |#3|) 48)) (|cos| ((|#3| |#3|) 120)) (|atanhIfCan| (((|Union| |#3| "failed") |#3|) 66)) (|atanh| ((|#3| |#3|) 137)) (|atanIfCan| (((|Union| |#3| "failed") |#3|) 104)) (|atan| ((|#3| |#3|) 142)) (|asinhIfCan| (((|Union| |#3| "failed") |#3|) 62)) (|asinh| ((|#3| |#3|) 135)) (|asinIfCan| (((|Union| |#3| "failed") |#3|) 50)) (|asin| ((|#3| |#3|) 125)) (|asechIfCan| (((|Union| |#3| "failed") |#3|) 70)) (|asech| ((|#3| |#3|) 139)) (|asecIfCan| (((|Union| |#3| "failed") |#3|) 54)) (|asec| ((|#3| |#3|) 127)) (|acschIfCan| (((|Union| |#3| "failed") |#3|) 72)) (|acsch| ((|#3| |#3|) 140)) (|acscIfCan| (((|Union| |#3| "failed") |#3|) 56)) (|acsc| ((|#3| |#3|) 128)) (|acothIfCan| (((|Union| |#3| "failed") |#3|) 68)) (|acoth| ((|#3| |#3|) 138)) (|acotIfCan| (((|Union| |#3| "failed") |#3|) 107)) (|acot| ((|#3| |#3|) 143)) (|acoshIfCan| (((|Union| |#3| "failed") |#3|) 64)) (|acosh| ((|#3| |#3|) 136)) (|acosIfCan| (((|Union| |#3| "failed") |#3|) 52)) (|acos| ((|#3| |#3|) 126)) (** ((|#3| |#3| (|Fraction| (|Integer|))) 40 (|has| |#1| (|Field|))))) 
(((|ElementaryFunctionsUnivariateLaurentSeries| |#1| |#2| |#3|) (|Join| (|PartialTranscendentalFunctions| |#3|) (CATEGORY |package| (IF (|has| |#1| (|Field|)) (SIGNATURE ** (|#3| |#3| (|Fraction| (|Integer|)))) |noBranch|) (SIGNATURE |exp| (|#3| |#3|)) (SIGNATURE |log| (|#3| |#3|)) (SIGNATURE |sin| (|#3| |#3|)) (SIGNATURE |cos| (|#3| |#3|)) (SIGNATURE |tan| (|#3| |#3|)) (SIGNATURE |cot| (|#3| |#3|)) (SIGNATURE |sec| (|#3| |#3|)) (SIGNATURE |csc| (|#3| |#3|)) (SIGNATURE |asin| (|#3| |#3|)) (SIGNATURE |acos| (|#3| |#3|)) (SIGNATURE |atan| (|#3| |#3|)) (SIGNATURE |acot| (|#3| |#3|)) (SIGNATURE |asec| (|#3| |#3|)) (SIGNATURE |acsc| (|#3| |#3|)) (SIGNATURE |sinh| (|#3| |#3|)) (SIGNATURE |cosh| (|#3| |#3|)) (SIGNATURE |tanh| (|#3| |#3|)) (SIGNATURE |coth| (|#3| |#3|)) (SIGNATURE |sech| (|#3| |#3|)) (SIGNATURE |csch| (|#3| |#3|)) (SIGNATURE |asinh| (|#3| |#3|)) (SIGNATURE |acosh| (|#3| |#3|)) (SIGNATURE |atanh| (|#3| |#3|)) (SIGNATURE |acoth| (|#3| |#3|)) (SIGNATURE |asech| (|#3| |#3|)) (SIGNATURE |acsch| (|#3| |#3|)))) (|Algebra| (|Fraction| (|Integer|))) (|UnivariateTaylorSeriesCategory| |#1|) (|UnivariateLaurentSeriesConstructorCategory| |#1| |#2|)) (T |ElementaryFunctionsUnivariateLaurentSeries|)) 
((** (*1 *2 *2 *3) (AND (|isDomain| *3 (|Fraction| (|Integer|))) (|ofCategory| *4 (|Field|)) (|ofCategory| *4 (|Algebra| *3)) (|ofCategory| *5 (|UnivariateTaylorSeriesCategory| *4)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *4 *5 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *4 *5)))) (|exp| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|log| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|sin| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|cos| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|tan| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|cot| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|sec| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|csc| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|asin| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|acos| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|atan| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|acot| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|asec| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|acsc| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|sinh| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|cosh| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|tanh| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|coth| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|sech| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|csch| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|asinh| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|acosh| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|atanh| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|acoth| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|asech| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|acsch| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))))) 
(|Join| (|PartialTranscendentalFunctions| |#3|) (CATEGORY |package| (IF (|has| |#1| (|Field|)) (SIGNATURE ** (|#3| |#3| (|Fraction| (|Integer|)))) |noBranch|) (SIGNATURE |exp| (|#3| |#3|)) (SIGNATURE |log| (|#3| |#3|)) (SIGNATURE |sin| (|#3| |#3|)) (SIGNATURE |cos| (|#3| |#3|)) (SIGNATURE |tan| (|#3| |#3|)) (SIGNATURE |cot| (|#3| |#3|)) (SIGNATURE |sec| (|#3| |#3|)) (SIGNATURE |csc| (|#3| |#3|)) (SIGNATURE |asin| (|#3| |#3|)) (SIGNATURE |acos| (|#3| |#3|)) (SIGNATURE |atan| (|#3| |#3|)) (SIGNATURE |acot| (|#3| |#3|)) (SIGNATURE |asec| (|#3| |#3|)) (SIGNATURE |acsc| (|#3| |#3|)) (SIGNATURE |sinh| (|#3| |#3|)) (SIGNATURE |cosh| (|#3| |#3|)) (SIGNATURE |tanh| (|#3| |#3|)) (SIGNATURE |coth| (|#3| |#3|)) (SIGNATURE |sech| (|#3| |#3|)) (SIGNATURE |csch| (|#3| |#3|)) (SIGNATURE |asinh| (|#3| |#3|)) (SIGNATURE |acosh| (|#3| |#3|)) (SIGNATURE |atanh| (|#3| |#3|)) (SIGNATURE |acoth| (|#3| |#3|)) (SIGNATURE |asech| (|#3| |#3|)) (SIGNATURE |acsch| (|#3| |#3|)))) 
((|tanhIfCan| (((|Union| |#3| "failed") |#3|) 66)) (|tanh| ((|#3| |#3|) 133)) (|tanIfCan| (((|Union| |#3| "failed") |#3|) 50)) (|tan| ((|#3| |#3|) 121)) (|sinhIfCan| (((|Union| |#3| "failed") |#3|) 62)) (|sinh| ((|#3| |#3|) 131)) (|sinIfCan| (((|Union| |#3| "failed") |#3|) 46)) (|sin| ((|#3| |#3|) 119)) (|sechIfCan| (((|Union| |#3| "failed") |#3|) 70)) (|sech| ((|#3| |#3|) 135)) (|secIfCan| (((|Union| |#3| "failed") |#3|) 54)) (|sec| ((|#3| |#3|) 123)) (|nthRootIfCan| (((|Union| |#3| "failed") |#3| (|NonNegativeInteger|)) 35)) (|logIfCan| (((|Union| |#3| "failed") |#3|) 44)) (|log| ((|#3| |#3|) 112)) (|expIfCan| (((|Union| |#3| "failed") |#3|) 42)) (|exp| ((|#3| |#3|) 118)) (|cschIfCan| (((|Union| |#3| "failed") |#3|) 72)) (|csch| ((|#3| |#3|) 136)) (|cscIfCan| (((|Union| |#3| "failed") |#3|) 56)) (|csc| ((|#3| |#3|) 124)) (|cothIfCan| (((|Union| |#3| "failed") |#3|) 68)) (|coth| ((|#3| |#3|) 134)) (|cotIfCan| (((|Union| |#3| "failed") |#3|) 52)) (|cot| ((|#3| |#3|) 122)) (|coshIfCan| (((|Union| |#3| "failed") |#3|) 64)) (|cosh| ((|#3| |#3|) 132)) (|cosIfCan| (((|Union| |#3| "failed") |#3|) 48)) (|cos| ((|#3| |#3|) 120)) (|atanhIfCan| (((|Union| |#3| "failed") |#3|) 78)) (|atanh| ((|#3| |#3|) 139)) (|atanIfCan| (((|Union| |#3| "failed") |#3|) 58)) (|atan| ((|#3| |#3|) 127)) (|asinhIfCan| (((|Union| |#3| "failed") |#3|) 74)) (|asinh| ((|#3| |#3|) 137)) (|asinIfCan| (((|Union| |#3| "failed") |#3|) 102)) (|asin| ((|#3| |#3|) 125)) (|asechIfCan| (((|Union| |#3| "failed") |#3|) 82)) (|asech| ((|#3| |#3|) 141)) (|asecIfCan| (((|Union| |#3| "failed") |#3|) 109)) (|asec| ((|#3| |#3|) 129)) (|acschIfCan| (((|Union| |#3| "failed") |#3|) 84)) (|acsch| ((|#3| |#3|) 142)) (|acscIfCan| (((|Union| |#3| "failed") |#3|) 111)) (|acsc| ((|#3| |#3|) 130)) (|acothIfCan| (((|Union| |#3| "failed") |#3|) 80)) (|acoth| ((|#3| |#3|) 140)) (|acotIfCan| (((|Union| |#3| "failed") |#3|) 60)) (|acot| ((|#3| |#3|) 128)) (|acoshIfCan| (((|Union| |#3| "failed") |#3|) 76)) (|acosh| ((|#3| |#3|) 138)) (|acosIfCan| (((|Union| |#3| "failed") |#3|) 105)) (|acos| ((|#3| |#3|) 126)) (** ((|#3| |#3| (|Fraction| (|Integer|))) 40 (|has| |#1| (|Field|))))) 
(((|ElementaryFunctionsUnivariatePuiseuxSeries| |#1| |#2| |#3| |#4|) (|Join| (|PartialTranscendentalFunctions| |#3|) (CATEGORY |package| (IF (|has| |#1| (|Field|)) (SIGNATURE ** (|#3| |#3| (|Fraction| (|Integer|)))) |noBranch|) (SIGNATURE |exp| (|#3| |#3|)) (SIGNATURE |log| (|#3| |#3|)) (SIGNATURE |sin| (|#3| |#3|)) (SIGNATURE |cos| (|#3| |#3|)) (SIGNATURE |tan| (|#3| |#3|)) (SIGNATURE |cot| (|#3| |#3|)) (SIGNATURE |sec| (|#3| |#3|)) (SIGNATURE |csc| (|#3| |#3|)) (SIGNATURE |asin| (|#3| |#3|)) (SIGNATURE |acos| (|#3| |#3|)) (SIGNATURE |atan| (|#3| |#3|)) (SIGNATURE |acot| (|#3| |#3|)) (SIGNATURE |asec| (|#3| |#3|)) (SIGNATURE |acsc| (|#3| |#3|)) (SIGNATURE |sinh| (|#3| |#3|)) (SIGNATURE |cosh| (|#3| |#3|)) (SIGNATURE |tanh| (|#3| |#3|)) (SIGNATURE |coth| (|#3| |#3|)) (SIGNATURE |sech| (|#3| |#3|)) (SIGNATURE |csch| (|#3| |#3|)) (SIGNATURE |asinh| (|#3| |#3|)) (SIGNATURE |acosh| (|#3| |#3|)) (SIGNATURE |atanh| (|#3| |#3|)) (SIGNATURE |acoth| (|#3| |#3|)) (SIGNATURE |asech| (|#3| |#3|)) (SIGNATURE |acsch| (|#3| |#3|)))) (|Algebra| (|Fraction| (|Integer|))) (|UnivariateLaurentSeriesCategory| |#1|) (|UnivariatePuiseuxSeriesConstructorCategory| |#1| |#2|) (|PartialTranscendentalFunctions| |#2|)) (T |ElementaryFunctionsUnivariatePuiseuxSeries|)) 
((** (*1 *2 *2 *3) (AND (|isDomain| *3 (|Fraction| (|Integer|))) (|ofCategory| *4 (|Field|)) (|ofCategory| *4 (|Algebra| *3)) (|ofCategory| *5 (|UnivariateLaurentSeriesCategory| *4)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *4 *5 *2 *6)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *4 *5)) (|ofCategory| *6 (|PartialTranscendentalFunctions| *5)))) (|exp| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|log| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|sin| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|cos| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|tan| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|cot| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|sec| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|csc| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|asin| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|acos| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|atan| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|acot| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|asec| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|acsc| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|sinh| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|cosh| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|tanh| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|coth| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|sech| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|csch| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|asinh| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|acosh| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|atanh| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|acoth| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|asech| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|acsch| (*1 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4))))) 
(|Join| (|PartialTranscendentalFunctions| |#3|) (CATEGORY |package| (IF (|has| |#1| (|Field|)) (SIGNATURE ** (|#3| |#3| (|Fraction| (|Integer|)))) |noBranch|) (SIGNATURE |exp| (|#3| |#3|)) (SIGNATURE |log| (|#3| |#3|)) (SIGNATURE |sin| (|#3| |#3|)) (SIGNATURE |cos| (|#3| |#3|)) (SIGNATURE |tan| (|#3| |#3|)) (SIGNATURE |cot| (|#3| |#3|)) (SIGNATURE |sec| (|#3| |#3|)) (SIGNATURE |csc| (|#3| |#3|)) (SIGNATURE |asin| (|#3| |#3|)) (SIGNATURE |acos| (|#3| |#3|)) (SIGNATURE |atan| (|#3| |#3|)) (SIGNATURE |acot| (|#3| |#3|)) (SIGNATURE |asec| (|#3| |#3|)) (SIGNATURE |acsc| (|#3| |#3|)) (SIGNATURE |sinh| (|#3| |#3|)) (SIGNATURE |cosh| (|#3| |#3|)) (SIGNATURE |tanh| (|#3| |#3|)) (SIGNATURE |coth| (|#3| |#3|)) (SIGNATURE |sech| (|#3| |#3|)) (SIGNATURE |csch| (|#3| |#3|)) (SIGNATURE |asinh| (|#3| |#3|)) (SIGNATURE |acosh| (|#3| |#3|)) (SIGNATURE |atanh| (|#3| |#3|)) (SIGNATURE |acoth| (|#3| |#3|)) (SIGNATURE |asech| (|#3| |#3|)) (SIGNATURE |acsch| (|#3| |#3|)))) 
((|select| (($ (|Mapping| (|Boolean|) |#2|) $) 23)) (|removeDuplicates| (($ $) 36)) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) NIL) (($ |#2| $) 34)) (|remove| (($ |#2| $) 31) (($ (|Mapping| (|Boolean|) |#2|) $) 17)) (|merge!| (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) NIL) (($ $ $) 40)) (|insert| (($ |#2| $ (|Integer|)) 19) (($ $ $ (|Integer|)) 21)) (|delete| (($ $ (|Integer|)) 11) (($ $ (|UniversalSegment| (|Integer|))) 14)) (|concat!| (($ $ |#2|) 29) (($ $ $) NIL)) (|concat| (($ $ |#2|) 28) (($ |#2| $) NIL) (($ $ $) 25) (($ (|List| $)) NIL))) 
(((|ExtensibleLinearAggregate&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |merge!| (|#1| |#1| |#1|)) (SIGNATURE |remove!| (|#1| |#2| |#1|)) (SIGNATURE |merge!| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1| |#1|)) (SIGNATURE |remove!| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |concat!| (|#1| |#1| |#1|)) (SIGNATURE |concat!| (|#1| |#1| |#2|)) (SIGNATURE |insert| (|#1| |#1| |#1| (|Integer|))) (SIGNATURE |insert| (|#1| |#2| |#1| (|Integer|))) (SIGNATURE |delete| (|#1| |#1| (|UniversalSegment| (|Integer|)))) (SIGNATURE |delete| (|#1| |#1| (|Integer|))) (SIGNATURE |concat| (|#1| (|List| |#1|))) (SIGNATURE |concat| (|#1| |#1| |#1|)) (SIGNATURE |concat| (|#1| |#2| |#1|)) (SIGNATURE |concat| (|#1| |#1| |#2|)) (SIGNATURE |remove| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |select| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |remove| (|#1| |#2| |#1|)) (SIGNATURE |removeDuplicates| (|#1| |#1|))) (|ExtensibleLinearAggregate| |#2|) (|Type|)) (T |ExtensibleLinearAggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |merge!| (|#1| |#1| |#1|)) (SIGNATURE |remove!| (|#1| |#2| |#1|)) (SIGNATURE |merge!| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1| |#1|)) (SIGNATURE |remove!| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |concat!| (|#1| |#1| |#1|)) (SIGNATURE |concat!| (|#1| |#1| |#2|)) (SIGNATURE |insert| (|#1| |#1| |#1| (|Integer|))) (SIGNATURE |insert| (|#1| |#2| |#1| (|Integer|))) (SIGNATURE |delete| (|#1| |#1| (|UniversalSegment| (|Integer|)))) (SIGNATURE |delete| (|#1| |#1| (|Integer|))) (SIGNATURE |concat| (|#1| (|List| |#1|))) (SIGNATURE |concat| (|#1| |#1| |#1|)) (SIGNATURE |concat| (|#1| |#2| |#1|)) (SIGNATURE |concat| (|#1| |#1| |#2|)) (SIGNATURE |remove| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |select| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |remove| (|#1| |#2| |#1|)) (SIGNATURE |removeDuplicates| (|#1| |#1|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setelt| ((|#1| $ (|Integer|) |#1|) 49 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) 53 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) 78)) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 70 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) 7 T CONST)) (|removeDuplicates!| (($ $) 76 (|has| |#1| (|SetCategory|)))) (|removeDuplicates| (($ $) 73 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) 82) (($ |#1| $) 77 (|has| |#1| (|SetCategory|)))) (|remove| (($ |#1| $) 72 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#1|) $) 69 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 71 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 68 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 67 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| ((|#1| $ (|Integer|) |#1|) 50 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#1| $ (|Integer|)) 48)) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|new| (($ (|NonNegativeInteger|) |#1|) 64)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|minIndex| (((|Integer|) $) 40 (|has| (|Integer|) (|OrderedSet|)))) (|merge!| (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) 79) (($ $ $) 75 (|has| |#1| (|OrderedSet|)))) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|maxIndex| (((|Integer|) $) 41 (|has| (|Integer|) (|OrderedSet|)))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35) (($ (|Mapping| |#1| |#1| |#1|) $ $) 59)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|insert!| (($ |#1| $ (|Integer|)) 81) (($ $ $ (|Integer|)) 80)) (|insert| (($ |#1| $ (|Integer|)) 55) (($ $ $ (|Integer|)) 54)) (|indices| (((|List| (|Integer|)) $) 43)) (|index?| (((|Boolean|) (|Integer|) $) 44)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|first| ((|#1| $) 39 (|has| (|Integer|) (|OrderedSet|)))) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) 66)) (|fill!| (($ $ |#1|) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|entry?| (((|Boolean|) |#1| $) 42 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|entries| (((|List| |#1|) $) 45)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| ((|#1| $ (|Integer|) |#1|) 47) ((|#1| $ (|Integer|)) 46) (($ $ (|UniversalSegment| (|Integer|))) 58)) (|delete!| (($ $ (|Integer|)) 84) (($ $ (|UniversalSegment| (|Integer|))) 83)) (|delete| (($ $ (|Integer|)) 57) (($ $ (|UniversalSegment| (|Integer|))) 56)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|convert| (((|InputForm|) $) 74 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 65)) (|concat!| (($ $ |#1|) 86) (($ $ $) 85)) (|concat| (($ $ |#1|) 63) (($ |#1| $) 62) (($ $ $) 61) (($ (|List| $)) 60)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|ExtensibleLinearAggregate| |#1|) (|Category|) (|Type|)) (T |ExtensibleLinearAggregate|)) 
((|concat!| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|ExtensibleLinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|concat!| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|ExtensibleLinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|delete!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|ExtensibleLinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|delete!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|UniversalSegment| (|Integer|))) (|ofCategory| *1 (|ExtensibleLinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|remove!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|ExtensibleLinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|insert!| (*1 *1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|ExtensibleLinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|insert!| (*1 *1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|ExtensibleLinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|merge!| (*1 *1 *2 *1 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3 *3)) (|ofCategory| *1 (|ExtensibleLinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|select!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|ExtensibleLinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|remove!| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|ExtensibleLinearAggregate| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|SetCategory|)))) (|removeDuplicates!| (*1 *1 *1) (AND (|ofCategory| *1 (|ExtensibleLinearAggregate| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|SetCategory|)))) (|merge!| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|ExtensibleLinearAggregate| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|OrderedSet|))))) 
(|Join| (|LinearAggregate| |t#1|) (CATEGORY |domain| (ATTRIBUTE |shallowlyMutable|) (SIGNATURE |concat!| ($ $ |t#1|)) (SIGNATURE |concat!| ($ $ $)) (SIGNATURE |delete!| ($ $ (|Integer|))) (SIGNATURE |delete!| ($ $ (|UniversalSegment| (|Integer|)))) (SIGNATURE |remove!| ($ (|Mapping| (|Boolean|) |t#1|) $)) (SIGNATURE |insert!| ($ |t#1| $ (|Integer|))) (SIGNATURE |insert!| ($ $ $ (|Integer|))) (SIGNATURE |merge!| ($ (|Mapping| (|Boolean|) |t#1| |t#1|) $ $)) (SIGNATURE |select!| ($ (|Mapping| (|Boolean|) |t#1|) $)) (IF (|has| |t#1| (|SetCategory|)) (PROGN (SIGNATURE |remove!| ($ |t#1| $)) (SIGNATURE |removeDuplicates!| ($ $))) |noBranch|) (IF (|has| |t#1| (|OrderedSet|)) (SIGNATURE |merge!| ($ $ $)) |noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| (|Integer|) |#1|) . T) ((|EltableAggregate| (|Integer|) |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| (|Integer|) |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|LinearAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((** (($ $ $) 10))) 
(((|ElementaryFunctionCategory&| |#1|) (CATEGORY |domain| (SIGNATURE ** (|#1| |#1| |#1|))) (|ElementaryFunctionCategory|)) (T |ElementaryFunctionCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE ** (|#1| |#1| |#1|))) 
((|log| (($ $) 6)) (|exp| (($ $) 7)) (** (($ $ $) 8))) 
(((|ElementaryFunctionCategory|) (|Category|)) (T |ElementaryFunctionCategory|)) 
((** (*1 *1 *1 *1) (|ofCategory| *1 (|ElementaryFunctionCategory|))) (|exp| (*1 *1 *1) (|ofCategory| *1 (|ElementaryFunctionCategory|))) (|log| (*1 *1 *1) (|ofCategory| *1 (|ElementaryFunctionCategory|)))) 
(|Join| (CATEGORY |domain| (SIGNATURE |log| ($ $)) (SIGNATURE |exp| ($ $)) (SIGNATURE ** ($ $ $)))) 
((|sncndn| (((|List| (|Stream| |#1|)) (|Stream| |#1|) |#1|) 35)) (|sn| ((|#2| |#2| |#1|) 38)) (|dn| ((|#2| |#2| |#1|) 40)) (|cn| ((|#2| |#2| |#1|) 39))) 
(((|EllipticFunctionsUnivariateTaylorSeries| |#1| |#2|) (CATEGORY |package| (SIGNATURE |sn| (|#2| |#2| |#1|)) (SIGNATURE |cn| (|#2| |#2| |#1|)) (SIGNATURE |dn| (|#2| |#2| |#1|)) (SIGNATURE |sncndn| ((|List| (|Stream| |#1|)) (|Stream| |#1|) |#1|))) (|Field|) (|UnivariateTaylorSeriesCategory| |#1|)) (T |EllipticFunctionsUnivariateTaylorSeries|)) 
((|sncndn| (*1 *2 *3 *4) (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|List| (|Stream| *4))) (|isDomain| *1 (|EllipticFunctionsUnivariateTaylorSeries| *4 *5)) (|isDomain| *3 (|Stream| *4)) (|ofCategory| *5 (|UnivariateTaylorSeriesCategory| *4)))) (|dn| (*1 *2 *2 *3) (AND (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|EllipticFunctionsUnivariateTaylorSeries| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|cn| (*1 *2 *2 *3) (AND (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|EllipticFunctionsUnivariateTaylorSeries| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|sn| (*1 *2 *2 *3) (AND (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|EllipticFunctionsUnivariateTaylorSeries| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))) 
(CATEGORY |package| (SIGNATURE |sn| (|#2| |#2| |#1|)) (SIGNATURE |cn| (|#2| |#2| |#1|)) (SIGNATURE |dn| (|#2| |#2| |#1|)) (SIGNATURE |sncndn| ((|List| (|Stream| |#1|)) (|Stream| |#1|) |#1|))) 
((|elt| ((|#2| $ |#1|) 6))) 
(((|Eltable| |#1| |#2|) (|Category|) (|SetCategory|) (|Type|)) (T |Eltable|)) 
((|elt| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|Eltable| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|Type|))))) 
(|Join| (CATEGORY |domain| (SIGNATURE |elt| (|t#2| $ |t#1|)))) 
((|qsetelt!| ((|#3| $ |#2| |#3|) 12)) (|qelt| ((|#3| $ |#2|) 10))) 
(((|EltableAggregate&| |#1| |#2| |#3|) (CATEGORY |domain| (SIGNATURE |qsetelt!| (|#3| |#1| |#2| |#3|)) (SIGNATURE |qelt| (|#3| |#1| |#2|))) (|EltableAggregate| |#2| |#3|) (|SetCategory|) (|Type|)) (T |EltableAggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |qsetelt!| (|#3| |#1| |#2| |#3|)) (SIGNATURE |qelt| (|#3| |#1| |#2|))) 
((|setelt| ((|#2| $ |#1| |#2|) 8 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qsetelt!| ((|#2| $ |#1| |#2|) 7 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#2| $ |#1|) 9)) (|elt| ((|#2| $ |#1|) 6) ((|#2| $ |#1| |#2|) 10))) 
(((|EltableAggregate| |#1| |#2|) (|Category|) (|SetCategory|) (|Type|)) (T |EltableAggregate|)) 
((|elt| (*1 *2 *1 *3 *2) (AND (|ofCategory| *1 (|EltableAggregate| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|Type|)))) (|qelt| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|EltableAggregate| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|Type|)))) (|setelt| (*1 *2 *1 *3 *2) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|EltableAggregate| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|Type|)))) (|qsetelt!| (*1 *2 *1 *3 *2) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|EltableAggregate| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|Eltable| |t#1| |t#2|) (CATEGORY |domain| (SIGNATURE |elt| (|t#2| $ |t#1| |t#2|)) (SIGNATURE |qelt| (|t#2| $ |t#1|)) (IF (|has| $ (ATTRIBUTE |shallowlyMutable|)) (PROGN (SIGNATURE |setelt| (|t#2| $ |t#1| |t#2|)) (SIGNATURE |qsetelt!| (|t#2| $ |t#1| |t#2|))) |noBranch|))) 
(((|Eltable| |#1| |#2|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 34)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 39)) (|unitCanonical| (($ $) 37)) (|unit?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sample| (($) NIL T CONST)) (|rem| (($ $ $) 32)) (|reduce| (($ |#2| |#3|) 19)) (|recip| (((|Union| $ "failed") $) NIL)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|one?| (((|Boolean|) $) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|modulus| ((|#3| $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 20)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|exQuo| (((|Union| $ "failed") $ $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) 33)) (|elt| ((|#2| $ |#2|) 41)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 24)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) ((|#2| $) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|associates?| (((|Boolean|) $ $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 27 T CONST)) (|One| (($) 35 T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 36))) 
(((|EuclideanModularRing| |#1| |#2| |#3| |#4| |#5| |#6|) (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |modulus| (|#3| $)) (SIGNATURE |coerce| (|#2| $)) (SIGNATURE |reduce| ($ |#2| |#3|)) (SIGNATURE |exQuo| ((|Union| $ "failed") $ $)) (SIGNATURE |recip| ((|Union| $ "failed") $)) (SIGNATURE |inv| ($ $)) (SIGNATURE |elt| (|#2| $ |#2|)))) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#1|) (|AbelianMonoid|) (|Mapping| |#2| |#2| |#3|) (|Mapping| (|Union| |#3| "failed") |#3| |#3|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| |#3|)) (T |EuclideanModularRing|)) 
((|recip| (*1 *1 *1) (|partial| AND (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|EuclideanModularRing| *2 *3 *4 *5 *6 *7)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 (|Mapping| *3 *3 *4)) (|ofType| *6 (|Mapping| (|Union| *4 "failed") *4 *4)) (|ofType| *7 (|Mapping| (|Union| *3 "failed") *3 *3 *4)))) (|modulus| (*1 *2 *1) (AND (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *2 (|AbelianMonoid|)) (|isDomain| *1 (|EuclideanModularRing| *3 *4 *2 *5 *6 *7)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofType| *5 (|Mapping| *4 *4 *2)) (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2)) (|ofType| *7 (|Mapping| (|Union| *4 "failed") *4 *4 *2)))) (|coerce| (*1 *2 *1) (AND (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)) (|isDomain| *1 (|EuclideanModularRing| *3 *2 *4 *5 *6 *7)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 (|Mapping| *2 *2 *4)) (|ofType| *6 (|Mapping| (|Union| *4 "failed") *4 *4)) (|ofType| *7 (|Mapping| (|Union| *2 "failed") *2 *2 *4)))) (|reduce| (*1 *1 *2 *3) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *1 (|EuclideanModularRing| *4 *2 *3 *5 *6 *7)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *5 (|Mapping| *2 *2 *3)) (|ofType| *6 (|Mapping| (|Union| *3 "failed") *3 *3)) (|ofType| *7 (|Mapping| (|Union| *2 "failed") *2 *2 *3)))) (|exQuo| (*1 *1 *1 *1) (|partial| AND (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|EuclideanModularRing| *2 *3 *4 *5 *6 *7)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 (|Mapping| *3 *3 *4)) (|ofType| *6 (|Mapping| (|Union| *4 "failed") *4 *4)) (|ofType| *7 (|Mapping| (|Union| *3 "failed") *3 *3 *4)))) (|inv| (*1 *1 *1) (AND (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|EuclideanModularRing| *2 *3 *4 *5 *6 *7)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 (|Mapping| *3 *3 *4)) (|ofType| *6 (|Mapping| (|Union| *4 "failed") *4 *4)) (|ofType| *7 (|Mapping| (|Union| *3 "failed") *3 *3 *4)))) (|elt| (*1 *2 *1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *1 (|EuclideanModularRing| *3 *2 *4 *5 *6 *7)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 (|Mapping| *2 *2 *4)) (|ofType| *6 (|Mapping| (|Union| *4 "failed") *4 *4)) (|ofType| *7 (|Mapping| (|Union| *2 "failed") *2 *2 *4))))) 
(|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |modulus| (|#3| $)) (SIGNATURE |coerce| (|#2| $)) (SIGNATURE |reduce| ($ |#2| |#3|)) (SIGNATURE |exQuo| ((|Union| $ "failed") $ $)) (SIGNATURE |recip| ((|Union| $ "failed") $)) (SIGNATURE |inv| ($ $)) (SIGNATURE |elt| (|#2| $ |#2|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|EntireRing|) (|Category|)) (T |EntireRing|)) 
NIL 
(|Join| (|Ring|) (|BiModule| $ $) (CATEGORY |package| (ATTRIBUTE |noZeroDivisors|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|generalizedEigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |geneigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) 83)) (|generalizedEigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) 78) (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) 36)) (|eigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) 80)) (|eigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) 60)) (|eigenvalues| (((|List| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) 59)) (|characteristicPolynomial| (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) 47) (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) 48))) 
(((|EigenPackage| |#1|) (CATEGORY |package| (SIGNATURE |characteristicPolynomial| ((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Symbol|))) (SIGNATURE |characteristicPolynomial| ((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |eigenvalues| ((|List| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|Matrix| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |eigenvector| ((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |generalizedEigenvector| ((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |generalizedEigenvector| ((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) (|Matrix| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |generalizedEigenvectors| ((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |geneigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |eigenvectors| ((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) (|GcdDomain|)) (T |EigenPackage|)) 
((|eigenvectors| (*1 *2 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|isDomain| *2 (|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| *4)) (|SuchThat| (|Symbol|) (|Polynomial| *4)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| *4)))))))) (|isDomain| *1 (|EigenPackage| *4)) (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| *4)))))) (|generalizedEigenvectors| (*1 *2 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|isDomain| *2 (|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| *4)) (|SuchThat| (|Symbol|) (|Polynomial| *4)))) (|:| |geneigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| *4)))))))) (|isDomain| *1 (|EigenPackage| *4)) (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| *4)))))) (|generalizedEigenvector| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| *5)) (|SuchThat| (|Symbol|) (|Polynomial| *5)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| *4)))) (|ofCategory| *5 (|GcdDomain|)) (|isDomain| *2 (|List| (|Matrix| (|Fraction| (|Polynomial| *5))))) (|isDomain| *1 (|EigenPackage| *5)) (|isDomain| *4 (|Matrix| (|Fraction| (|Polynomial| *5)))))) (|generalizedEigenvector| (*1 *2 *3 *4 *5 *5) (AND (|isDomain| *3 (|Union| (|Fraction| (|Polynomial| *6)) (|SuchThat| (|Symbol|) (|Polynomial| *6)))) (|isDomain| *5 (|NonNegativeInteger|)) (|ofCategory| *6 (|GcdDomain|)) (|isDomain| *2 (|List| (|Matrix| (|Fraction| (|Polynomial| *6))))) (|isDomain| *1 (|EigenPackage| *6)) (|isDomain| *4 (|Matrix| (|Fraction| (|Polynomial| *6)))))) (|eigenvector| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Union| (|Fraction| (|Polynomial| *5)) (|SuchThat| (|Symbol|) (|Polynomial| *5)))) (|ofCategory| *5 (|GcdDomain|)) (|isDomain| *2 (|List| (|Matrix| (|Fraction| (|Polynomial| *5))))) (|isDomain| *1 (|EigenPackage| *5)) (|isDomain| *4 (|Matrix| (|Fraction| (|Polynomial| *5)))))) (|eigenvalues| (*1 *2 *3) (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| *4)))) (|ofCategory| *4 (|GcdDomain|)) (|isDomain| *2 (|List| (|Union| (|Fraction| (|Polynomial| *4)) (|SuchThat| (|Symbol|) (|Polynomial| *4))))) (|isDomain| *1 (|EigenPackage| *4)))) (|characteristicPolynomial| (*1 *2 *3) (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| *4)))) (|isDomain| *2 (|Polynomial| *4)) (|isDomain| *1 (|EigenPackage| *4)) (|ofCategory| *4 (|GcdDomain|)))) (|characteristicPolynomial| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| *5)))) (|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Polynomial| *5)) (|isDomain| *1 (|EigenPackage| *5)) (|ofCategory| *5 (|GcdDomain|))))) 
(CATEGORY |package| (SIGNATURE |characteristicPolynomial| ((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Symbol|))) (SIGNATURE |characteristicPolynomial| ((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |eigenvalues| ((|List| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|Matrix| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |eigenvector| ((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |generalizedEigenvector| ((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |generalizedEigenvector| ((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) (|Matrix| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |generalizedEigenvectors| ((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |geneigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |eigenvectors| ((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) 
((|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) 14))) 
(((|EquationFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)))) (|Type|) (|Type|)) (T |EquationFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Equation| *5)) (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|Equation| *6)) (|isDomain| *1 (|EquationFunctions2| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |map| ((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)))) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|zero?| (((|Boolean|) $) NIL (|has| |#1| (|AbelianGroup|)))) (|swap| (($ $) 22)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|AbelianGroup|)))) (|subst| (($ $ $) 93 (|has| |#1| (|ExpressionSpace|)))) (|sample| (($) NIL (OR (|has| |#1| (|AbelianGroup|)) (|has| |#1| (|Monoid|))) CONST)) (|rightZero| (($ $) 8 (|has| |#1| (|AbelianGroup|)))) (|rightOne| (((|Union| $ "failed") $) 68 (|has| |#1| (|Monoid|)))) (|rhs| ((|#1| $) 21)) (|recip| (((|Union| $ "failed") $) 66 (|has| |#1| (|Monoid|)))) (|one?| (((|Boolean|) $) NIL (|has| |#1| (|Monoid|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 24)) (|lhs| ((|#1| $) 9)) (|leftZero| (($ $) 57 (|has| |#1| (|AbelianGroup|)))) (|leftOne| (((|Union| $ "failed") $) 67 (|has| |#1| (|Monoid|)))) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|inv| (($ $) 70 (OR (|has| |#1| (|Field|)) (|has| |#1| (|Group|))))) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|factorAndSplit| (((|List| $) $) 19 (|has| |#1| (|IntegralDomain|)))) (|eval| (($ $ $) 34 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| $)) 37 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Symbol|) |#1|) 27 (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|))) (($ $ (|List| (|Symbol|)) (|List| |#1|)) 31 (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|)))) (|equation| (($ |#1| |#1|) 17)) (|dimension| (((|CardinalNumber|)) 88 (|has| |#1| (|Field|)))) (|differentiate| (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|)) 85 (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (|conjugate| (($ $ $) NIL (|has| |#1| (|Group|)))) (|commutator| (($ $ $) NIL (|has| |#1| (|Group|)))) (|coerce| (($ (|Integer|)) NIL (|has| |#1| (|Ring|))) (((|Boolean|) $) 45 (|has| |#1| (|SetCategory|))) (((|OutputForm|) $) 44 (|has| |#1| (|SetCategory|)))) (|characteristic| (((|NonNegativeInteger|)) 73 (|has| |#1| (|Ring|)))) (^ (($ $ (|Integer|)) NIL (|has| |#1| (|Group|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Monoid|))) (($ $ (|PositiveInteger|)) NIL (|has| |#1| (|SemiGroup|)))) (|Zero| (($) 55 (|has| |#1| (|AbelianGroup|)) CONST)) (|One| (($) 63 (|has| |#1| (|Monoid|)) CONST)) (D (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (= (($ |#1| |#1|) 20) (((|Boolean|) $ $) 40 (|has| |#1| (|SetCategory|)))) (/ (($ $ |#1|) NIL (|has| |#1| (|Field|))) (($ $ $) 90 (OR (|has| |#1| (|Field|)) (|has| |#1| (|Group|))))) (- (($ |#1| $) 53 (|has| |#1| (|AbelianGroup|))) (($ $ |#1|) 54 (|has| |#1| (|AbelianGroup|))) (($ $ $) 52 (|has| |#1| (|AbelianGroup|))) (($ $) 51 (|has| |#1| (|AbelianGroup|)))) (+ (($ |#1| $) 48 (|has| |#1| (|AbelianSemiGroup|))) (($ $ |#1|) 49 (|has| |#1| (|AbelianSemiGroup|))) (($ $ $) 47 (|has| |#1| (|AbelianSemiGroup|)))) (** (($ $ (|Integer|)) NIL (|has| |#1| (|Group|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Monoid|))) (($ $ (|PositiveInteger|)) NIL (|has| |#1| (|SemiGroup|)))) (* (($ $ |#1|) 61 (|has| |#1| (|SemiGroup|))) (($ |#1| $) 60 (|has| |#1| (|SemiGroup|))) (($ $ $) 59 (|has| |#1| (|SemiGroup|))) (($ (|Integer|) $) 76 (|has| |#1| (|AbelianGroup|))) (($ (|NonNegativeInteger|) $) NIL (|has| |#1| (|AbelianGroup|))) (($ (|PositiveInteger|) $) NIL (|has| |#1| (|AbelianSemiGroup|))))) 
(((|Equation| |#1|) (|Join| (|Type|) (CATEGORY |domain| (SIGNATURE = ($ |#1| |#1|)) (SIGNATURE |equation| ($ |#1| |#1|)) (SIGNATURE |swap| ($ $)) (SIGNATURE |lhs| (|#1| $)) (SIGNATURE |rhs| (|#1| $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (IF (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) (ATTRIBUTE (|InnerEvalable| (|Symbol|) |#1|)) |noBranch|) (IF (|has| |#1| (|SetCategory|)) (PROGN (ATTRIBUTE (|SetCategory|)) (ATTRIBUTE (|CoercibleTo| (|Boolean|))) (IF (|has| |#1| (|Evalable| |#1|)) (PROGN (SIGNATURE |eval| ($ $ $)) (SIGNATURE |eval| ($ $ (|List| $)))) |noBranch|)) |noBranch|) (IF (|has| |#1| (|AbelianSemiGroup|)) (PROGN (ATTRIBUTE (|AbelianSemiGroup|)) (SIGNATURE + ($ |#1| $)) (SIGNATURE + ($ $ |#1|))) |noBranch|) (IF (|has| |#1| (|AbelianGroup|)) (PROGN (ATTRIBUTE (|AbelianGroup|)) (SIGNATURE |leftZero| ($ $)) (SIGNATURE |rightZero| ($ $)) (SIGNATURE - ($ |#1| $)) (SIGNATURE - ($ $ |#1|))) |noBranch|) (IF (|has| |#1| (|SemiGroup|)) (PROGN (ATTRIBUTE (|SemiGroup|)) (SIGNATURE * ($ |#1| $)) (SIGNATURE * ($ $ |#1|))) |noBranch|) (IF (|has| |#1| (|Monoid|)) (PROGN (ATTRIBUTE (|Monoid|)) (SIGNATURE |leftOne| ((|Union| $ "failed") $)) (SIGNATURE |rightOne| ((|Union| $ "failed") $))) |noBranch|) (IF (|has| |#1| (|Group|)) (PROGN (ATTRIBUTE (|Group|)) (SIGNATURE |leftOne| ((|Union| $ "failed") $)) (SIGNATURE |rightOne| ((|Union| $ "failed") $))) |noBranch|) (IF (|has| |#1| (|Ring|)) (PROGN (ATTRIBUTE (|Ring|)) (ATTRIBUTE (|BiModule| |#1| |#1|))) |noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Module| |#1|)) |noBranch|) (IF (|has| |#1| (|IntegralDomain|)) (SIGNATURE |factorAndSplit| ((|List| $) $)) |noBranch|) (IF (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (ATTRIBUTE (|PartialDifferentialRing| (|Symbol|))) |noBranch|) (IF (|has| |#1| (|Field|)) (PROGN (ATTRIBUTE (|VectorSpace| |#1|)) (SIGNATURE / ($ $ $)) (SIGNATURE |inv| ($ $))) |noBranch|) (IF (|has| |#1| (|ExpressionSpace|)) (SIGNATURE |subst| ($ $ $)) |noBranch|))) (|Type|)) (T |Equation|)) 
((= (*1 *1 *2 *2) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Type|)))) (|equation| (*1 *1 *2 *2) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Type|)))) (|swap| (*1 *1 *1) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Type|)))) (|lhs| (*1 *2 *1) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Type|)))) (|rhs| (*1 *2 *1) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Type|)))) (|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|Equation| *3)))) (|eval| (*1 *1 *1 *1) (AND (|ofCategory| *2 (|Evalable| *2)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|Type|)) (|isDomain| *1 (|Equation| *2)))) (|eval| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Equation| *3))) (|ofCategory| *3 (|Evalable| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|Equation| *3)))) (+ (*1 *1 *2 *1) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|AbelianSemiGroup|)) (|ofCategory| *2 (|Type|)))) (+ (*1 *1 *1 *2) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|AbelianSemiGroup|)) (|ofCategory| *2 (|Type|)))) (|leftZero| (*1 *1 *1) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|AbelianGroup|)) (|ofCategory| *2 (|Type|)))) (|rightZero| (*1 *1 *1) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|AbelianGroup|)) (|ofCategory| *2 (|Type|)))) (- (*1 *1 *2 *1) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|AbelianGroup|)) (|ofCategory| *2 (|Type|)))) (- (*1 *1 *1 *2) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|AbelianGroup|)) (|ofCategory| *2 (|Type|)))) (|leftOne| (*1 *1 *1) (|partial| AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Monoid|)) (|ofCategory| *2 (|Type|)))) (|rightOne| (*1 *1 *1) (|partial| AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Monoid|)) (|ofCategory| *2 (|Type|)))) (|factorAndSplit| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Equation| *3))) (|isDomain| *1 (|Equation| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Type|)))) (|subst| (*1 *1 *1 *1) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|ExpressionSpace|)) (|ofCategory| *2 (|Type|)))) (* (*1 *1 *1 *2) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|SemiGroup|)) (|ofCategory| *2 (|Type|)))) (* (*1 *1 *2 *1) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|SemiGroup|)) (|ofCategory| *2 (|Type|)))) (/ (*1 *1 *1 *1) (OR (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Field|)) (|ofCategory| *2 (|Type|))) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Group|)) (|ofCategory| *2 (|Type|))))) (|inv| (*1 *1 *1) (OR (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Field|)) (|ofCategory| *2 (|Type|))) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Group|)) (|ofCategory| *2 (|Type|)))))) 
(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE = ($ |#1| |#1|)) (SIGNATURE |equation| ($ |#1| |#1|)) (SIGNATURE |swap| ($ $)) (SIGNATURE |lhs| (|#1| $)) (SIGNATURE |rhs| (|#1| $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (IF (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) (ATTRIBUTE (|InnerEvalable| (|Symbol|) |#1|)) |noBranch|) (IF (|has| |#1| (|SetCategory|)) (PROGN (ATTRIBUTE (|SetCategory|)) (ATTRIBUTE (|CoercibleTo| (|Boolean|))) (IF (|has| |#1| (|Evalable| |#1|)) (PROGN (SIGNATURE |eval| ($ $ $)) (SIGNATURE |eval| ($ $ (|List| $)))) |noBranch|)) |noBranch|) (IF (|has| |#1| (|AbelianSemiGroup|)) (PROGN (ATTRIBUTE (|AbelianSemiGroup|)) (SIGNATURE + ($ |#1| $)) (SIGNATURE + ($ $ |#1|))) |noBranch|) (IF (|has| |#1| (|AbelianGroup|)) (PROGN (ATTRIBUTE (|AbelianGroup|)) (SIGNATURE |leftZero| ($ $)) (SIGNATURE |rightZero| ($ $)) (SIGNATURE - ($ |#1| $)) (SIGNATURE - ($ $ |#1|))) |noBranch|) (IF (|has| |#1| (|SemiGroup|)) (PROGN (ATTRIBUTE (|SemiGroup|)) (SIGNATURE * ($ |#1| $)) (SIGNATURE * ($ $ |#1|))) |noBranch|) (IF (|has| |#1| (|Monoid|)) (PROGN (ATTRIBUTE (|Monoid|)) (SIGNATURE |leftOne| ((|Union| $ "failed") $)) (SIGNATURE |rightOne| ((|Union| $ "failed") $))) |noBranch|) (IF (|has| |#1| (|Group|)) (PROGN (ATTRIBUTE (|Group|)) (SIGNATURE |leftOne| ((|Union| $ "failed") $)) (SIGNATURE |rightOne| ((|Union| $ "failed") $))) |noBranch|) (IF (|has| |#1| (|Ring|)) (PROGN (ATTRIBUTE (|Ring|)) (ATTRIBUTE (|BiModule| |#1| |#1|))) |noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Module| |#1|)) |noBranch|) (IF (|has| |#1| (|IntegralDomain|)) (SIGNATURE |factorAndSplit| ((|List| $) $)) |noBranch|) (IF (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (ATTRIBUTE (|PartialDifferentialRing| (|Symbol|))) |noBranch|) (IF (|has| |#1| (|Field|)) (PROGN (ATTRIBUTE (|VectorSpace| |#1|)) (SIGNATURE / ($ $ $)) (SIGNATURE |inv| ($ $))) |noBranch|) (IF (|has| |#1| (|ExpressionSpace|)) (SIGNATURE |subst| ($ $ $)) |noBranch|))) 
((~= (((|Boolean|) $ $) NIL (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))))) (|table| (($) NIL) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL)) (|swap!| (((|Void|) $ |#1| |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setelt| ((|#2| $ |#1| |#2|) NIL)) (|select!| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|select| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|search| (((|Union| |#2| "failed") |#1| $) NIL)) (|sample| (($) NIL T CONST)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))))) (|remove!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| |#2| "failed") |#1| $) NIL)) (|remove| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| ((|#2| $ |#1| |#2|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#2| $ |#1|) NIL)) (|parts| (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|List| |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| ((|#1| $) NIL (|has| |#1| (|OrderedSet|)))) (|members| (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|List| |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (((|Boolean|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|maxIndex| ((|#1| $) NIL (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ (|Mapping| |#2| |#2|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL) (($ (|Mapping| |#2| |#2|) $) NIL) (($ (|Mapping| |#2| |#2| |#2|) $ $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) 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(CATEGORY |package| (SIGNATURE |map| (|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)))) 
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(CATEGORY |package| (SIGNATURE |map| (|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)))) 
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(CATEGORY |package| (SIGNATURE |in?| ((|Boolean|) (|DoubleFloat|)))) 
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(CATEGORY |package| (SIGNATURE |neglist| ((|List| |#1|) (|List| |#1|)))) 
((|map| (((|Matrix| |#2|) (|Mapping| |#2| |#1|) (|Matrix| |#1|)) 15))) 
(((|ExpertSystemToolsPackage2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Matrix| |#2|) (|Mapping| |#2| |#1|) (|Matrix| |#1|)))) (|Ring|) (|Ring|)) (T |ExpertSystemToolsPackage2|)) 
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(CATEGORY |package| (SIGNATURE |map| ((|Matrix| |#2|) (|Mapping| |#2| |#1|) (|Matrix| |#1|)))) 
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(((|EuclideanDomain&| |#1|) (CATEGORY |domain| (SIGNATURE |multiEuclidean| ((|Union| (|List| |#1|) "failed") (|List| |#1|) |#1|)) (SIGNATURE |extendedEuclidean| ((|Union| (|Record| (|:| |coef1| |#1|) (|:| |coef2| |#1|)) "failed") |#1| |#1| |#1|)) (SIGNATURE |extendedEuclidean| ((|Record| (|:| |coef1| |#1|) (|:| |coef2| |#1|) (|:| |generator| |#1|)) |#1| |#1|)) (SIGNATURE |rem| (|#1| |#1| |#1|)) (SIGNATURE |quo| (|#1| |#1| |#1|)) (SIGNATURE |sizeLess?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |expressIdealMember| ((|Union| (|List| |#1|) "failed") (|List| |#1|) |#1|)) (SIGNATURE |principalIdeal| ((|Record| (|:| |coef| (|List| |#1|)) (|:| |generator| |#1|)) (|List| |#1|))) (SIGNATURE |gcd| (|#1| (|List| |#1|))) (SIGNATURE |gcd| (|#1| |#1| |#1|)) (SIGNATURE |exquo| ((|Union| |#1| "failed") |#1| |#1|))) (|EuclideanDomain|)) (T |EuclideanDomain&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |multiEuclidean| ((|Union| (|List| |#1|) "failed") (|List| |#1|) |#1|)) (SIGNATURE |extendedEuclidean| ((|Union| (|Record| (|:| |coef1| |#1|) (|:| |coef2| |#1|)) "failed") |#1| |#1| |#1|)) (SIGNATURE |extendedEuclidean| ((|Record| (|:| |coef1| |#1|) (|:| |coef2| |#1|) (|:| |generator| |#1|)) |#1| |#1|)) (SIGNATURE |rem| (|#1| |#1| |#1|)) (SIGNATURE |quo| (|#1| |#1| |#1|)) (SIGNATURE |sizeLess?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |expressIdealMember| ((|Union| (|List| |#1|) "failed") (|List| |#1|) |#1|)) (SIGNATURE |principalIdeal| ((|Record| (|:| |coef| (|List| |#1|)) (|:| |generator| |#1|)) (|List| |#1|))) (SIGNATURE |gcd| (|#1| (|List| |#1|))) (SIGNATURE |gcd| (|#1| |#1| |#1|)) (SIGNATURE |exquo| ((|Union| |#1| "failed") |#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sizeLess?| (((|Boolean|) $ $) 58)) (|sample| (($) 16 T CONST)) (|rem| (($ $ $) 54)) (|recip| (((|Union| $ "failed") $) 33)) (|quo| (($ $ $) 55)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 50)) (|one?| (((|Boolean|) $) 30)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 51)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 53) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 52)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 49)) (|euclideanSize| (((|NonNegativeInteger|) $) 57)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 56)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|EuclideanDomain|) (|Category|)) (T |EuclideanDomain|)) 
((|sizeLess?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|EuclideanDomain|)) (|isDomain| *2 (|Boolean|)))) (|euclideanSize| (*1 *2 *1) (AND (|ofCategory| *1 (|EuclideanDomain|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|divide| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|EuclideanDomain|)))) (|quo| (*1 *1 *1 *1) (|ofCategory| *1 (|EuclideanDomain|))) (|rem| (*1 *1 *1 *1) (|ofCategory| *1 (|EuclideanDomain|))) (|extendedEuclidean| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |coef1| *1) (|:| |coef2| *1) (|:| |generator| *1))) (|ofCategory| *1 (|EuclideanDomain|)))) (|extendedEuclidean| (*1 *2 *1 *1 *1) (|partial| AND (|isDomain| *2 (|Record| (|:| |coef1| *1) (|:| |coef2| *1))) (|ofCategory| *1 (|EuclideanDomain|)))) (|multiEuclidean| (*1 *2 *2 *1) (|partial| AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|EuclideanDomain|))))) 
(|Join| (|PrincipalIdealDomain|) (CATEGORY |domain| (SIGNATURE |sizeLess?| ((|Boolean|) $ $)) (SIGNATURE |euclideanSize| ((|NonNegativeInteger|) $)) (SIGNATURE |divide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |quo| ($ $ $)) (SIGNATURE |rem| ($ $ $)) (SIGNATURE |extendedEuclidean| ((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $)) (SIGNATURE |extendedEuclidean| ((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $)) (SIGNATURE |multiEuclidean| ((|Union| (|List| $) "failed") (|List| $) $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|eval| (($ $ (|List| |#2|) (|List| |#2|)) 14) (($ $ |#2| |#2|) NIL) (($ $ (|Equation| |#2|)) 11) (($ $ (|List| (|Equation| |#2|))) NIL))) 
(((|Evalable&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |eval| (|#1| |#1| (|List| (|Equation| |#2|)))) (SIGNATURE |eval| (|#1| |#1| (|Equation| |#2|))) (SIGNATURE |eval| (|#1| |#1| |#2| |#2|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#2|) (|List| |#2|)))) (|Evalable| |#2|) (|SetCategory|)) (T |Evalable&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |eval| (|#1| |#1| (|List| (|Equation| |#2|)))) (SIGNATURE |eval| (|#1| |#1| (|Equation| |#2|))) (SIGNATURE |eval| (|#1| |#1| |#2| |#2|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#2|) (|List| |#2|)))) 
((|eval| (($ $ (|List| |#1|) (|List| |#1|)) 7) (($ $ |#1| |#1|) 6) (($ $ (|Equation| |#1|)) 9) (($ $ (|List| (|Equation| |#1|))) 8))) 
(((|Evalable| |#1|) (|Category|) (|SetCategory|)) (T |Evalable|)) 
((|eval| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Equation| *3)) (|ofCategory| *1 (|Evalable| *3)) (|ofCategory| *3 (|SetCategory|)))) (|eval| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Equation| *3))) (|ofCategory| *1 (|Evalable| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(|Join| (|InnerEvalable| |t#1| |t#1|) (CATEGORY |domain| (SIGNATURE |eval| ($ $ (|Equation| |t#1|))) (SIGNATURE |eval| ($ $ (|List| (|Equation| |t#1|)))))) 
(((|InnerEvalable| |#1| |#1|) . T)) 
((|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) 24))) 
(((|EvaluateCycleIndicators| |#1|) (CATEGORY |package| (SIGNATURE |eval| (|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))))) (|Algebra| (|Fraction| (|Integer|)))) (T |EvaluateCycleIndicators|)) 
((|eval| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *2 (|Integer|))) (|isDomain| *4 (|SymmetricPolynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|EvaluateCycleIndicators| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))))) 
(CATEGORY |package| (SIGNATURE |eval| (|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))))) 
((~= (((|Boolean|) $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 7)) (= (((|Boolean|) $ $) 9))) 
(((|Exit|) (|SetCategory|)) (T |Exit|)) 
NIL 
(|SetCategory|) 
((|writeObj| (((|Void|) (|SubSpace| 3 (|DoubleFloat|)) (|String|)) 38))) 
(((|Export3D|) (CATEGORY |package| (SIGNATURE |writeObj| ((|Void|) (|SubSpace| 3 (|DoubleFloat|)) (|String|))))) (T |Export3D|)) 
((|writeObj| (*1 *2 *3 *4) (AND (|isDomain| *3 (|SubSpace| 3 (|DoubleFloat|))) (|isDomain| *4 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Export3D|))))) 
(CATEGORY |package| (SIGNATURE |writeObj| ((|Void|) (|SubSpace| 3 (|DoubleFloat|)) (|String|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 62)) (|wholePart| (((|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) $) NIL (|has| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (|EuclideanDomain|)))) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (|PolynomialFactorizationExplicit|)))) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sign| (((|Integer|) $) NIL (|has| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (|OrderedIntegralDomain|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) "failed") $) NIL) (((|Union| (|Symbol|) "failed") $) NIL (|has| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (|RetractableTo| (|Symbol|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (|RetractableTo| (|Integer|)))) (((|Union| (|Integer|) "failed") $) NIL (|has| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (|RetractableTo| (|Integer|)))) (((|Union| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|) "failed") $) 24)) (|retract| (((|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) $) NIL) (((|Symbol|) $) NIL (|has| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (|RetractableTo| (|Symbol|)))) (((|Fraction| (|Integer|)) $) NIL (|has| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (|RetractableTo| (|Integer|)))) (((|Integer|) $) NIL (|has| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (|RetractableTo| (|Integer|)))) (((|UnivariatePuiseuxSeries| |#2| |#3| |#4|) $) NIL)) (|rem| (($ $ $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|))) (|:| |vec| (|Vector| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|)))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|)) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) NIL (|has| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (|IntegerNumberSystem|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|positive?| (((|Boolean|) $) NIL (|has| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (|OrderedIntegralDomain|)))) (|patternMatch| (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (|has| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| 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(|inv| (($ $) NIL (|has| |#1| (|Field|)))) (|integrate| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Symbol|)) NIL (OR (AND (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| (|Symbol|)))) (|has| |#1| (SIGNATURE |variables| ((|List| (|Symbol|)) |#1|))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (AND (|has| |#1| (|AlgebraicallyClosedFunctionSpace| (|Integer|))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|)))))) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|Field|)))) (|gcd| (($ (|List| $)) NIL (|has| |#1| (|Field|))) (($ $ $) NIL (|has| |#1| (|Field|)))) (|factor| (((|Factored| $) $) NIL (|has| |#1| (|Field|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL (|has| |#1| (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|extend| (($ $ (|Fraction| (|Integer|))) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) (|exponentialOrder| (((|Fraction| (|Integer|)) $) 16)) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) 11)) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) 12)) (|exp| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|eval| (((|Stream| |#1|) $ |#1|) NIL (|has| |#1| (SIGNATURE ** (|#1| |#1| (|Fraction| (|Integer|))))))) (|euclideanSize| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|Field|)))) (|elt| ((|#1| $ (|Fraction| (|Integer|))) NIL) (($ $ $) NIL (|has| (|Fraction| (|Integer|)) (|SemiGroup|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|Field|)))) (|differentiate| (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) (($ $) NIL (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))))) (|degree| (((|Fraction| (|Integer|)) $) NIL)) (|csch| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|csc| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|coth| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cot| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cosh| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cos| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|complete| (($ $) 10)) (|coerce| (((|OutputForm|) $) 36) (($ (|Integer|)) NIL) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|))) (($ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|coefficient| ((|#1| $ (|Fraction| (|Integer|))) 28)) (|charthRoot| (((|Union| $ "failed") $) NIL (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|center| ((|#1| $) NIL)) (|atanh| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|atan| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|associates?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|asinh| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asin| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asech| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asec| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|approximate| ((|#1| $ (|Fraction| (|Integer|))) NIL (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| (|Fraction| (|Integer|))))) (|has| |#1| (SIGNATURE |coerce| (|#1| (|Symbol|))))))) (|acsch| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acsc| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acoth| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acot| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acosh| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acos| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| |#1| (|Field|)))) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) (($ $) NIL (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))))) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 26)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 31)) (/ (($ $ |#1|) NIL (|has| |#1| (|Field|))) (($ $ $) NIL (|has| |#1| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| |#1| (|Field|))) (($ $ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ |#1|) NIL) (($ |#1| $) NIL) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) 
(((|ExponentialOfUnivariatePuiseuxSeries| |#1| |#2| |#3|) (|Join| (|UnivariatePuiseuxSeriesCategory| |#1|) (|OrderedAbelianMonoid|) (CATEGORY |domain| (SIGNATURE |exponential| ($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|))) (SIGNATURE |exponent| ((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $)) (SIGNATURE |exponentialOrder| ((|Fraction| (|Integer|)) $)))) (|Join| (|Field|) (|OrderedSet|)) (|Symbol|) |#1|) (T |ExponentialOfUnivariatePuiseuxSeries|)) 
((|exponential| (*1 *1 *2) (AND (|isDomain| *2 (|UnivariatePuiseuxSeries| *3 *4 *5)) (|ofCategory| *3 (|Join| (|Field|) (|OrderedSet|))) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3) (|isDomain| *1 (|ExponentialOfUnivariatePuiseuxSeries| *3 *4 *5)))) (|exponent| (*1 *2 *1) (AND (|isDomain| *2 (|UnivariatePuiseuxSeries| *3 *4 *5)) (|isDomain| *1 (|ExponentialOfUnivariatePuiseuxSeries| *3 *4 *5)) (|ofCategory| *3 (|Join| (|Field|) (|OrderedSet|))) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3))) (|exponentialOrder| (*1 *2 *1) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|ExponentialOfUnivariatePuiseuxSeries| *3 *4 *5)) (|ofCategory| *3 (|Join| (|Field|) (|OrderedSet|))) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3)))) 
(|Join| (|UnivariatePuiseuxSeriesCategory| |#1|) (|OrderedAbelianMonoid|) (CATEGORY |domain| (SIGNATURE |exponential| ($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|))) (SIGNATURE |exponent| ((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $)) (SIGNATURE |exponentialOrder| ((|Fraction| (|Integer|)) $)))) 
((|factorSqFree| (((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|) |#1|) 15)) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|) |#1|) 24))) 
(((|FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber| |#1|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|) |#1|)) (SIGNATURE |factorSqFree| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|) |#1|))) (|PseudoAlgebraicClosureOfAlgExtOfRationalNumberCategory|)) (T |FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber|)) 
((|factorSqFree| (*1 *2 *3 *4) (AND (|ofCategory| *4 (|PseudoAlgebraicClosureOfAlgExtOfRationalNumberCategory|)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *4))) (|isDomain| *1 (|FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber| *4)) (|isDomain| *3 (|SparseUnivariatePolynomial| *4)))) (|factor| (*1 *2 *3 *4) (AND (|ofCategory| *4 (|PseudoAlgebraicClosureOfAlgExtOfRationalNumberCategory|)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *4))) (|isDomain| *1 (|FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber| *4)) (|isDomain| *3 (|SparseUnivariatePolynomial| *4))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|) |#1|)) (SIGNATURE |factorSqFree| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|) |#1|))) 
((|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) 24)) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) 28))) 
(((|FactoredFunctions| |#1|) (CATEGORY |package| (SIGNATURE |nthRoot| ((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|))) (SIGNATURE |log| ((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)))) (|IntegralDomain|)) (T |FactoredFunctions|)) 
((|log| (*1 *2 *3) (AND (|isDomain| *3 (|Factored| *4)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| *4)))) (|isDomain| *1 (|FactoredFunctions| *4)))) (|nthRoot| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Factored| *5)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| *5) (|:| |radicand| (|List| *5)))) (|isDomain| *1 (|FactoredFunctions| *5)) (|isDomain| *4 (|NonNegativeInteger|))))) 
(CATEGORY |package| (SIGNATURE |nthRoot| ((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|))) (SIGNATURE |log| ((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)))) 
((|factorSqFree| (((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|) |#1|) 15)) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|) |#1|) 24))) 
(((|FactorisationOverPseudoAlgebraicClosureOfRationalNumber| |#1|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|) |#1|)) (SIGNATURE |factorSqFree| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|) |#1|))) (|PseudoAlgebraicClosureOfRationalNumberCategory|)) (T |FactorisationOverPseudoAlgebraicClosureOfRationalNumber|)) 
((|factorSqFree| (*1 *2 *3 *4) (AND (|ofCategory| *4 (|PseudoAlgebraicClosureOfRationalNumberCategory|)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *4))) (|isDomain| *1 (|FactorisationOverPseudoAlgebraicClosureOfRationalNumber| *4)) (|isDomain| *3 (|SparseUnivariatePolynomial| *4)))) (|factor| (*1 *2 *3 *4) (AND (|ofCategory| *4 (|PseudoAlgebraicClosureOfRationalNumberCategory|)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *4))) (|isDomain| *1 (|FactorisationOverPseudoAlgebraicClosureOfRationalNumber| *4)) (|isDomain| *3 (|SparseUnivariatePolynomial| *4))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|) |#1|)) (SIGNATURE |factorSqFree| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|) |#1|))) 
((|variables| (((|List| |#2|) (|SparseUnivariatePolynomial| |#4|)) 43)) (|ran| ((|#3| (|Integer|)) 46)) (|raisePolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|)) 30)) (|normalDeriv| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|Integer|)) 55)) (|lowerPolynomial| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|)) 21)) (|degree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|)) 40)) (|completeEval| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|)) 35))) 
(((|FactoringUtilities| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |completeEval| ((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|))) (SIGNATURE |degree| ((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|))) (SIGNATURE |variables| ((|List| |#2|) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |lowerPolynomial| ((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |raisePolynomial| ((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|))) (SIGNATURE |normalDeriv| ((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|Integer|))) (SIGNATURE |ran| (|#3| (|Integer|)))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|Ring|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |FactoringUtilities|)) 
((|ran| (*1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|FactoringUtilities| *4 *5 *2 *6)) (|ofCategory| *6 (|PolynomialCategory| *2 *4 *5)))) (|normalDeriv| (*1 *2 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *7)) (|isDomain| *3 (|Integer|)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Ring|)) (|isDomain| *1 (|FactoringUtilities| *4 *5 *6 *7)))) (|raisePolynomial| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *6)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *7)) (|isDomain| *1 (|FactoringUtilities| *4 *5 *6 *7)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)))) (|lowerPolynomial| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *7)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Ring|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *6)) (|isDomain| *1 (|FactoringUtilities| *4 *5 *6 *7)))) (|variables| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *7)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Ring|)) (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|FactoringUtilities| *4 *5 *6 *7)))) (|degree| (*1 *2 *3 *4) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *8)) (|isDomain| *4 (|List| *6)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *8 (|PolynomialCategory| *7 *5 *6)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|Ring|)) (|isDomain| *2 (|List| (|NonNegativeInteger|))) (|isDomain| *1 (|FactoringUtilities| *5 *6 *7 *8)))) (|completeEval| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *9)) (|isDomain| *4 (|List| *7)) (|isDomain| *5 (|List| *8)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|Ring|)) (|ofCategory| *9 (|PolynomialCategory| *8 *6 *7)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *8)) (|isDomain| *1 (|FactoringUtilities| *6 *7 *8 *9))))) 
(CATEGORY |package| (SIGNATURE |completeEval| ((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|))) (SIGNATURE |degree| ((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|))) (SIGNATURE |variables| ((|List| |#2|) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |lowerPolynomial| ((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |raisePolynomial| ((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|))) (SIGNATURE |normalDeriv| ((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|Integer|))) (SIGNATURE |ran| (|#3| (|Integer|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 14)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) 18)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|size| (((|NonNegativeInteger|) $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL)) (|retract| ((|#1| $) NIL)) (|nthFactor| ((|#1| $ (|Integer|)) NIL)) (|nthCoef| (((|Integer|) $ (|Integer|)) NIL)) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|mapGen| (($ (|Mapping| |#1| |#1|) $) NIL)) (|mapCoef| (($ (|Mapping| (|Integer|) (|Integer|)) $) 10)) (|latex| (((|String|) $) NIL)) (|highCommonTerms| (($ $ $) NIL (|has| (|Integer|) (|OrderedAbelianMonoid|)))) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ |#1|) NIL)) (|coefficient| (((|Integer|) |#1| $) NIL)) (|Zero| (($) 15 T CONST)) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) 21 (|has| |#1| (|OrderedSet|)))) (- (($ $) 11) (($ $ $) 20)) (+ (($ $ $) NIL) (($ |#1| $) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ (|Integer|)) NIL) (($ (|Integer|) |#1|) 19))) 
(((|FreeAbelianGroup| |#1|) (|Join| (|AbelianGroup|) (|Module| (|Integer|)) (|FreeAbelianMonoidCategory| |#1| (|Integer|)) (CATEGORY |package| (IF (|has| |#1| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |noBranch|))) (|SetCategory|)) (T |FreeAbelianGroup|)) 
NIL 
(|Join| (|AbelianGroup|) (|Module| (|Integer|)) (|FreeAbelianMonoidCategory| |#1| (|Integer|)) (CATEGORY |package| (IF (|has| |#1| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |noBranch|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) 26)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|size| (((|NonNegativeInteger|) $) 27)) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 31)) (|retract| ((|#1| $) 30)) (|nthFactor| ((|#1| $ (|Integer|)) 24)) (|nthCoef| ((|#2| $ (|Integer|)) 25)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 21)) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) 22)) (|latex| (((|String|) $) 9)) (|highCommonTerms| (($ $ $) 20 (|has| |#2| (|OrderedAbelianMonoid|)))) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11) (($ |#1|) 32)) (|coefficient| ((|#2| |#1| $) 23)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (+ (($ $ $) 13) (($ |#1| $) 29)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ |#2| |#1|) 28))) 
(((|FreeAbelianMonoidCategory| |#1| |#2|) (|Category|) (|SetCategory|) (|CancellationAbelianMonoid|)) (T |FreeAbelianMonoidCategory|)) 
((+ (*1 *1 *2 *1) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|CancellationAbelianMonoid|)))) (* (*1 *1 *2 *3) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|CancellationAbelianMonoid|)))) (|size| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|CancellationAbelianMonoid|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|terms| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|CancellationAbelianMonoid|)) (|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| *4)))))) (|nthCoef| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|FreeAbelianMonoidCategory| *4 *2)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *2 (|CancellationAbelianMonoid|)))) (|nthFactor| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|FreeAbelianMonoidCategory| *2 *4)) (|ofCategory| *4 (|CancellationAbelianMonoid|)) (|ofCategory| *2 (|SetCategory|)))) (|coefficient| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|CancellationAbelianMonoid|)))) (|mapCoef| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|CancellationAbelianMonoid|)))) (|mapGen| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|CancellationAbelianMonoid|)))) (|highCommonTerms| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|CancellationAbelianMonoid|)) (|ofCategory| *3 (|OrderedAbelianMonoid|))))) 
(|Join| (|CancellationAbelianMonoid|) (|RetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE + ($ |t#1| $)) (SIGNATURE * ($ |t#2| |t#1|)) (SIGNATURE |size| ((|NonNegativeInteger|) $)) (SIGNATURE |terms| ((|List| (|Record| (|:| |gen| |t#1|) (|:| |exp| |t#2|))) $)) (SIGNATURE |nthCoef| (|t#2| $ (|Integer|))) (SIGNATURE |nthFactor| (|t#1| $ (|Integer|))) (SIGNATURE |coefficient| (|t#2| |t#1| $)) (SIGNATURE |mapCoef| ($ (|Mapping| |t#2| |t#2|) $)) (SIGNATURE |mapGen| ($ (|Mapping| |t#1| |t#1|) $)) (IF (|has| |t#2| (|OrderedAbelianMonoid|)) (SIGNATURE |highCommonTerms| ($ $ $)) |noBranch|))) 
(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|RetractableTo| |#1|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|size| (((|NonNegativeInteger|) $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL)) (|retract| ((|#1| $) NIL)) (|nthFactor| ((|#1| $ (|Integer|)) NIL)) (|nthCoef| (((|NonNegativeInteger|) $ (|Integer|)) NIL)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) NIL)) (|mapCoef| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) NIL)) (|latex| (((|String|) $) NIL)) (|highCommonTerms| (($ $ $) NIL (|has| (|NonNegativeInteger|) (|OrderedAbelianMonoid|)))) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ |#1|) NIL)) (|coefficient| (((|NonNegativeInteger|) |#1| $) NIL)) (|Zero| (($) NIL T CONST)) (= (((|Boolean|) $ $) NIL)) (+ (($ $ $) NIL) (($ |#1| $) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|NonNegativeInteger|) |#1|) NIL))) 
(((|FreeAbelianMonoid| |#1|) (|FreeAbelianMonoidCategory| |#1| (|NonNegativeInteger|)) (|SetCategory|)) (T |FreeAbelianMonoid|)) 
NIL 
(|FreeAbelianMonoidCategory| |#1| (|NonNegativeInteger|)) 
((|map| ((|#5| (|Mapping| |#4| |#2|) |#3|) 19))) 
(((|FiniteAbelianMonoidRingFunctions2| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |map| (|#5| (|Mapping| |#4| |#2|) |#3|))) (|OrderedAbelianMonoid|) (|Ring|) (|FiniteAbelianMonoidRing| |#2| |#1|) (|Ring|) (|FiniteAbelianMonoidRing| |#4| |#1|)) (T |FiniteAbelianMonoidRingFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *7 *6)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *7 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|FiniteAbelianMonoidRing| *7 *5)) (|isDomain| *1 (|FiniteAbelianMonoidRingFunctions2| *5 *6 *4 *7 *2)) (|ofCategory| *4 (|FiniteAbelianMonoidRing| *6 *5))))) 
(CATEGORY |package| (SIGNATURE |map| (|#5| (|Mapping| |#4| |#2|) |#3|))) 
((|primitivePart| (($ $) 52)) (|pomopo!| (($ $ |#2| |#3| $) 14)) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) 35)) (|ground?| (((|Boolean|) $) 27)) (|ground| ((|#2| $) 29)) (|exquo| (((|Union| $ "failed") $ $) NIL) (((|Union| $ "failed") $ |#2|) 45)) (|content| ((|#2| $) 48)) (|coefficients| (((|List| |#2|) $) 38)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) 23)) (/ (($ $ |#2|) 42))) 
(((|FiniteAbelianMonoidRing&| |#1| |#2| |#3|) (CATEGORY |domain| (SIGNATURE |primitivePart| (|#1| |#1|)) (SIGNATURE |content| (|#2| |#1|)) (SIGNATURE |exquo| ((|Union| |#1| "failed") |#1| |#2|)) (SIGNATURE |binomThmExpt| (|#1| |#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |pomopo!| (|#1| |#1| |#2| |#3| |#1|)) (SIGNATURE |mapExponents| (|#1| (|Mapping| |#3| |#3|) |#1|)) (SIGNATURE |coefficients| ((|List| |#2|) |#1|)) (SIGNATURE |ground| (|#2| |#1|)) (SIGNATURE |ground?| ((|Boolean|) |#1|)) (SIGNATURE |exquo| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE / (|#1| |#1| |#2|))) (|FiniteAbelianMonoidRing| |#2| |#3|) (|Ring|) (|OrderedAbelianMonoid|)) (T |FiniteAbelianMonoidRing&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |primitivePart| (|#1| |#1|)) (SIGNATURE |content| (|#2| |#1|)) (SIGNATURE |exquo| ((|Union| |#1| "failed") |#1| |#2|)) (SIGNATURE |binomThmExpt| (|#1| |#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |pomopo!| (|#1| |#1| |#2| |#3| |#1|)) (SIGNATURE |mapExponents| (|#1| (|Mapping| |#3| |#3|) |#1|)) (SIGNATURE |coefficients| ((|List| |#2|) |#1|)) (SIGNATURE |ground| (|#2| |#1|)) (SIGNATURE |ground?| ((|Boolean|) |#1|)) (SIGNATURE |exquo| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE / (|#1| |#1| |#2|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 50 (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) 51 (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) 53 (|has| |#1| (|IntegralDomain|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 86 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) 84 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) 83)) (|retract| (((|Integer|) $) 87 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) 85 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) 82)) (|reductum| (($ $) 59)) (|recip| (((|Union| $ "failed") $) 33)) (|primitivePart| (($ $) 71 (|has| |#1| (|GcdDomain|)))) (|pomopo!| (($ $ |#1| |#2| $) 75)) (|one?| (((|Boolean|) $) 30)) (|numberOfMonomials| (((|NonNegativeInteger|) $) 78)) (|monomial?| (((|Boolean|) $) 61)) (|monomial| (($ |#1| |#2|) 60)) (|minimumDegree| ((|#2| $) 77)) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) 76)) (|map| (($ (|Mapping| |#1| |#1|) $) 62)) (|leadingMonomial| (($ $) 64)) (|leadingCoefficient| ((|#1| $) 65)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|ground?| (((|Boolean|) $) 81)) (|ground| ((|#1| $) 80)) (|exquo| (((|Union| $ "failed") $ $) 49 (|has| |#1| (|IntegralDomain|))) (((|Union| $ "failed") $ |#1|) 73 (|has| |#1| (|IntegralDomain|)))) (|degree| ((|#2| $) 63)) (|content| ((|#1| $) 72 (|has| |#1| (|GcdDomain|)))) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 48 (|has| |#1| (|IntegralDomain|))) (($ |#1|) 46) (($ (|Fraction| (|Integer|))) 56 (OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) (|coefficients| (((|List| |#1|) $) 79)) (|coefficient| ((|#1| $ |#2|) 58)) (|charthRoot| (((|Union| $ "failed") $) 47 (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) 74 (|has| |#1| (|CommutativeRing|)))) (|associates?| (((|Boolean|) $ $) 52 (|has| |#1| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (/ (($ $ |#1|) 57 (|has| |#1| (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 67) (($ |#1| $) 66) (($ (|Fraction| (|Integer|)) $) 55 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) 54 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) 
(((|FiniteAbelianMonoidRing| |#1| |#2|) (|Category|) (|Ring|) (|OrderedAbelianMonoid|)) (T |FiniteAbelianMonoidRing|)) 
((|ground?| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|Boolean|)))) (|ground| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *2 *3)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Ring|)))) (|coefficients| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|List| *3)))) (|numberOfMonomials| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|minimumDegree| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|mapExponents| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)))) (|pomopo!| (*1 *1 *1 *2 *3 *1) (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)))) (|binomThmExpt| (*1 *1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|ofCategory| *3 (|CommutativeRing|)))) (|exquo| (*1 *1 *1 *2) (|partial| AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|IntegralDomain|)))) (|content| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *2 *3)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|GcdDomain|)))) (|primitivePart| (*1 *1 *1) (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|GcdDomain|))))) 
(|Join| (|AbelianMonoidRing| |t#1| |t#2|) (|FullyRetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE |ground?| ((|Boolean|) $)) (SIGNATURE |ground| (|t#1| $)) (SIGNATURE |coefficients| ((|List| |t#1|) $)) (SIGNATURE |numberOfMonomials| ((|NonNegativeInteger|) $)) (SIGNATURE |minimumDegree| (|t#2| $)) (SIGNATURE |mapExponents| ($ (|Mapping| |t#2| |t#2|) $)) (SIGNATURE |pomopo!| ($ $ |t#1| |t#2| $)) (IF (|has| |t#1| (|CommutativeRing|)) (SIGNATURE |binomThmExpt| ($ $ $ (|NonNegativeInteger|))) |noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (SIGNATURE |exquo| ((|Union| $ "failed") $ |t#1|)) |noBranch|) (IF (|has| |t#1| (|GcdDomain|)) (PROGN (SIGNATURE |content| (|t#1| $)) (SIGNATURE |primitivePart| ($ $))) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| |#2|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|FullyRetractableTo| |#1|) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|Module| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) NIL) (((|Boolean|) $) NIL (|has| |#1| (|OrderedSet|)))) (|sort!| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $) NIL (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|has| |#1| (|OrderedSet|))))) (|sort| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) NIL) (($ $) NIL (|has| |#1| (|OrderedSet|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|shrinkable| (((|Boolean|) (|Boolean|)) NIL)) (|setelt| ((|#1| $ (|Integer|) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) NIL)) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) NIL T CONST)) (|reverse!| (($ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) NIL)) (|removeDuplicates!| (($ $) NIL (|has| |#1| (|SetCategory|)))) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|remove!| (($ |#1| $) NIL (|has| |#1| (|SetCategory|))) (($ (|Mapping| (|Boolean|) |#1|) $) NIL)) (|remove| (($ |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| ((|#1| $ (|Integer|) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#1| $ (|Integer|)) NIL)) (|position| (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) NIL) (((|Integer|) |#1| $) NIL (|has| |#1| (|SetCategory|))) (((|Integer|) |#1| $ (|Integer|)) NIL (|has| |#1| (|SetCategory|)))) (|physicalLength!| (($ $ (|Integer|)) NIL)) (|physicalLength| (((|NonNegativeInteger|) $) NIL)) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|new| (($ (|NonNegativeInteger|) |#1|) NIL)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|merge!| (($ $ $) NIL (|has| |#1| (|OrderedSet|))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) NIL)) (|merge| (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) NIL) (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|maxIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|insert!| (($ $ $ (|Integer|)) NIL) (($ |#1| $ (|Integer|)) NIL)) (|insert| (($ |#1| $ (|Integer|)) NIL) (($ $ $ (|Integer|)) NIL)) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|flexibleArray| (($ (|List| |#1|)) NIL)) (|first| ((|#1| $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) NIL)) (|fill!| (($ $ |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|entry?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|entries| (((|List| |#1|) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#1| $ (|Integer|) |#1|) NIL) ((|#1| $ (|Integer|)) NIL) (($ $ (|UniversalSegment| (|Integer|))) NIL)) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) NIL) (($ $ (|Integer|)) NIL)) (|delete| (($ $ (|Integer|)) NIL) (($ $ (|UniversalSegment| (|Integer|))) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copyInto!| (($ $ $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) NIL)) (|concat!| (($ $ $) NIL) (($ $ |#1|) NIL)) (|concat| (($ $ |#1|) NIL) (($ |#1| $) NIL) (($ $ $) NIL) (($ (|List| $)) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|FlexibleArray| |#1|) (|Join| (|OneDimensionalArrayAggregate| |#1|) (|ExtensibleLinearAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |flexibleArray| ($ (|List| |#1|))) (SIGNATURE |physicalLength| ((|NonNegativeInteger|) $)) (SIGNATURE |physicalLength!| ($ $ (|Integer|))) (SIGNATURE |shrinkable| ((|Boolean|) (|Boolean|))))) (|Type|)) (T |FlexibleArray|)) 
((|flexibleArray| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|FlexibleArray| *3)))) (|physicalLength| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FlexibleArray| *3)) (|ofCategory| *3 (|Type|)))) (|physicalLength!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|FlexibleArray| *3)) (|ofCategory| *3 (|Type|)))) (|shrinkable| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FlexibleArray| *3)) (|ofCategory| *3 (|Type|))))) 
(|Join| (|OneDimensionalArrayAggregate| |#1|) (|ExtensibleLinearAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |flexibleArray| ($ (|List| |#1|))) (SIGNATURE |physicalLength| ((|NonNegativeInteger|) $)) (SIGNATURE |physicalLength!| ($ $ (|Integer|))) (SIGNATURE |shrinkable| ((|Boolean|) (|Boolean|))))) 
((|transcendent?| (((|Boolean|) $) 37)) (|transcendenceDegree| (((|NonNegativeInteger|)) 22)) (|trace| ((|#2| $) 41) (($ $ (|PositiveInteger|)) 99)) (|size| (((|NonNegativeInteger|)) 93)) (|represents| (($ (|Vector| |#2|)) 20)) (|normal?| (((|Boolean|) $) 111)) (|norm| ((|#2| $) 43) (($ $ (|PositiveInteger|)) 97)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) NIL) (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) 88)) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) 78)) (|linearAssociatedLog| (((|SparseUnivariatePolynomial| |#2|) $) 75) (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) 72)) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) 48)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) 91) (((|PositiveInteger|)) 38)) (|dimension| (((|CardinalNumber|)) 25)) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL) (((|PositiveInteger|) $) 112)) (|createNormalElement| (($) 105)) (|coordinates| (((|Vector| |#2|) $) NIL) (((|Matrix| |#2|) (|Vector| $)) 34)) (|charthRoot| (($ $) NIL) (((|Union| $ "failed") $) 81)) (|algebraic?| (((|Boolean|) $) 36))) 
(((|FiniteAlgebraicExtensionField&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |charthRoot| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |size| ((|NonNegativeInteger|))) (SIGNATURE |charthRoot| (|#1| |#1|)) (SIGNATURE |linearAssociatedLog| ((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") |#1| |#1|)) (SIGNATURE |linearAssociatedLog| ((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |linearAssociatedOrder| ((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |linearAssociatedExp| (|#1| |#1| (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |normal?| ((|Boolean|) |#1|)) (SIGNATURE |createNormalElement| (|#1|)) (SIGNATURE |trace| (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |norm| (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |minimalPolynomial| ((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|))) (SIGNATURE |trace| (|#2| |#1|)) (SIGNATURE |norm| (|#2| |#1|)) (SIGNATURE |degree| ((|PositiveInteger|) |#1|)) (SIGNATURE |extensionDegree| ((|PositiveInteger|))) (SIGNATURE |minimalPolynomial| ((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |represents| (|#1| (|Vector| |#2|))) (SIGNATURE |coordinates| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#2|) |#1|)) (SIGNATURE |transcendenceDegree| ((|NonNegativeInteger|))) (SIGNATURE |extensionDegree| ((|OnePointCompletion| (|PositiveInteger|)))) (SIGNATURE |degree| ((|OnePointCompletion| (|PositiveInteger|)) |#1|)) (SIGNATURE |transcendent?| ((|Boolean|) |#1|)) (SIGNATURE |algebraic?| ((|Boolean|) |#1|)) (SIGNATURE |dimension| ((|CardinalNumber|)))) (|FiniteAlgebraicExtensionField| |#2|) (|Field|)) (T |FiniteAlgebraicExtensionField&|)) 
((|dimension| (*1 *2) (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|CardinalNumber|)) (|isDomain| *1 (|FiniteAlgebraicExtensionField&| *3 *4)) (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))) (|extensionDegree| (*1 *2) (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|OnePointCompletion| (|PositiveInteger|))) (|isDomain| *1 (|FiniteAlgebraicExtensionField&| *3 *4)) (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))) (|transcendenceDegree| (*1 *2) (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FiniteAlgebraicExtensionField&| *3 *4)) (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))) (|extensionDegree| (*1 *2) (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|FiniteAlgebraicExtensionField&| *3 *4)) (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))) (|size| (*1 *2) (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FiniteAlgebraicExtensionField&| *3 *4)) (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4))))) 
(CATEGORY |domain| (SIGNATURE |charthRoot| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |size| ((|NonNegativeInteger|))) (SIGNATURE |charthRoot| (|#1| |#1|)) (SIGNATURE |linearAssociatedLog| ((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") |#1| |#1|)) (SIGNATURE |linearAssociatedLog| ((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |linearAssociatedOrder| ((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |linearAssociatedExp| (|#1| |#1| (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |normal?| ((|Boolean|) |#1|)) (SIGNATURE |createNormalElement| (|#1|)) (SIGNATURE |trace| (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |norm| (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |minimalPolynomial| ((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|))) (SIGNATURE |trace| (|#2| |#1|)) (SIGNATURE |norm| (|#2| |#1|)) (SIGNATURE |degree| ((|PositiveInteger|) |#1|)) (SIGNATURE |extensionDegree| ((|PositiveInteger|))) (SIGNATURE |minimalPolynomial| ((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |represents| (|#1| (|Vector| |#2|))) (SIGNATURE |coordinates| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#2|) |#1|)) (SIGNATURE |transcendenceDegree| ((|NonNegativeInteger|))) (SIGNATURE |extensionDegree| ((|OnePointCompletion| (|PositiveInteger|)))) (SIGNATURE |degree| ((|OnePointCompletion| (|PositiveInteger|)) |#1|)) (SIGNATURE |transcendent?| ((|Boolean|) |#1|)) (SIGNATURE |algebraic?| ((|Boolean|) |#1|)) (SIGNATURE |dimension| ((|CardinalNumber|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|transcendent?| (((|Boolean|) $) 92)) (|transcendenceDegree| (((|NonNegativeInteger|)) 88)) (|trace| ((|#1| $) 136) (($ $ (|PositiveInteger|)) 133 (|has| |#1| (|Finite|)))) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) 118 (|has| |#1| (|Finite|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 73)) (|squareFree| (((|Factored| $) $) 72)) (|sizeLess?| (((|Boolean|) $ $) 58)) (|size| (((|NonNegativeInteger|)) 108 (|has| |#1| (|Finite|)))) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 99)) (|retract| ((|#1| $) 98)) (|represents| (($ (|Vector| |#1|)) 142)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 124 (|has| |#1| (|Finite|)))) (|rem| (($ $ $) 54)) (|recip| (((|Union| $ "failed") $) 33)) (|random| (($) 105 (|has| |#1| (|Finite|)))) (|quo| (($ $ $) 55)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 50)) (|primitiveElement| (($) 120 (|has| |#1| (|Finite|)))) (|primitive?| (((|Boolean|) $) 121 (|has| |#1| (|Finite|)))) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) 85 (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|)))) (($ $) 84 (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|prime?| (((|Boolean|) $) 71)) (|order| (((|PositiveInteger|) $) 123 (|has| |#1| (|Finite|))) (((|OnePointCompletion| (|PositiveInteger|)) $) 82 (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|one?| (((|Boolean|) $) 30)) (|normalElement| (($) 131 (|has| |#1| (|Finite|)))) (|normal?| (((|Boolean|) $) 130 (|has| |#1| (|Finite|)))) (|norm| ((|#1| $) 137) (($ $ (|PositiveInteger|)) 134 (|has| |#1| (|Finite|)))) (|nextItem| (((|Union| $ "failed") $) 109 (|has| |#1| (|Finite|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 51)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 141) (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) 135 (|has| |#1| (|Finite|)))) (|lookup| (((|PositiveInteger|) $) 106 (|has| |#1| (|Finite|)))) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) 127 (|has| |#1| (|Finite|)))) (|linearAssociatedLog| (((|SparseUnivariatePolynomial| |#1|) $) 126 (|has| |#1| (|Finite|))) (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) 125 (|has| |#1| (|Finite|)))) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) 128 (|has| |#1| (|Finite|)))) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 70)) (|init| (($) 110 (|has| |#1| (|Finite|)) CONST)) (|index| (($ (|PositiveInteger|)) 107 (|has| |#1| (|Finite|)))) (|inGroundField?| 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(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE |forLoop| ($ (|SegmentBinding| (|Polynomial| (|Integer|))) $)) (SIGNATURE |forLoop| ($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $)) (SIGNATURE |whileLoop| ($ (|Switch|) $)) (SIGNATURE |repeatUntilLoop| ($ (|Switch|) $)) (SIGNATURE |goto| ($ (|SingleInteger|))) (SIGNATURE |continue| ($ (|SingleInteger|))) (SIGNATURE |comment| ($ (|String|))) (SIGNATURE |comment| ($ (|List| (|String|)))) (SIGNATURE |call| ($ (|String|))) (SIGNATURE |returns| ($)) (SIGNATURE |returns| ($ (|Expression| (|MachineFloat|)))) (SIGNATURE |returns| ($ (|Expression| (|MachineInteger|)))) (SIGNATURE |returns| ($ (|Expression| (|MachineComplex|)))) (SIGNATURE |returns| ($ (|Expression| (|Float|)))) (SIGNATURE |returns| ($ (|Expression| (|Integer|)))) (SIGNATURE |returns| ($ (|Expression| (|Complex| (|Float|))))) (SIGNATURE |cond| ($ (|Switch|) $)) (SIGNATURE |cond| ($ (|Switch|) $ $)) (SIGNATURE |assign| ($ (|Symbol|) (|String|))) (SIGNATURE |assign| ($ (|Symbol|) (|Expression| (|MachineInteger|)))) (SIGNATURE |assign| ($ (|Symbol|) (|Expression| (|MachineFloat|)))) (SIGNATURE |assign| ($ (|Symbol|) (|Expression| (|MachineComplex|)))) (SIGNATURE |assign| ($ (|Symbol|) (|Matrix| (|MachineInteger|)))) (SIGNATURE |assign| ($ (|Symbol|) (|Matrix| (|MachineFloat|)))) (SIGNATURE |assign| ($ (|Symbol|) (|Matrix| (|MachineComplex|)))) (SIGNATURE |assign| ($ (|Symbol|) (|Vector| (|MachineInteger|)))) (SIGNATURE |assign| ($ (|Symbol|) (|Vector| (|MachineFloat|)))) (SIGNATURE |assign| ($ (|Symbol|) (|Vector| (|MachineComplex|)))) (SIGNATURE |assign| ($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|))))) (SIGNATURE |assign| ($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|))))) (SIGNATURE |assign| ($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|))))) (SIGNATURE |assign| ($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|))))) (SIGNATURE |assign| ($ 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|Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $)) (SIGNATURE |code| ((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $)) (SIGNATURE |printCode| ((|Void|) $)) (SIGNATURE |getCode| ((|SExpression|) $)) (SIGNATURE |setLabelValue| ((|SingleInteger|) (|SingleInteger|))))) 
((~= (((|Boolean|) $ $) NIL)) (|sin?| (((|Boolean|) $) 11)) (|sin| (($ |#1|) 8)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|cos| (($ |#1|) 9)) (|coerce| (((|OutputForm|) $) 17)) (|argument| ((|#1| $) 12)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 19))) 
(((|FourierComponent| |#1|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |sin| ($ |#1|)) (SIGNATURE |cos| ($ |#1|)) (SIGNATURE |sin?| ((|Boolean|) $)) (SIGNATURE |argument| (|#1| $)))) (|OrderedSet|)) (T |FourierComponent|)) 
((|sin| (*1 *1 *2) (AND (|isDomain| *1 (|FourierComponent| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|cos| (*1 *1 *2) (AND (|isDomain| *1 (|FourierComponent| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|sin?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FourierComponent| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|argument| (*1 *2 *1) (AND (|isDomain| *1 (|FourierComponent| *2)) (|ofCategory| *2 (|OrderedSet|))))) 
(|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |sin| ($ |#1|)) (SIGNATURE |cos| ($ |#1|)) (SIGNATURE |sin?| ((|Boolean|) $)) (SIGNATURE |argument| (|#1| $)))) 
((|zeroVector| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) 22)) (|zeroSquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) 26)) (|zeroMatrix| (((|FortranCode|) (|Symbol|) (|SegmentBinding| (|Polynomial| (|Integer|))) (|SegmentBinding| (|Polynomial| (|Integer|)))) 25) (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|)) (|Polynomial| (|Integer|))) 23)) (|identitySquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) 30))) 
(((|FortranCodePackage1|) (CATEGORY |package| (SIGNATURE |zeroVector| ((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|)))) (SIGNATURE |zeroMatrix| ((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|)) (|Polynomial| (|Integer|)))) (SIGNATURE |zeroMatrix| ((|FortranCode|) (|Symbol|) (|SegmentBinding| (|Polynomial| (|Integer|))) (|SegmentBinding| (|Polynomial| (|Integer|))))) (SIGNATURE |zeroSquareMatrix| ((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|)))) (SIGNATURE |identitySquareMatrix| ((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|)))))) (T |FortranCodePackage1|)) 
((|identitySquareMatrix| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|Polynomial| (|Integer|))) (|isDomain| *2 (|FortranCode|)) (|isDomain| *1 (|FortranCodePackage1|)))) (|zeroSquareMatrix| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|Polynomial| (|Integer|))) (|isDomain| *2 (|FortranCode|)) (|isDomain| *1 (|FortranCodePackage1|)))) (|zeroMatrix| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|SegmentBinding| (|Polynomial| (|Integer|)))) (|isDomain| *2 (|FortranCode|)) (|isDomain| *1 (|FortranCodePackage1|)))) (|zeroMatrix| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|Polynomial| (|Integer|))) (|isDomain| *2 (|FortranCode|)) (|isDomain| *1 (|FortranCodePackage1|)))) (|zeroVector| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|Polynomial| (|Integer|))) (|isDomain| *2 (|FortranCode|)) (|isDomain| *1 (|FortranCodePackage1|))))) 
(CATEGORY |package| (SIGNATURE |zeroVector| ((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|)))) (SIGNATURE |zeroMatrix| ((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|)) (|Polynomial| (|Integer|)))) (SIGNATURE |zeroMatrix| ((|FortranCode|) (|Symbol|) (|SegmentBinding| (|Polynomial| (|Integer|))) (|SegmentBinding| (|Polynomial| (|Integer|))))) (SIGNATURE |zeroSquareMatrix| ((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|)))) (SIGNATURE |identitySquareMatrix| ((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))))) 
((|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) 31))) 
(((|FiniteDivisorFunctions2| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (CATEGORY |package| (SIGNATURE |map| ((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)))) (|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|) (|Field|) (|UnivariatePolynomialCategory| |#5|) (|UnivariatePolynomialCategory| (|Fraction| |#6|)) (|FunctionFieldCategory| |#5| |#6| |#7|)) (T |FiniteDivisorFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *9 *5)) (|isDomain| *4 (|FiniteDivisor| *5 *6 *7 *8)) (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|ofCategory| *8 (|FunctionFieldCategory| *5 *6 *7)) (|ofCategory| *9 (|Field|)) (|ofCategory| *10 (|UnivariatePolynomialCategory| *9)) (|ofCategory| *11 (|UnivariatePolynomialCategory| (|Fraction| *10))) (|isDomain| *2 (|FiniteDivisor| *9 *10 *11 *12)) (|isDomain| *1 (|FiniteDivisorFunctions2| *5 *6 *7 *8 *9 *10 *11 *12)) (|ofCategory| *12 (|FunctionFieldCategory| *9 *10 *11))))) 
(CATEGORY |package| (SIGNATURE |map| ((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)))) 
((|principal?| (((|Boolean|) $) 14))) 
(((|FiniteDivisorCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |domain| (SIGNATURE |principal?| ((|Boolean|) |#1|))) (|FiniteDivisorCategory| |#2| |#3| |#4| |#5|) (|Field|) (|UnivariatePolynomialCategory| |#2|) (|UnivariatePolynomialCategory| (|Fraction| |#3|)) (|FunctionFieldCategory| |#2| |#3| |#4|)) (T |FiniteDivisorCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |principal?| ((|Boolean|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|reduce| (($ $) 25)) (|principal?| (((|Boolean|) $) 24)) (|latex| (((|String|) $) 9)) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) 31)) (|hash| (((|SingleInteger|) $) 10)) (|generator| (((|Union| |#4| "failed") $) 23)) (|divisor| (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) 30) (($ |#4|) 29) (($ |#1| |#1|) 28) (($ |#1| |#1| (|Integer|)) 27) (($ |#4| |#2| |#2| |#2| |#1|) 22)) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) 26)) (|coerce| (((|OutputForm|) $) 11)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19))) 
(((|FiniteDivisorCategory| |#1| |#2| |#3| |#4|) (|Category|) (|Field|) (|UnivariatePolynomialCategory| |t#1|) (|UnivariatePolynomialCategory| (|Fraction| |t#2|)) (|FunctionFieldCategory| |t#1| |t#2| |t#3|)) (T |FiniteDivisorCategory|)) 
((|ideal| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5)) (|isDomain| *2 (|FractionalIdeal| *4 (|Fraction| *4) *5 *6)))) (|divisor| (*1 *1 *2) (AND (|isDomain| *2 (|FractionalIdeal| *4 (|Fraction| *4) *5 *6)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *6)))) (|divisor| (*1 *1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *2)) (|ofCategory| *2 (|FunctionFieldCategory| *3 *4 *5)))) (|divisor| (*1 *1 *2 *2) (AND (|ofCategory| *2 (|Field|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|ofCategory| *1 (|FiniteDivisorCategory| *2 *3 *4 *5)) (|ofCategory| *5 (|FunctionFieldCategory| *2 *3 *4)))) (|divisor| (*1 *1 *2 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *1 (|FiniteDivisorCategory| *2 *4 *5 *6)) (|ofCategory| *6 (|FunctionFieldCategory| *2 *4 *5)))) (|decompose| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5)) (|isDomain| *2 (|Record| (|:| |id| (|FractionalIdeal| *4 (|Fraction| *4) *5 *6)) (|:| |principalPart| *6))))) (|reduce| (*1 *1 *1) (AND (|ofCategory| *1 (|FiniteDivisorCategory| *2 *3 *4 *5)) (|ofCategory| *2 (|Field|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|ofCategory| *5 (|FunctionFieldCategory| *2 *3 *4)))) (|principal?| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5)) (|isDomain| *2 (|Boolean|)))) (|generator| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *2 (|FunctionFieldCategory| *3 *4 *5)))) (|divisor| (*1 *1 *2 *3 *3 *3 *4) (AND (|ofCategory| *4 (|Field|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|ofCategory| *1 (|FiniteDivisorCategory| *4 *3 *5 *2)) (|ofCategory| *2 (|FunctionFieldCategory| *4 *3 *5))))) 
(|Join| (|AbelianGroup|) (CATEGORY |domain| (SIGNATURE |ideal| ((|FractionalIdeal| |t#2| (|Fraction| |t#2|) |t#3| |t#4|) $)) (SIGNATURE |divisor| ($ (|FractionalIdeal| |t#2| (|Fraction| |t#2|) |t#3| |t#4|))) (SIGNATURE |divisor| ($ |t#4|)) (SIGNATURE |divisor| ($ |t#1| |t#1|)) (SIGNATURE |divisor| ($ |t#1| |t#1| (|Integer|))) (SIGNATURE |decompose| ((|Record| (|:| |id| (|FractionalIdeal| |t#2| (|Fraction| |t#2|) |t#3| |t#4|)) (|:| |principalPart| |t#4|)) $)) (SIGNATURE |reduce| ($ $)) (SIGNATURE |principal?| ((|Boolean|) $)) (SIGNATURE |generator| ((|Union| |t#4| "failed") $)) (SIGNATURE |divisor| ($ |t#4| |t#2| |t#2| |t#2| |t#1|)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|reduce| (($ $) 32)) (|principal?| (((|Boolean|) $) NIL)) (|latex| (((|String|) $) NIL)) (|lSpaceBasis| (((|Vector| |#4|) $) 124)) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) 30)) (|hash| (((|SingleInteger|) $) NIL)) (|generator| (((|Union| |#4| "failed") $) 35)) (|finiteBasis| (((|Vector| |#4|) $) 117)) (|divisor| (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) 40) (($ |#4|) 42) (($ |#1| |#1|) 44) (($ |#1| |#1| (|Integer|)) 46) (($ |#4| |#2| |#2| |#2| |#1|) 48)) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) 38)) (|coerce| (((|OutputForm|) $) 17)) (|Zero| (($) 14 T CONST)) (= (((|Boolean|) $ $) 20)) (- (($ $) 27) (($ $ $) NIL)) (+ (($ $ $) 25)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 23))) 
(((|FiniteDivisor| |#1| |#2| |#3| |#4|) (|Join| (|FiniteDivisorCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |finiteBasis| ((|Vector| |#4|) $)) (SIGNATURE |lSpaceBasis| ((|Vector| |#4|) $)))) (|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|)) (T |FiniteDivisor|)) 
((|finiteBasis| (*1 *2 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Vector| *6)) (|isDomain| *1 (|FiniteDivisor| *3 *4 *5 *6)) (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5)))) (|lSpaceBasis| (*1 *2 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Vector| *6)) (|isDomain| *1 (|FiniteDivisor| *3 *4 *5 *6)) (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5))))) 
(|Join| (|FiniteDivisorCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |finiteBasis| ((|Vector| |#4|) $)) (SIGNATURE |lSpaceBasis| ((|Vector| |#4|) $)))) 
((|eval| (($ $ (|Symbol|) |#2|) NIL) (($ $ (|List| (|Symbol|)) (|List| |#2|)) 18) (($ $ (|List| (|Equation| |#2|))) 14) (($ $ (|Equation| |#2|)) NIL) (($ $ |#2| |#2|) NIL) (($ $ (|List| |#2|) (|List| |#2|)) NIL)) (|elt| (($ $ |#2|) 11))) 
(((|FullyEvalableOver&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |elt| (|#1| |#1| |#2|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#2|) (|List| |#2|))) (SIGNATURE |eval| (|#1| |#1| |#2| |#2|)) (SIGNATURE |eval| (|#1| |#1| (|Equation| |#2|))) (SIGNATURE |eval| (|#1| |#1| (|List| (|Equation| |#2|)))) (SIGNATURE |eval| (|#1| |#1| (|List| (|Symbol|)) (|List| |#2|))) (SIGNATURE |eval| (|#1| |#1| (|Symbol|) |#2|))) (|FullyEvalableOver| |#2|) (|SetCategory|)) (T |FullyEvalableOver&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |elt| (|#1| |#1| |#2|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#2|) (|List| |#2|))) (SIGNATURE |eval| (|#1| |#1| |#2| |#2|)) (SIGNATURE |eval| (|#1| |#1| (|Equation| |#2|))) (SIGNATURE |eval| (|#1| |#1| (|List| (|Equation| |#2|)))) (SIGNATURE |eval| (|#1| |#1| (|List| (|Symbol|)) (|List| |#2|))) (SIGNATURE |eval| (|#1| |#1| (|Symbol|) |#2|))) 
((|map| (($ (|Mapping| |#1| |#1|) $) 6)) (|eval| (($ $ (|Symbol|) |#1|) 16 (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|))) (($ $ (|List| (|Symbol|)) (|List| |#1|)) 15 (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|))) (($ $ (|List| (|Equation| |#1|))) 14 (|has| |#1| (|Evalable| |#1|))) (($ $ (|Equation| |#1|)) 13 (|has| |#1| (|Evalable| |#1|))) (($ $ |#1| |#1|) 12 (|has| |#1| (|Evalable| |#1|))) (($ $ (|List| |#1|) (|List| |#1|)) 11 (|has| |#1| (|Evalable| |#1|)))) (|elt| (($ $ |#1|) 10 (|has| |#1| (|Eltable| |#1| |#1|))))) 
(((|FullyEvalableOver| |#1|) (|Category|) (|SetCategory|)) (T |FullyEvalableOver|)) 
((|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|FullyEvalableOver| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(|Join| (CATEGORY |domain| (SIGNATURE |map| ($ (|Mapping| |t#1| |t#1|) $)) (IF (|has| |t#1| (|Eltable| |t#1| |t#1|)) (ATTRIBUTE (|Eltable| |t#1| $)) |noBranch|) (IF (|has| |t#1| (|Evalable| |t#1|)) (ATTRIBUTE (|Evalable| |t#1|)) |noBranch|) (IF (|has| |t#1| (|InnerEvalable| (|Symbol|) |t#1|)) (ATTRIBUTE (|InnerEvalable| (|Symbol|) |t#1|)) |noBranch|))) 
(((|Eltable| |#1| $) |has| |#1| (|Eltable| |#1| |#1|)) ((|Evalable| |#1|) |has| |#1| (|Evalable| |#1|)) ((|InnerEvalable| (|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|variables| (((|List| (|Symbol|)) $) NIL)) (|useNagFunctions| (((|Boolean|)) 87) (((|Boolean|) (|Boolean|)) 88)) (|tower| (((|List| (|Kernel| $)) $) NIL)) (|tanh| (($ $) NIL)) (|tan| (($ $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|subst| (($ $ (|Equation| $)) NIL) (($ $ (|List| (|Equation| $))) NIL) (($ $ (|List| (|Kernel| $)) (|List| $)) NIL)) (|sqrt| (($ $) NIL)) (|sinh| (($ $) NIL)) (|sin| (($ $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Kernel| $) "failed") $) NIL) (((|Union| |#3| "failed") $) NIL) (((|Union| $ "failed") (|Expression| |#3|)) 69) (((|Union| $ "failed") (|Symbol|)) 93) (((|Union| $ "failed") (|Expression| (|Integer|))) 56 (|has| |#3| (|RetractableTo| (|Integer|)))) (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) 62 (|has| |#3| (|RetractableTo| (|Integer|)))) (((|Union| $ "failed") (|Polynomial| (|Integer|))) 57 (|has| |#3| (|RetractableTo| (|Integer|)))) (((|Union| $ "failed") (|Expression| (|Float|))) 74 (|has| |#3| (|RetractableTo| (|Float|)))) (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) 80 (|has| |#3| (|RetractableTo| (|Float|)))) (((|Union| $ "failed") (|Polynomial| (|Float|))) 75 (|has| |#3| (|RetractableTo| (|Float|))))) (|retract| (((|Kernel| $) $) NIL) ((|#3| $) NIL) (($ (|Expression| |#3|)) 70) (($ (|Symbol|)) 94) (($ (|Expression| (|Integer|))) 58 (|has| |#3| (|RetractableTo| (|Integer|)))) (($ (|Fraction| (|Polynomial| (|Integer|)))) 63 (|has| |#3| (|RetractableTo| (|Integer|)))) (($ (|Polynomial| (|Integer|))) 59 (|has| |#3| (|RetractableTo| (|Integer|)))) (($ (|Expression| (|Float|))) 76 (|has| |#3| (|RetractableTo| (|Float|)))) (($ (|Fraction| (|Polynomial| (|Float|)))) 81 (|has| |#3| (|RetractableTo| (|Float|)))) (($ (|Polynomial| (|Float|))) 77 (|has| |#3| (|RetractableTo| (|Float|))))) (|recip| (((|Union| $ "failed") $) NIL)) (|pi| (($) 10)) (|paren| (($ $) NIL) (($ (|List| $)) NIL)) (|operators| (((|List| (|BasicOperator|)) $) NIL)) (|operator| (((|BasicOperator|) (|BasicOperator|)) NIL)) (|one?| (((|Boolean|) $) NIL)) (|odd?| (((|Boolean|) $) NIL (|has| $ (|RetractableTo| (|Integer|))))) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) NIL (|has| $ (|Ring|)))) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|map| (($ (|Mapping| $ $) (|Kernel| $)) NIL)) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) NIL)) (|log10| (($ $) 90)) (|log| (($ $) NIL)) (|latex| (((|String|) $) NIL)) (|kernels| (((|List| (|Kernel| $)) $) NIL)) (|kernel| (($ (|BasicOperator|) $) 89) (($ (|BasicOperator|) (|List| $)) NIL)) (|is?| (((|Boolean|) $ (|BasicOperator|)) NIL) (((|Boolean|) $ (|Symbol|)) NIL)) (|height| (((|NonNegativeInteger|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|freeOf?| (((|Boolean|) $ $) NIL) (((|Boolean|) $ (|Symbol|)) NIL)) (|exp| (($ $) NIL)) (|even?| (((|Boolean|) $) NIL (|has| $ (|RetractableTo| (|Integer|))))) (|eval| (($ $ (|Kernel| $) $) NIL) (($ $ (|List| (|Kernel| $)) (|List| $)) NIL) (($ $ (|List| (|Equation| $))) NIL) (($ $ (|Equation| $)) NIL) (($ $ $ $) NIL) (($ $ (|List| $) (|List| $)) NIL) (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) NIL) (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) NIL) (($ $ (|Symbol|) (|Mapping| $ (|List| $))) NIL) (($ $ (|Symbol|) (|Mapping| $ $)) NIL) (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) NIL) (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) NIL) (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) NIL) (($ $ (|BasicOperator|) (|Mapping| $ $)) NIL)) (|elt| (($ (|BasicOperator|) $) NIL) (($ (|BasicOperator|) $ $) NIL) (($ (|BasicOperator|) $ $ $) NIL) (($ (|BasicOperator|) $ $ $ $) NIL) (($ (|BasicOperator|) (|List| $)) NIL)) (|distribute| (($ $) NIL) (($ $ $) NIL)) (|differentiate| (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|))) NIL) (($ $ (|Symbol|)) NIL)) (|definingPolynomial| (($ $) NIL (|has| $ (|Ring|)))) (|cosh| (($ $) NIL)) (|cos| (($ $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Kernel| $)) NIL) (($ |#3|) NIL) (($ (|Integer|)) NIL) (((|Expression| |#3|) $) 92)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|box| (($ $) NIL) (($ (|List| $)) NIL)) (|belong?| (((|Boolean|) (|BasicOperator|)) NIL)) (|atan| (($ $) NIL)) (|asin| (($ $) NIL)) (|acos| (($ $) NIL)) (|abs| (($ $) NIL)) (^ (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|PositiveInteger|)) NIL)) (|Zero| (($) 91 T CONST)) (|One| (($) 22 T CONST)) (D (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|))) NIL) (($ $ (|Symbol|)) NIL)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) NIL)) (- (($ $ $) NIL) (($ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|PositiveInteger|)) NIL)) (* (($ |#3| $) NIL) (($ $ |#3|) NIL) (($ $ $) NIL) (($ (|Integer|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|PositiveInteger|) $) NIL))) 
(((|FortranExpression| |#1| |#2| |#3|) (|Join| (|ExpressionSpace|) (|Algebra| |#3|) (|RetractableTo| |#3|) (|PartialDifferentialRing| (|Symbol|)) (CATEGORY |domain| (SIGNATURE |retract| ($ (|Expression| |#3|))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Expression| |#3|))) (SIGNATURE |retract| ($ (|Symbol|))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Symbol|))) (SIGNATURE |coerce| ((|Expression| |#3|) $)) (IF (|has| |#3| (|RetractableTo| (|Integer|))) (PROGN (SIGNATURE |retract| ($ (|Expression| (|Integer|)))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Expression| (|Integer|)))) (SIGNATURE |retract| ($ (|Fraction| (|Polynomial| (|Integer|))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|))))) (SIGNATURE |retract| ($ (|Polynomial| (|Integer|)))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| (|Integer|))))) |noBranch|) (IF (|has| |#3| (|RetractableTo| (|Float|))) (PROGN (SIGNATURE |retract| ($ (|Expression| (|Float|)))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Expression| (|Float|)))) (SIGNATURE |retract| ($ (|Fraction| (|Polynomial| (|Float|))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|))))) (SIGNATURE |retract| ($ (|Polynomial| (|Float|)))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| (|Float|))))) |noBranch|) (SIGNATURE |abs| ($ $)) (SIGNATURE |sqrt| ($ $)) (SIGNATURE |exp| ($ $)) (SIGNATURE |log| ($ $)) (SIGNATURE |log10| ($ $)) (SIGNATURE |sin| ($ $)) (SIGNATURE |cos| ($ $)) (SIGNATURE |tan| ($ $)) (SIGNATURE |asin| ($ $)) (SIGNATURE |acos| ($ $)) (SIGNATURE |atan| ($ $)) (SIGNATURE |sinh| ($ $)) (SIGNATURE |cosh| ($ $)) (SIGNATURE |tanh| ($ $)) (SIGNATURE |pi| ($)) (SIGNATURE |variables| ((|List| (|Symbol|)) $)) (SIGNATURE |useNagFunctions| ((|Boolean|))) (SIGNATURE |useNagFunctions| ((|Boolean|) (|Boolean|))))) (|List| (|Symbol|)) (|List| (|Symbol|)) (|FortranMachineTypeCategory|)) (T |FortranExpression|)) 
((|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Expression| *5)) (|ofCategory| *5 (|FortranMachineTypeCategory|)) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|Symbol|))))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Expression| *5)) (|ofCategory| *5 (|FortranMachineTypeCategory|)) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|Symbol|))))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofType| *3 (|List| *2)) (|ofType| *4 (|List| *2)) (|ofCategory| *5 (|FortranMachineTypeCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofType| *3 (|List| *2)) (|ofType| *4 (|List| *2)) (|ofCategory| *5 (|FortranMachineTypeCategory|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Expression| *5)) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|FortranMachineTypeCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Expression| (|Integer|))) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofCategory| *5 (|RetractableTo| (|Integer|))) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|FortranMachineTypeCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Expression| (|Integer|))) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofCategory| *5 (|RetractableTo| (|Integer|))) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|FortranMachineTypeCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Polynomial| (|Integer|)))) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofCategory| *5 (|RetractableTo| (|Integer|))) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|FortranMachineTypeCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Fraction| (|Polynomial| (|Integer|)))) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofCategory| *5 (|RetractableTo| (|Integer|))) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|FortranMachineTypeCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| (|Integer|))) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofCategory| *5 (|RetractableTo| (|Integer|))) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|FortranMachineTypeCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Polynomial| (|Integer|))) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofCategory| *5 (|RetractableTo| (|Integer|))) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|FortranMachineTypeCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Expression| (|Float|))) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofCategory| *5 (|RetractableTo| (|Float|))) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|FortranMachineTypeCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Expression| (|Float|))) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofCategory| *5 (|RetractableTo| (|Float|))) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|FortranMachineTypeCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Polynomial| (|Float|)))) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofCategory| *5 (|RetractableTo| (|Float|))) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|FortranMachineTypeCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Fraction| (|Polynomial| (|Float|)))) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofCategory| *5 (|RetractableTo| (|Float|))) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|FortranMachineTypeCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| (|Float|))) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofCategory| *5 (|RetractableTo| (|Float|))) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|FortranMachineTypeCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Polynomial| (|Float|))) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofCategory| *5 (|RetractableTo| (|Float|))) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|FortranMachineTypeCategory|)))) (|abs| (*1 *1 *1) (AND (|isDomain| *1 (|FortranExpression| *2 *3 *4)) (|ofType| *2 (|List| (|Symbol|))) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|FortranMachineTypeCategory|)))) (|sqrt| (*1 *1 *1) (AND (|isDomain| *1 (|FortranExpression| *2 *3 *4)) (|ofType| *2 (|List| (|Symbol|))) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|FortranMachineTypeCategory|)))) (|exp| (*1 *1 *1) (AND (|isDomain| *1 (|FortranExpression| *2 *3 *4)) (|ofType| *2 (|List| (|Symbol|))) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|FortranMachineTypeCategory|)))) (|log| (*1 *1 *1) (AND (|isDomain| *1 (|FortranExpression| *2 *3 *4)) (|ofType| *2 (|List| (|Symbol|))) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|FortranMachineTypeCategory|)))) (|log10| (*1 *1 *1) (AND (|isDomain| *1 (|FortranExpression| *2 *3 *4)) (|ofType| *2 (|List| (|Symbol|))) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|FortranMachineTypeCategory|)))) (|sin| (*1 *1 *1) (AND (|isDomain| *1 (|FortranExpression| *2 *3 *4)) (|ofType| *2 (|List| (|Symbol|))) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|FortranMachineTypeCategory|)))) (|cos| (*1 *1 *1) (AND (|isDomain| *1 (|FortranExpression| *2 *3 *4)) (|ofType| *2 (|List| (|Symbol|))) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|FortranMachineTypeCategory|)))) (|tan| (*1 *1 *1) (AND (|isDomain| *1 (|FortranExpression| *2 *3 *4)) (|ofType| *2 (|List| (|Symbol|))) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|FortranMachineTypeCategory|)))) (|asin| (*1 *1 *1) (AND (|isDomain| *1 (|FortranExpression| *2 *3 *4)) (|ofType| *2 (|List| (|Symbol|))) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|FortranMachineTypeCategory|)))) (|acos| (*1 *1 *1) (AND (|isDomain| *1 (|FortranExpression| *2 *3 *4)) (|ofType| *2 (|List| (|Symbol|))) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|FortranMachineTypeCategory|)))) (|atan| (*1 *1 *1) (AND (|isDomain| *1 (|FortranExpression| *2 *3 *4)) (|ofType| *2 (|List| (|Symbol|))) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|FortranMachineTypeCategory|)))) (|sinh| (*1 *1 *1) (AND (|isDomain| *1 (|FortranExpression| *2 *3 *4)) (|ofType| *2 (|List| (|Symbol|))) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|FortranMachineTypeCategory|)))) (|cosh| (*1 *1 *1) (AND (|isDomain| *1 (|FortranExpression| *2 *3 *4)) (|ofType| *2 (|List| (|Symbol|))) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|FortranMachineTypeCategory|)))) (|tanh| (*1 *1 *1) (AND (|isDomain| *1 (|FortranExpression| *2 *3 *4)) (|ofType| *2 (|List| (|Symbol|))) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|FortranMachineTypeCategory|)))) (|pi| (*1 *1) (AND (|isDomain| *1 (|FortranExpression| *2 *3 *4)) (|ofType| *2 (|List| (|Symbol|))) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|FortranMachineTypeCategory|)))) (|variables| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofType| *3 *2) (|ofType| *4 *2) (|ofCategory| *5 (|FortranMachineTypeCategory|)))) (|useNagFunctions| (*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|FortranMachineTypeCategory|)))) (|useNagFunctions| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranExpression| *3 *4 *5)) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|FortranMachineTypeCategory|))))) 
(|Join| (|ExpressionSpace|) (|Algebra| |#3|) (|RetractableTo| |#3|) (|PartialDifferentialRing| (|Symbol|)) (CATEGORY |domain| (SIGNATURE |retract| ($ (|Expression| |#3|))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Expression| |#3|))) (SIGNATURE |retract| ($ (|Symbol|))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Symbol|))) (SIGNATURE |coerce| ((|Expression| |#3|) $)) (IF (|has| |#3| (|RetractableTo| (|Integer|))) (PROGN (SIGNATURE |retract| ($ (|Expression| (|Integer|)))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Expression| (|Integer|)))) (SIGNATURE |retract| ($ (|Fraction| (|Polynomial| (|Integer|))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|))))) (SIGNATURE |retract| ($ (|Polynomial| (|Integer|)))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| (|Integer|))))) |noBranch|) (IF (|has| |#3| (|RetractableTo| (|Float|))) (PROGN (SIGNATURE |retract| ($ (|Expression| (|Float|)))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Expression| (|Float|)))) (SIGNATURE |retract| ($ (|Fraction| (|Polynomial| (|Float|))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|))))) (SIGNATURE |retract| ($ (|Polynomial| (|Float|)))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| (|Float|))))) |noBranch|) (SIGNATURE |abs| ($ $)) (SIGNATURE |sqrt| ($ $)) (SIGNATURE |exp| ($ $)) (SIGNATURE |log| ($ $)) (SIGNATURE |log10| ($ $)) (SIGNATURE |sin| ($ $)) (SIGNATURE |cos| ($ $)) (SIGNATURE |tan| ($ $)) (SIGNATURE |asin| ($ $)) (SIGNATURE |acos| ($ $)) (SIGNATURE |atan| ($ $)) (SIGNATURE |sinh| ($ $)) (SIGNATURE |cosh| ($ $)) (SIGNATURE |tanh| ($ $)) (SIGNATURE |pi| ($)) (SIGNATURE |variables| ((|List| (|Symbol|)) $)) (SIGNATURE |useNagFunctions| ((|Boolean|))) (SIGNATURE |useNagFunctions| ((|Boolean|) (|Boolean|))))) 
((|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) 19))) 
(((|FunctionFieldCategoryFunctions2| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (CATEGORY |package| (SIGNATURE |map| (|#8| (|Mapping| |#5| |#1|) |#4|))) (|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|) (|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |#5|) (|UnivariatePolynomialCategory| (|Fraction| |#6|)) (|FunctionFieldCategory| |#5| |#6| |#7|)) (T |FunctionFieldCategoryFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *8 *5)) (|ofCategory| *5 (|UniqueFactorizationDomain|)) (|ofCategory| *8 (|UniqueFactorizationDomain|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|ofCategory| *9 (|UnivariatePolynomialCategory| *8)) (|ofCategory| *2 (|FunctionFieldCategory| *8 *9 *10)) (|isDomain| *1 (|FunctionFieldCategoryFunctions2| *5 *6 *7 *4 *8 *9 *10 *2)) (|ofCategory| *4 (|FunctionFieldCategory| *5 *6 *7)) (|ofCategory| *10 (|UnivariatePolynomialCategory| (|Fraction| *9)))))) 
(CATEGORY |package| (SIGNATURE |map| (|#8| (|Mapping| |#5| |#1|) |#4|))) 
((|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) 37)) (|represents| (($ (|Vector| (|Fraction| |#3|)) (|Vector| $)) NIL) (($ (|Vector| (|Fraction| |#3|))) NIL) (($ (|Vector| |#3|) |#3|) 158)) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) 142)) (|rationalPoints| (((|List| (|List| |#2|))) 115)) (|rationalPoint?| (((|Boolean|) |#2| |#2|) 71)) (|primitivePart| (($ $) 136)) (|numberOfComponents| (((|NonNegativeInteger|)) 30)) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) 195)) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) 108)) (|integralAtInfinity?| (((|Boolean|) $) 155)) (|integral?| (((|Boolean|) $) 24) (((|Boolean|) $ |#2|) 28) (((|Boolean|) $ |#3|) 199)) (|hyperelliptic| (((|Union| |#3| "failed")) 48)) (|genus| (((|NonNegativeInteger|)) 167)) (|elt| ((|#2| $ |#2| |#2|) 129)) (|elliptic| (((|Union| |#3| "failed")) 66)) (|differentiate| (($ $ (|Mapping| (|Fraction| |#3|) (|Fraction| |#3|)) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| (|Fraction| |#3|) (|Fraction| |#3|))) NIL) (($ $ (|Mapping| |#3| |#3|)) 203) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|))) NIL) (($ $ (|Symbol|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (|complementaryBasis| (((|Vector| $) (|Vector| $)) 148)) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) 64)) (|absolutelyIrreducible?| (((|Boolean|)) 32))) 
(((|FunctionFieldCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |rationalPoints| ((|List| (|List| |#2|)))) (SIGNATURE |nonSingularModel| ((|List| (|Polynomial| |#2|)) (|Symbol|))) (SIGNATURE |algSplitSimple| ((|Record| (|:| |num| |#1|) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) |#1| (|Mapping| |#3| |#3|))) (SIGNATURE |hyperelliptic| ((|Union| |#3| "failed"))) (SIGNATURE |elliptic| ((|Union| |#3| "failed"))) (SIGNATURE |elt| (|#2| |#1| |#2| |#2|)) (SIGNATURE |primitivePart| (|#1| |#1|)) (SIGNATURE |represents| (|#1| (|Vector| |#3|) |#3|)) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#3| |#3|))) (SIGNATURE |integral?| ((|Boolean|) |#1| |#3|)) (SIGNATURE |integral?| ((|Boolean|) |#1| |#2|)) (SIGNATURE |yCoordinates| ((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) |#1|)) (SIGNATURE |reduceBasisAtInfinity| ((|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |normalizeAtInfinity| ((|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |complementaryBasis| ((|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |integral?| ((|Boolean|) |#1|)) (SIGNATURE |integralAtInfinity?| ((|Boolean|) |#1|)) (SIGNATURE |rationalPoint?| ((|Boolean|) |#2| |#2|)) (SIGNATURE |absolutelyIrreducible?| ((|Boolean|))) (SIGNATURE |genus| ((|NonNegativeInteger|))) (SIGNATURE |numberOfComponents| ((|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| (|Fraction| |#3|) (|Fraction| |#3|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| (|Fraction| |#3|) (|Fraction| |#3|)) (|NonNegativeInteger|))) (SIGNATURE |represents| (|#1| (|Vector| (|Fraction| |#3|)))) (SIGNATURE |represents| (|#1| (|Vector| (|Fraction| |#3|)) (|Vector| |#1|)))) (|FunctionFieldCategory| |#2| |#3| |#4|) (|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |#2|) (|UnivariatePolynomialCategory| (|Fraction| |#3|))) (T |FunctionFieldCategory&|)) 
((|numberOfComponents| (*1 *2) (AND (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *5 *6)) (|ofCategory| *3 (|FunctionFieldCategory| *4 *5 *6)))) (|genus| (*1 *2) (AND (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *5 *6)) (|ofCategory| *3 (|FunctionFieldCategory| *4 *5 *6)))) (|absolutelyIrreducible?| (*1 *2) (AND (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *5 *6)) (|ofCategory| *3 (|FunctionFieldCategory| *4 *5 *6)))) (|rationalPoint?| (*1 *2 *3 *3) (AND (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FunctionFieldCategory&| *4 *3 *5 *6)) (|ofCategory| *4 (|FunctionFieldCategory| *3 *5 *6)))) (|elliptic| (*1 *2) (|partial| AND (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *2))) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *2 *5)) (|ofCategory| *3 (|FunctionFieldCategory| *4 *2 *5)))) (|hyperelliptic| (*1 *2) (|partial| AND (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *2))) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *2 *5)) (|ofCategory| *3 (|FunctionFieldCategory| *4 *2 *5)))) (|nonSingularModel| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *5 (|UniqueFactorizationDomain|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|isDomain| *2 (|List| (|Polynomial| *5))) (|isDomain| *1 (|FunctionFieldCategory&| *4 *5 *6 *7)) (|ofCategory| *4 (|FunctionFieldCategory| *5 *6 *7)))) (|rationalPoints| (*1 *2) (AND (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|isDomain| *2 (|List| (|List| *4))) (|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *5 *6)) (|ofCategory| *3 (|FunctionFieldCategory| *4 *5 *6))))) 
(CATEGORY |domain| (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |rationalPoints| ((|List| (|List| |#2|)))) (SIGNATURE |nonSingularModel| ((|List| (|Polynomial| |#2|)) (|Symbol|))) (SIGNATURE |algSplitSimple| ((|Record| (|:| |num| |#1|) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) |#1| (|Mapping| |#3| |#3|))) (SIGNATURE |hyperelliptic| ((|Union| |#3| "failed"))) (SIGNATURE |elliptic| ((|Union| |#3| "failed"))) (SIGNATURE |elt| (|#2| |#1| |#2| |#2|)) (SIGNATURE |primitivePart| (|#1| |#1|)) (SIGNATURE |represents| (|#1| (|Vector| |#3|) |#3|)) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#3| |#3|))) (SIGNATURE |integral?| ((|Boolean|) |#1| |#3|)) (SIGNATURE |integral?| ((|Boolean|) |#1| |#2|)) (SIGNATURE |yCoordinates| ((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) |#1|)) (SIGNATURE |reduceBasisAtInfinity| ((|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |normalizeAtInfinity| ((|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |complementaryBasis| ((|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |integral?| ((|Boolean|) |#1|)) (SIGNATURE |integralAtInfinity?| ((|Boolean|) |#1|)) (SIGNATURE |rationalPoint?| ((|Boolean|) |#2| |#2|)) (SIGNATURE |absolutelyIrreducible?| ((|Boolean|))) (SIGNATURE |genus| ((|NonNegativeInteger|))) (SIGNATURE |numberOfComponents| ((|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| (|Fraction| |#3|) (|Fraction| |#3|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| (|Fraction| |#3|) (|Fraction| |#3|)) (|NonNegativeInteger|))) (SIGNATURE |represents| (|#1| (|Vector| (|Fraction| |#3|)))) (SIGNATURE |represents| (|#1| (|Vector| (|Fraction| |#3|)) (|Vector| |#1|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) 183)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 89 (|has| (|Fraction| |#2|) (|Field|)))) (|unitCanonical| (($ $) 90 (|has| (|Fraction| |#2|) (|Field|)))) (|unit?| (((|Boolean|) $) 92 (|has| (|Fraction| |#2|) (|Field|)))) (|traceMatrix| (((|Matrix| (|Fraction| |#2|)) (|Vector| $)) 44) (((|Matrix| (|Fraction| |#2|))) 55)) (|trace| (((|Fraction| |#2|) $) 50)) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) 144 (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 110 (|has| (|Fraction| |#2|) (|Field|)))) (|squareFree| (((|Factored| $) $) 111 (|has| (|Fraction| |#2|) (|Field|)))) (|sizeLess?| (((|Boolean|) $ $) 101 (|has| (|Fraction| |#2|) (|Field|)))) (|size| (((|NonNegativeInteger|)) 82 (|has| (|Fraction| |#2|) (|Finite|)))) (|singularAtInfinity?| (((|Boolean|)) 200)) (|singular?| (((|Boolean|) |#1|) 199) (((|Boolean|) |#2|) 198)) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 166 (|has| (|Fraction| |#2|) (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) 164 (|has| (|Fraction| |#2|) (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Fraction| |#2|) "failed") $) 163)) (|retract| (((|Integer|) $) 167 (|has| (|Fraction| |#2|) (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) 165 (|has| (|Fraction| |#2|) (|RetractableTo| (|Fraction| (|Integer|))))) (((|Fraction| |#2|) $) 162)) (|represents| (($ (|Vector| (|Fraction| |#2|)) (|Vector| $)) 46) (($ (|Vector| (|Fraction| |#2|))) 58) (($ (|Vector| |#2|) |#2|) 176)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 150 (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|rem| (($ $ $) 105 (|has| (|Fraction| |#2|) (|Field|)))) (|regularRepresentation| (((|Matrix| (|Fraction| |#2|)) $ (|Vector| $)) 51) (((|Matrix| (|Fraction| |#2|)) $) 53)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) 161 (|has| (|Fraction| |#2|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) 160 (|has| (|Fraction| |#2|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Fraction| |#2|))) (|:| |vec| (|Vector| (|Fraction| |#2|)))) (|Matrix| $) (|Vector| $)) 159) (((|Matrix| (|Fraction| |#2|)) (|Matrix| $)) 158)) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) 188)) (|reduce| (($ |#3|) 155) (((|Union| $ "failed") (|Fraction| |#3|)) 152 (|has| (|Fraction| |#2|) (|Field|)))) (|recip| (((|Union| $ "failed") $) 33)) (|rationalPoints| (((|List| (|List| |#1|))) 169 (|has| |#1| (|Finite|)))) (|rationalPoint?| (((|Boolean|) |#1| |#1|) 204)) (|rank| (((|PositiveInteger|)) 52)) (|random| (($) 85 (|has| (|Fraction| |#2|) (|Finite|)))) (|ramifiedAtInfinity?| (((|Boolean|)) 197)) (|ramified?| (((|Boolean|) |#1|) 196) (((|Boolean|) |#2|) 195)) (|quo| (($ $ $) 104 (|has| (|Fraction| |#2|) (|Field|)))) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 99 (|has| (|Fraction| |#2|) (|Field|)))) (|primitivePart| (($ $) 175)) (|primitiveElement| (($) 146 (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|primitive?| (((|Boolean|) $) 147 (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) 138 (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))) (($ $) 137 (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|prime?| (((|Boolean|) $) 112 (|has| (|Fraction| |#2|) (|Field|)))) (|order| (((|PositiveInteger|) $) 149 (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))) (((|OnePointCompletion| (|PositiveInteger|)) $) 135 (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|one?| (((|Boolean|) $) 30)) (|numberOfComponents| (((|NonNegativeInteger|)) 207)) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) 189)) (|norm| (((|Fraction| |#2|) $) 49)) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) 170 (|has| |#1| (|Field|)))) (|nextItem| (((|Union| $ "failed") $) 139 (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 108 (|has| (|Fraction| |#2|) (|Field|)))) (|minimalPolynomial| ((|#3| $) 42 (|has| (|Fraction| |#2|) (|Field|)))) (|lookup| (((|PositiveInteger|) $) 84 (|has| (|Fraction| |#2|) (|Finite|)))) (|lift| ((|#3| $) 153)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 93 (|has| (|Fraction| |#2|) (|Field|)))) (|lcm| (($ (|List| $)) 97 (|has| (|Fraction| |#2|) (|Field|))) (($ $ $) 96 (|has| (|Fraction| |#2|) (|Field|)))) (|latex| (((|String|) $) 9)) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) 184)) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) 186)) (|inv| (($ $) 113 (|has| (|Fraction| |#2|) (|Field|)))) (|integralRepresents| (($ (|Vector| |#2|) |#2|) 181)) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) 185)) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) 187)) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) 180)) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) 182)) (|integralBasisAtInfinity| (((|Vector| $)) 193)) (|integralBasis| (((|Vector| $)) 194)) (|integralAtInfinity?| (((|Boolean|) $) 192)) (|integral?| (((|Boolean|) $) 191) (((|Boolean|) $ |#1|) 179) (((|Boolean|) $ |#2|) 178)) (|init| (($) 140 (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) CONST)) (|index| (($ (|PositiveInteger|)) 83 (|has| (|Fraction| |#2|) (|Finite|)))) (|hyperelliptic| (((|Union| |#2| "failed")) 172)) (|hash| (((|SingleInteger|) $) 10)) (|genus| (((|NonNegativeInteger|)) 206)) (|generator| (($) 157)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 98 (|has| (|Fraction| |#2|) (|Field|)))) (|gcd| (($ (|List| $)) 95 (|has| (|Fraction| |#2|) (|Field|))) (($ $ $) 94 (|has| (|Fraction| |#2|) (|Field|)))) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) 143 (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|factor| (((|Factored| $) $) 109 (|has| (|Fraction| |#2|) (|Field|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 107 (|has| (|Fraction| |#2|) (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 106 (|has| (|Fraction| |#2|) (|Field|)))) (|exquo| (((|Union| $ "failed") $ $) 88 (|has| (|Fraction| |#2|) (|Field|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 100 (|has| (|Fraction| |#2|) (|Field|)))) (|euclideanSize| (((|NonNegativeInteger|) $) 102 (|has| (|Fraction| |#2|) (|Field|)))) (|enumerate| (((|List| $)) 86 (|has| (|Fraction| |#2|) (|Finite|)))) (|elt| ((|#1| $ |#1| |#1|) 174)) (|elliptic| (((|Union| |#2| "failed")) 173)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 103 (|has| (|Fraction| |#2|) (|Field|)))) (|discriminant| (((|Fraction| |#2|) (|Vector| $)) 45) (((|Fraction| |#2|)) 54)) (|discreteLog| (((|NonNegativeInteger|) $) 148 (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))) (((|Union| (|NonNegativeInteger|) "failed") $ $) 136 (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|differentiate| (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|)) (|NonNegativeInteger|)) 120 (|has| (|Fraction| |#2|) (|Field|))) (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|))) 119 (|has| (|Fraction| |#2|) (|Field|))) (($ $ (|Mapping| |#2| |#2|)) 177) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 127 (OR (|and| (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|)))) (|and| (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))) (|has| (|Fraction| |#2|) (|Field|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 128 (OR (|and| (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|)))) (|and| (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))) (|has| (|Fraction| |#2|) (|Field|))))) (($ $ (|List| (|Symbol|))) 129 (OR (|and| (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|)))) (|and| (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))) (|has| (|Fraction| |#2|) (|Field|))))) (($ $ (|Symbol|)) 130 (OR (|and| (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|)))) (|and| (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))) (|has| (|Fraction| |#2|) (|Field|))))) (($ $ (|NonNegativeInteger|)) 132 (OR (|and| (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|DifferentialRing|))) (|and| (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|))) (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (($ $) 134 (OR (|and| (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|DifferentialRing|))) (|and| (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|))) (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))))) (|derivationCoordinates| (((|Matrix| (|Fraction| |#2|)) (|Vector| $) (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|))) 151 (|has| (|Fraction| |#2|) (|Field|)))) (|definingPolynomial| ((|#3|) 156)) (|createPrimitiveElement| (($) 145 (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|coordinates| (((|Vector| (|Fraction| |#2|)) $ (|Vector| $)) 48) (((|Matrix| (|Fraction| |#2|)) (|Vector| $) (|Vector| $)) 47) (((|Vector| (|Fraction| |#2|)) $) 60) (((|Matrix| (|Fraction| |#2|)) (|Vector| $)) 59)) (|convert| (((|Vector| (|Fraction| |#2|)) $) 57) (($ (|Vector| (|Fraction| |#2|))) 56) ((|#3| $) 168) (($ |#3|) 154)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 142 (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|complementaryBasis| (((|Vector| $) (|Vector| $)) 190)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ (|Fraction| |#2|)) 36) (($ (|Fraction| (|Integer|))) 81 (OR (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|RetractableTo| (|Fraction| (|Integer|)))))) (($ $) 87 (|has| (|Fraction| |#2|) (|Field|)))) (|charthRoot| (($ $) 141 (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))) (((|Union| $ "failed") $) 41 (|has| (|Fraction| |#2|) (|CharacteristicNonZero|)))) (|characteristicPolynomial| ((|#3| $) 43)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|branchPointAtInfinity?| (((|Boolean|)) 203)) (|branchPoint?| (((|Boolean|) |#1|) 202) (((|Boolean|) |#2|) 201)) (|basis| (((|Vector| $)) 61)) (|associates?| (((|Boolean|) $ $) 91 (|has| (|Fraction| |#2|) (|Field|)))) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) 171)) (|absolutelyIrreducible?| (((|Boolean|)) 205)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 114 (|has| (|Fraction| |#2|) (|Field|)))) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|)) (|NonNegativeInteger|)) 122 (|has| (|Fraction| |#2|) (|Field|))) (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|))) 121 (|has| (|Fraction| |#2|) (|Field|))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 123 (OR (|and| (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|)))) (|and| (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))) (|has| (|Fraction| |#2|) (|Field|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 124 (OR (|and| (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|)))) (|and| (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))) (|has| (|Fraction| |#2|) (|Field|))))) (($ $ (|List| (|Symbol|))) 125 (OR (|and| (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|)))) (|and| (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))) (|has| (|Fraction| |#2|) (|Field|))))) (($ $ (|Symbol|)) 126 (OR (|and| (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|)))) (|and| (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))) (|has| (|Fraction| |#2|) (|Field|))))) (($ $ (|NonNegativeInteger|)) 131 (OR (|and| (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|DifferentialRing|))) (|and| (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|))) (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (($ $) 133 (OR (|and| (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|DifferentialRing|))) (|and| (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|))) (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))))) (= (((|Boolean|) $ $) 6)) (/ (($ $ $) 118 (|has| (|Fraction| |#2|) (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 115 (|has| (|Fraction| |#2|) (|Field|)))) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ (|Fraction| |#2|)) 38) (($ (|Fraction| |#2|) $) 37) (($ (|Fraction| (|Integer|)) $) 117 (|has| (|Fraction| |#2|) (|Field|))) (($ $ (|Fraction| (|Integer|))) 116 (|has| (|Fraction| |#2|) (|Field|))))) 
(((|FunctionFieldCategory| |#1| |#2| |#3|) (|Category|) (|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |t#1|) (|UnivariatePolynomialCategory| (|Fraction| |t#2|))) (T |FunctionFieldCategory|)) 
((|numberOfComponents| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|NonNegativeInteger|)))) (|genus| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|NonNegativeInteger|)))) (|absolutelyIrreducible?| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|rationalPoint?| (*1 *2 *3 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|branchPointAtInfinity?| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|branchPoint?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|branchPoint?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|isDomain| *2 (|Boolean|)))) (|singularAtInfinity?| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|singular?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|singular?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|isDomain| *2 (|Boolean|)))) (|ramifiedAtInfinity?| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|ramified?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|ramified?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|isDomain| *2 (|Boolean|)))) (|integralBasis| (*1 *2) (AND (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)))) (|integralBasisAtInfinity| (*1 *2) (AND (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)))) (|integralAtInfinity?| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|integral?| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|complementaryBasis| (*1 *2 *2) (AND (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|normalizeAtInfinity| (*1 *2 *2) (AND (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|reduceBasisAtInfinity| (*1 *2 *2) (AND (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|integralMatrix| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Matrix| (|Fraction| *4))))) (|inverseIntegralMatrix| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Matrix| (|Fraction| *4))))) (|integralMatrixAtInfinity| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Matrix| (|Fraction| *4))))) (|inverseIntegralMatrixAtInfinity| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Matrix| (|Fraction| *4))))) (|yCoordinates| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Record| (|:| |num| (|Vector| *4)) (|:| |den| *4))))) (|integralCoordinates| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Record| (|:| |num| (|Vector| *4)) (|:| |den| *4))))) (|integralRepresents| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))))) (|integralDerivationMatrix| (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| *5 *5)) (|ofCategory| *1 (|FunctionFieldCategory| *4 *5 *6)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|isDomain| *2 (|Record| (|:| |num| (|Matrix| *5)) (|:| |den| *5))))) (|integral?| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|integral?| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|isDomain| *2 (|Boolean|)))) (|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|represents| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))))) (|primitivePart| (*1 *1 *1) (AND (|ofCategory| *1 (|FunctionFieldCategory| *2 *3 *4)) (|ofCategory| *2 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3))))) (|elt| (*1 *2 *1 *2 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *2 *3 *4)) (|ofCategory| *2 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3))))) (|elliptic| (*1 *2) (|partial| AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *2 *4)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *2))) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|hyperelliptic| (*1 *2) (|partial| AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *2 *4)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *2))) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|algSplitSimple| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Mapping| *5 *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|isDomain| *2 (|Record| (|:| |num| *1) (|:| |den| *5) (|:| |derivden| *5) (|:| |gd| *5))) (|ofCategory| *1 (|FunctionFieldCategory| *4 *5 *6)))) (|nonSingularModel| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *1 (|FunctionFieldCategory| *4 *5 *6)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|List| (|Polynomial| *4))))) (|rationalPoints| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *3 (|Finite|)) (|isDomain| *2 (|List| (|List| *3)))))) 
(|Join| (|MonogenicAlgebra| (|Fraction| |t#2|) |t#3|) (CATEGORY |domain| (SIGNATURE |numberOfComponents| ((|NonNegativeInteger|))) (SIGNATURE |genus| ((|NonNegativeInteger|))) (SIGNATURE |absolutelyIrreducible?| ((|Boolean|))) (SIGNATURE |rationalPoint?| ((|Boolean|) |t#1| |t#1|)) (SIGNATURE |branchPointAtInfinity?| ((|Boolean|))) (SIGNATURE |branchPoint?| ((|Boolean|) |t#1|)) (SIGNATURE |branchPoint?| ((|Boolean|) |t#2|)) (SIGNATURE |singularAtInfinity?| ((|Boolean|))) (SIGNATURE |singular?| ((|Boolean|) |t#1|)) (SIGNATURE |singular?| ((|Boolean|) |t#2|)) (SIGNATURE |ramifiedAtInfinity?| ((|Boolean|))) (SIGNATURE |ramified?| ((|Boolean|) |t#1|)) (SIGNATURE |ramified?| ((|Boolean|) |t#2|)) (SIGNATURE |integralBasis| ((|Vector| $))) (SIGNATURE |integralBasisAtInfinity| ((|Vector| $))) (SIGNATURE |integralAtInfinity?| ((|Boolean|) $)) (SIGNATURE |integral?| ((|Boolean|) $)) (SIGNATURE |complementaryBasis| ((|Vector| $) (|Vector| $))) (SIGNATURE |normalizeAtInfinity| ((|Vector| $) (|Vector| $))) (SIGNATURE |reduceBasisAtInfinity| ((|Vector| $) (|Vector| $))) (SIGNATURE |integralMatrix| ((|Matrix| (|Fraction| |t#2|)))) (SIGNATURE |inverseIntegralMatrix| ((|Matrix| (|Fraction| |t#2|)))) (SIGNATURE |integralMatrixAtInfinity| ((|Matrix| (|Fraction| |t#2|)))) (SIGNATURE |inverseIntegralMatrixAtInfinity| ((|Matrix| (|Fraction| |t#2|)))) (SIGNATURE |yCoordinates| ((|Record| (|:| |num| (|Vector| |t#2|)) (|:| |den| |t#2|)) $)) (SIGNATURE |represents| ($ (|Vector| |t#2|) |t#2|)) (SIGNATURE |integralCoordinates| ((|Record| (|:| |num| (|Vector| |t#2|)) (|:| |den| |t#2|)) $)) (SIGNATURE |integralRepresents| ($ (|Vector| |t#2|) |t#2|)) (SIGNATURE |integralDerivationMatrix| ((|Record| (|:| |num| (|Matrix| |t#2|)) (|:| |den| |t#2|)) (|Mapping| |t#2| |t#2|))) (SIGNATURE |integral?| ((|Boolean|) $ |t#1|)) (SIGNATURE |integral?| ((|Boolean|) $ |t#2|)) (SIGNATURE |differentiate| ($ $ (|Mapping| |t#2| |t#2|))) (SIGNATURE |represents| ($ (|Vector| |t#2|) |t#2|)) (SIGNATURE |primitivePart| ($ $)) (SIGNATURE |elt| (|t#1| $ |t#1| |t#1|)) (SIGNATURE |elliptic| ((|Union| |t#2| "failed"))) (SIGNATURE |hyperelliptic| ((|Union| |t#2| "failed"))) (SIGNATURE |algSplitSimple| ((|Record| (|:| |num| $) (|:| |den| |t#2|) (|:| |derivden| |t#2|) (|:| |gd| |t#2|)) $ (|Mapping| |t#2| |t#2|))) (IF (|has| |t#1| (|Field|)) (SIGNATURE |nonSingularModel| ((|List| (|Polynomial| |t#1|)) (|Symbol|))) |noBranch|) (IF (|has| |t#1| (|Finite|)) (SIGNATURE |rationalPoints| ((|List| (|List| |t#1|)))) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|Algebra| (|Fraction| |#2|)) . T) ((|Algebra| $) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|BiModule| (|Fraction| |#2|) (|Fraction| |#2|)) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|CharacteristicNonZero|))) ((|CharacteristicZero|) |has| (|Fraction| |#2|) (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| |#3|) . T) ((|DifferentialExtension| (|Fraction| |#2|)) |has| (|Fraction| |#2|) (|Field|)) ((|DifferentialRing|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (AND (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|)))) ((|DivisionRing|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|EntireRing|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|EuclideanDomain|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|Field|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|FieldOfPrimeCharacteristic|) |has| (|Fraction| |#2|) (|FiniteFieldCategory|)) ((|Finite|) OR (|has| (|Fraction| |#2|) (|Finite|)) (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))) ((|FiniteFieldCategory|) |has| (|Fraction| |#2|) (|FiniteFieldCategory|)) ((|FiniteRankAlgebra| (|Fraction| |#2|) |#3|) . T) ((|FramedAlgebra| (|Fraction| |#2|) |#3|) . T) ((|FullyLinearlyExplicitRingOver| (|Fraction| |#2|)) . T) ((|FullyRetractableTo| (|Fraction| |#2|)) . T) ((|GcdDomain|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|IntegralDomain|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|LeftModule| (|Fraction| (|Integer|))) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|LeftModule| (|Fraction| |#2|)) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|LinearlyExplicitRingOver| (|Fraction| |#2|)) . T) ((|LinearlyExplicitRingOver| (|Integer|)) |has| (|Fraction| |#2|) (|LinearlyExplicitRingOver| (|Integer|))) ((|Module| (|Fraction| (|Integer|))) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|Module| (|Fraction| |#2|)) . T) ((|Module| $) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|MonogenicAlgebra| (|Fraction| |#2|) |#3|) . T) ((|Monoid|) . T) ((|PartialDifferentialRing| (|Symbol|)) AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|)))) ((|PrincipalIdealDomain|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|RetractableTo| (|Fraction| (|Integer|))) |has| (|Fraction| |#2|) (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Fraction| |#2|)) . T) ((|RetractableTo| (|Integer|)) |has| (|Fraction| |#2|) (|RetractableTo| (|Integer|))) ((|RightModule| (|Fraction| (|Integer|))) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|RightModule| (|Fraction| |#2|)) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| (|Fraction| |#2|) (|FiniteFieldCategory|)) ((|UniqueFactorizationDomain|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|transcendent?| (((|Boolean|) $) NIL)) (|transcendenceDegree| (((|NonNegativeInteger|)) NIL)) (|trace| (((|PrimeField| |#1|) $) NIL) (($ $ (|PositiveInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|size| (((|NonNegativeInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|PrimeField| |#1|) "failed") $) NIL)) (|retract| (((|PrimeField| |#1|) $) NIL)) (|represents| (($ (|Vector| (|PrimeField| |#1|))) NIL)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|primitiveElement| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|primitive?| (((|Boolean|) $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) NIL (OR (|has| (|PrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|PrimeField| |#1|) (|Finite|)))) (($ $) NIL (OR (|has| (|PrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|PrimeField| |#1|) (|Finite|))))) (|prime?| (((|Boolean|) $) NIL)) (|order| (((|PositiveInteger|) $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (((|OnePointCompletion| (|PositiveInteger|)) $) NIL (OR (|has| (|PrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|PrimeField| |#1|) (|Finite|))))) (|one?| (((|Boolean|) $) NIL)) (|normalElement| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|normal?| (((|Boolean|) $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|norm| (((|PrimeField| |#1|) $) NIL) (($ $ (|PositiveInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|nextItem| (((|Union| $ "failed") $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| (|PrimeField| |#1|)) $) NIL) (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|lookup| (((|PositiveInteger|) $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| (|PrimeField| |#1|)) $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|linearAssociatedLog| (((|SparseUnivariatePolynomial| (|PrimeField| |#1|)) $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (((|Union| (|SparseUnivariatePolynomial| (|PrimeField| |#1|)) "failed") $ $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| (|PrimeField| |#1|))) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|init| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)) CONST)) (|index| (($ (|PositiveInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|inGroundField?| (((|Boolean|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) NIL)) (|generator| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|factor| (((|Factored| $) $) NIL)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) NIL) (((|PositiveInteger|)) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|enumerate| (((|List| $)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|discreteLog| (((|NonNegativeInteger|) $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (((|Union| (|NonNegativeInteger|) "failed") $ $) NIL (OR (|has| (|PrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|PrimeField| |#1|) (|Finite|))))) (|dimension| (((|CardinalNumber|)) NIL)) (|differentiate| (($ $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL) (((|PositiveInteger|) $) NIL)) (|definingPolynomial| (((|SparseUnivariatePolynomial| (|PrimeField| |#1|))) NIL)) (|createPrimitiveElement| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|createNormalElement| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|coordinates| (((|Vector| (|PrimeField| |#1|)) $) NIL) (((|Matrix| (|PrimeField| |#1|)) (|Vector| $)) NIL)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ (|PrimeField| |#1|)) NIL)) (|charthRoot| (($ $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (((|Union| $ "failed") $) NIL (OR (|has| (|PrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|PrimeField| |#1|) (|Finite|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|basis| (((|Vector| $)) NIL) (((|Vector| $) (|PositiveInteger|)) NIL)) (|associates?| (((|Boolean|) $ $) NIL)) (|algebraic?| (((|Boolean|) $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (|Frobenius| (($ $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (D (($ $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (= (((|Boolean|) $ $) NIL)) (/ (($ $ $) NIL) (($ $ (|PrimeField| |#1|)) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ $ (|PrimeField| |#1|)) NIL) (($ (|PrimeField| |#1|) $) NIL))) 
(((|FiniteFieldCyclicGroup| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| (|PrimeField| |#1|)) (CATEGORY |package| (SIGNATURE |getZechTable| ((|PrimitiveArray| (|SingleInteger|)))))) (|PositiveInteger|) (|PositiveInteger|)) (T |FiniteFieldCyclicGroup|)) 
((|getZechTable| (*1 *2) (AND (|isDomain| *2 (|PrimitiveArray| (|SingleInteger|))) (|isDomain| *1 (|FiniteFieldCyclicGroup| *3 *4)) (|ofType| *3 (|PositiveInteger|)) (|ofType| *4 (|PositiveInteger|))))) 
(|Join| (|FiniteAlgebraicExtensionField| (|PrimeField| |#1|)) (CATEGORY |package| (SIGNATURE |getZechTable| ((|PrimitiveArray| (|SingleInteger|)))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 46)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|transcendent?| (((|Boolean|) $) NIL)) (|transcendenceDegree| (((|NonNegativeInteger|)) NIL)) (|trace| ((|#1| $) NIL) (($ $ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) 43 (|has| |#1| (|Finite|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|size| (((|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 113)) (|retract| ((|#1| $) 84)) (|represents| (($ (|Vector| |#1|)) 102)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 93 (|has| |#1| (|Finite|)))) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) 96 (|has| |#1| (|Finite|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|primitiveElement| (($) 128 (|has| |#1| (|Finite|)))) (|primitive?| (((|Boolean|) $) 49 (|has| |#1| (|Finite|)))) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|)))) (($ $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|prime?| (((|Boolean|) $) NIL)) (|order| (((|PositiveInteger|) $) 47 (|has| |#1| (|Finite|))) (((|OnePointCompletion| (|PositiveInteger|)) $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|one?| (((|Boolean|) $) NIL)) (|normalElement| (($) 130 (|has| |#1| (|Finite|)))) (|normal?| (((|Boolean|) $) NIL (|has| |#1| (|Finite|)))) (|norm| ((|#1| $) NIL) (($ $ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|nextItem| (((|Union| $ "failed") $) NIL (|has| |#1| (|Finite|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 88) (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|lookup| (((|PositiveInteger|) $) 138 (|has| |#1| (|Finite|)))) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) NIL (|has| |#1| (|Finite|)))) (|linearAssociatedLog| (((|SparseUnivariatePolynomial| |#1|) $) NIL (|has| |#1| (|Finite|))) (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) NIL (|has| |#1| (|Finite|)))) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) NIL (|has| |#1| (|Finite|)))) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 145)) (|init| (($) NIL (|has| |#1| (|Finite|)) CONST)) (|index| (($ (|PositiveInteger|)) 70 (|has| |#1| (|Finite|)))) (|inGroundField?| (((|Boolean|) $) 116)) (|hash| (((|SingleInteger|) $) NIL)) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) 44)) (|generator| (($) 126 (|has| |#1| (|Finite|)))) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) 91 (|has| |#1| (|Finite|)))) (|factor| (((|Factored| $) $) NIL)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) 67) (((|PositiveInteger|)) 68)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|enumerate| (((|List| $)) NIL (|has| |#1| (|Finite|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|discreteLog| (((|NonNegativeInteger|) $) 129 (|has| |#1| (|Finite|))) (((|Union| (|NonNegativeInteger|) "failed") $ $) 123 (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|dimension| (((|CardinalNumber|)) NIL)) (|differentiate| (($ $) NIL (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL) (((|PositiveInteger|) $) NIL)) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) 94)) (|createPrimitiveElement| (($) 127 (|has| |#1| (|Finite|)))) (|createNormalElement| (($) 135 (|has| |#1| (|Finite|)))) (|coordinates| (((|Vector| |#1|) $) 59) (((|Matrix| |#1|) (|Vector| $)) NIL)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (|has| |#1| (|Finite|)))) (|coerce| (((|OutputForm|) $) 141) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ |#1|) 74)) (|charthRoot| (($ $) NIL (|has| |#1| (|Finite|))) (((|Union| $ "failed") $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|characteristic| (((|NonNegativeInteger|)) 137)) (|basis| (((|Vector| $)) 115) (((|Vector| $) (|PositiveInteger|)) 72)) (|associates?| (((|Boolean|) $ $) NIL)) (|algebraic?| (((|Boolean|) $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) 32 T CONST)) (|One| (($) 19 T CONST)) (|Frobenius| (($ $) 80 (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (D (($ $) NIL (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (= (((|Boolean|) $ $) 48)) (/ (($ $ $) 143) (($ $ |#1|) 144)) (- (($ $) 125) (($ $ $) NIL)) (+ (($ $ $) 61)) (** (($ $ (|PositiveInteger|)) 147) (($ $ (|NonNegativeInteger|)) 148) (($ $ (|Integer|)) 146)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 76) (($ $ $) 75) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ $ |#1|) NIL) (($ |#1| $) 142))) 
(((|FiniteFieldCyclicGroupExtensionByPolynomial| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| |#1|) (CATEGORY |package| (SIGNATURE |getZechTable| ((|PrimitiveArray| (|SingleInteger|)))))) (|FiniteFieldCategory|) (|SparseUnivariatePolynomial| |#1|)) (T |FiniteFieldCyclicGroupExtensionByPolynomial|)) 
((|getZechTable| (*1 *2) (AND (|isDomain| *2 (|PrimitiveArray| (|SingleInteger|))) (|isDomain| *1 (|FiniteFieldCyclicGroupExtensionByPolynomial| *3 *4)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|SparseUnivariatePolynomial| *3))))) 
(|Join| (|FiniteAlgebraicExtensionField| |#1|) (CATEGORY |package| (SIGNATURE |getZechTable| ((|PrimitiveArray| (|SingleInteger|)))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|transcendent?| (((|Boolean|) $) NIL)) (|transcendenceDegree| (((|NonNegativeInteger|)) NIL)) (|trace| ((|#1| $) NIL) (($ $ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) NIL (|has| |#1| (|Finite|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|size| (((|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL)) (|retract| ((|#1| $) NIL)) (|represents| (($ (|Vector| |#1|)) NIL)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL (|has| |#1| (|Finite|)))) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) NIL (|has| |#1| (|Finite|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|primitiveElement| (($) NIL (|has| |#1| (|Finite|)))) (|primitive?| (((|Boolean|) $) NIL (|has| |#1| (|Finite|)))) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|)))) (($ $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|prime?| (((|Boolean|) $) NIL)) (|order| (((|PositiveInteger|) $) NIL (|has| |#1| (|Finite|))) (((|OnePointCompletion| (|PositiveInteger|)) $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|one?| (((|Boolean|) $) NIL)) (|normalElement| (($) NIL (|has| |#1| (|Finite|)))) (|normal?| (((|Boolean|) $) NIL (|has| |#1| (|Finite|)))) (|norm| ((|#1| $) NIL) (($ $ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|nextItem| (((|Union| $ "failed") $) NIL (|has| |#1| (|Finite|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) NIL) (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|lookup| (((|PositiveInteger|) $) NIL (|has| |#1| (|Finite|)))) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) NIL (|has| |#1| (|Finite|)))) (|linearAssociatedLog| (((|SparseUnivariatePolynomial| |#1|) $) NIL (|has| |#1| (|Finite|))) (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) NIL (|has| |#1| (|Finite|)))) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) NIL (|has| |#1| (|Finite|)))) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|init| (($) NIL (|has| |#1| (|Finite|)) CONST)) (|index| (($ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|inGroundField?| (((|Boolean|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) NIL)) (|generator| (($) NIL (|has| |#1| (|Finite|)))) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) NIL (|has| |#1| (|Finite|)))) (|factor| (((|Factored| $) $) NIL)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) NIL) (((|PositiveInteger|)) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|enumerate| (((|List| $)) NIL (|has| |#1| (|Finite|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|discreteLog| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|Finite|))) (((|Union| (|NonNegativeInteger|) "failed") $ $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|dimension| (((|CardinalNumber|)) NIL)) (|differentiate| (($ $) NIL (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL) (((|PositiveInteger|) $) NIL)) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) NIL)) (|createPrimitiveElement| (($) NIL (|has| |#1| (|Finite|)))) (|createNormalElement| (($) NIL (|has| |#1| (|Finite|)))) (|coordinates| (((|Vector| |#1|) $) NIL) (((|Matrix| |#1|) (|Vector| $)) NIL)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (|has| |#1| (|Finite|)))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ |#1|) NIL)) (|charthRoot| (($ $) NIL (|has| |#1| (|Finite|))) (((|Union| $ "failed") $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|basis| (((|Vector| $)) NIL) (((|Vector| $) (|PositiveInteger|)) NIL)) (|associates?| (((|Boolean|) $ $) NIL)) (|algebraic?| (((|Boolean|) $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (|Frobenius| (($ $) NIL (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (D (($ $) NIL (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (= (((|Boolean|) $ $) NIL)) (/ (($ $ $) NIL) (($ $ |#1|) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ $ |#1|) NIL) (($ |#1| $) NIL))) 
(((|FiniteFieldCyclicGroupExtension| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| |#1|) (CATEGORY |package| (SIGNATURE |getZechTable| ((|PrimitiveArray| (|SingleInteger|)))))) (|FiniteFieldCategory|) (|PositiveInteger|)) (T |FiniteFieldCyclicGroupExtension|)) 
((|getZechTable| (*1 *2) (AND (|isDomain| *2 (|PrimitiveArray| (|SingleInteger|))) (|isDomain| *1 (|FiniteFieldCyclicGroupExtension| *3 *4)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|PositiveInteger|))))) 
(|Join| (|FiniteAlgebraicExtensionField| |#1|) (CATEGORY |package| (SIGNATURE |getZechTable| ((|PrimitiveArray| (|SingleInteger|)))))) 
((|irreducible?| (((|Boolean|) |#2|) 68)) (|factorUsingYun| (((|Factored| |#2|) |#2|) 56)) (|factorUsingMusser| (((|Factored| |#2|) |#2|) 58)) (|factorSquareFree| (((|List| |#2|) |#2|) 61)) (|factorCantorZassenhaus| (((|List| |#2|) |#2| (|NonNegativeInteger|)) 62)) (|factor| (((|Factored| |#2|) |#2|) 59))) 
(((|FiniteFieldFactorization| |#1| |#2|) (CATEGORY |package| (SIGNATURE |factorSquareFree| ((|List| |#2|) |#2|)) (SIGNATURE |factorCantorZassenhaus| ((|List| |#2|) |#2| (|NonNegativeInteger|))) (SIGNATURE |factor| ((|Factored| |#2|) |#2|)) (SIGNATURE |factorUsingYun| ((|Factored| |#2|) |#2|)) (SIGNATURE |factorUsingMusser| ((|Factored| |#2|) |#2|)) (SIGNATURE |irreducible?| ((|Boolean|) |#2|))) (|FiniteFieldCategory|) (|UnivariatePolynomialCategory| |#1|)) (T |FiniteFieldFactorization|)) 
((|irreducible?| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteFieldFactorization| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|factorUsingMusser| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|FiniteFieldFactorization| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|factorUsingYun| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|FiniteFieldFactorization| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|FiniteFieldFactorization| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|factorCantorZassenhaus| (*1 *2 *3 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|FiniteFieldCategory|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|FiniteFieldFactorization| *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|factorSquareFree| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|FiniteFieldFactorization| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |factorSquareFree| ((|List| |#2|) |#2|)) (SIGNATURE |factorCantorZassenhaus| ((|List| |#2|) |#2| (|NonNegativeInteger|))) (SIGNATURE |factor| ((|Factored| |#2|) |#2|)) (SIGNATURE |factorUsingYun| ((|Factored| |#2|) |#2|)) (SIGNATURE |factorUsingMusser| ((|Factored| |#2|) |#2|)) (SIGNATURE |irreducible?| ((|Boolean|) |#2|))) 
((|irreducible?| (((|Boolean|) |#2|) 68)) (|factorUsingYun| (((|Factored| |#2|) |#2|) 56)) (|factorUsingMusser| (((|Factored| |#2|) |#2|) 58)) (|factorSquareFree| (((|List| |#2|) |#2|) 61)) (|factorCantorZassenhaus| (((|List| |#2|) |#2| (|NonNegativeInteger|)) 62)) (|factor| (((|Factored| |#2|) |#2|) 59))) 
(((|FiniteFieldFactorizationWithSizeParseBySideEffect| |#1| |#2|) (CATEGORY |package| (SIGNATURE |factorSquareFree| ((|List| |#2|) |#2|)) (SIGNATURE |factorCantorZassenhaus| ((|List| |#2|) |#2| (|NonNegativeInteger|))) (SIGNATURE |factor| ((|Factored| |#2|) |#2|)) (SIGNATURE |factorUsingYun| ((|Factored| |#2|) |#2|)) (SIGNATURE |factorUsingMusser| ((|Factored| |#2|) |#2|)) (SIGNATURE |irreducible?| ((|Boolean|) |#2|))) (|FiniteFieldCategory|) (|UnivariatePolynomialCategory| |#1|)) (T |FiniteFieldFactorizationWithSizeParseBySideEffect|)) 
((|irreducible?| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteFieldFactorizationWithSizeParseBySideEffect| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|factorUsingMusser| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|FiniteFieldFactorizationWithSizeParseBySideEffect| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|factorUsingYun| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|FiniteFieldFactorizationWithSizeParseBySideEffect| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|FiniteFieldFactorizationWithSizeParseBySideEffect| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|factorCantorZassenhaus| (*1 *2 *3 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|FiniteFieldCategory|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|FiniteFieldFactorizationWithSizeParseBySideEffect| *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|factorSquareFree| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|FiniteFieldFactorizationWithSizeParseBySideEffect| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |factorSquareFree| ((|List| |#2|) |#2|)) (SIGNATURE |factorCantorZassenhaus| ((|List| |#2|) |#2| (|NonNegativeInteger|))) (SIGNATURE |factor| ((|Factored| |#2|) |#2|)) (SIGNATURE |factorUsingYun| ((|Factored| |#2|) |#2|)) (SIGNATURE |factorUsingMusser| ((|Factored| |#2|) |#2|)) (SIGNATURE |irreducible?| ((|Boolean|) |#2|))) 
((|generalInterpolation| (((|Stream| (|Matrix| (|SparseUnivariatePolynomial| |#1|))) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#3|) (|NonNegativeInteger|) (|NonNegativeInteger|)) 54) (((|Matrix| (|SparseUnivariatePolynomial| |#1|)) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#3|) (|List| (|NonNegativeInteger|))) 42))) 
(((|FractionFreeFastGaussianFractions| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |generalInterpolation| ((|Matrix| (|SparseUnivariatePolynomial| |#1|)) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#3|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |generalInterpolation| ((|Stream| (|Matrix| (|SparseUnivariatePolynomial| |#1|))) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#3|) (|NonNegativeInteger|) (|NonNegativeInteger|)))) (|Join| (|IntegralDomain|) (|GcdDomain|)) (|FiniteAbelianMonoidRing| |#1| (|NonNegativeInteger|)) (|FiniteAbelianMonoidRing| (|Fraction| |#1|) (|NonNegativeInteger|))) (T |FractionFreeFastGaussianFractions|)) 
((|generalInterpolation| (*1 *2 *3 *4 *5 *6 *6) (AND (|isDomain| *3 (|List| *7)) (|isDomain| *4 (|Mapping| *7 (|NonNegativeInteger|) (|NonNegativeInteger|) *8)) (|isDomain| *5 (|Vector| *9)) (|isDomain| *6 (|NonNegativeInteger|)) (|ofCategory| *7 (|Join| (|IntegralDomain|) (|GcdDomain|))) (|ofCategory| *8 (|FiniteAbelianMonoidRing| *7 *6)) (|ofCategory| *9 (|FiniteAbelianMonoidRing| (|Fraction| *7) *6)) (|isDomain| *2 (|Stream| (|Matrix| (|SparseUnivariatePolynomial| *7)))) (|isDomain| *1 (|FractionFreeFastGaussianFractions| *7 *8 *9)))) (|generalInterpolation| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *3 (|List| *7)) (|isDomain| *4 (|Mapping| *7 (|NonNegativeInteger|) (|NonNegativeInteger|) *8)) (|isDomain| *5 (|Vector| *9)) (|isDomain| *6 (|List| (|NonNegativeInteger|))) (|ofCategory| *7 (|Join| (|IntegralDomain|) (|GcdDomain|))) (|ofCategory| *8 (|FiniteAbelianMonoidRing| *7 (|NonNegativeInteger|))) (|ofCategory| *9 (|FiniteAbelianMonoidRing| (|Fraction| *7) (|NonNegativeInteger|))) (|isDomain| *2 (|Matrix| (|SparseUnivariatePolynomial| *7))) (|isDomain| *1 (|FractionFreeFastGaussianFractions| *7 *8 *9))))) 
(CATEGORY |package| (SIGNATURE |generalInterpolation| ((|Matrix| (|SparseUnivariatePolynomial| |#1|)) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#3|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |generalInterpolation| ((|Stream| (|Matrix| (|SparseUnivariatePolynomial| |#1|))) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#3|) (|NonNegativeInteger|) (|NonNegativeInteger|)))) 
((|qShiftC| (((|List| |#1|) |#1| (|NonNegativeInteger|)) 21)) (|qShiftAction| ((|#1| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) 20)) (|interpolate| (((|Fraction| (|SparseUnivariatePolynomial| |#1|)) (|List| (|Fraction| |#1|)) (|List| (|Fraction| |#1|)) (|NonNegativeInteger|)) 75) (((|Fraction| (|SparseUnivariatePolynomial| |#1|)) (|List| |#1|) (|List| |#1|) (|NonNegativeInteger|)) 68)) (|generalInterpolation| (((|Stream| (|Matrix| (|SparseUnivariatePolynomial| |#1|))) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#2|) (|NonNegativeInteger|) (|NonNegativeInteger|)) 62) (((|Matrix| (|SparseUnivariatePolynomial| |#1|)) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#2|) (|List| (|NonNegativeInteger|))) 44)) (|generalCoefficient| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#2|) (|NonNegativeInteger|) (|Vector| (|SparseUnivariatePolynomial| |#1|))) 37)) (|fffg| (((|Matrix| (|SparseUnivariatePolynomial| |#1|)) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|Vector| (|SparseUnivariatePolynomial| |#1|))) (|List| (|NonNegativeInteger|))) 43)) (|ShiftC| (((|List| |#1|) (|NonNegativeInteger|)) 17)) (|ShiftAction| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) 11)) (|DiffC| (((|List| |#1|) (|NonNegativeInteger|)) 24)) (|DiffAction| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) 22))) 
(((|FractionFreeFastGaussian| |#1| |#2|) (CATEGORY |package| (SIGNATURE |fffg| ((|Matrix| (|SparseUnivariatePolynomial| |#1|)) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|Vector| (|SparseUnivariatePolynomial| |#1|))) (|List| (|NonNegativeInteger|)))) (SIGNATURE |interpolate| ((|Fraction| (|SparseUnivariatePolynomial| |#1|)) (|List| |#1|) (|List| |#1|) (|NonNegativeInteger|))) (SIGNATURE |interpolate| ((|Fraction| (|SparseUnivariatePolynomial| |#1|)) (|List| (|Fraction| |#1|)) (|List| (|Fraction| |#1|)) (|NonNegativeInteger|))) (SIGNATURE |generalInterpolation| ((|Matrix| (|SparseUnivariatePolynomial| |#1|)) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#2|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |generalInterpolation| ((|Stream| (|Matrix| (|SparseUnivariatePolynomial| |#1|))) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#2|) (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |generalCoefficient| (|#1| (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#2|) (|NonNegativeInteger|) (|Vector| (|SparseUnivariatePolynomial| |#1|)))) (SIGNATURE |ShiftAction| (|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|)) (SIGNATURE |ShiftC| ((|List| |#1|) (|NonNegativeInteger|))) (SIGNATURE |DiffAction| (|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|)) (SIGNATURE |DiffC| ((|List| |#1|) (|NonNegativeInteger|))) (SIGNATURE |qShiftAction| (|#1| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|)) (SIGNATURE |qShiftC| ((|List| |#1|) |#1| (|NonNegativeInteger|)))) (|Join| (|IntegralDomain|) (|GcdDomain|)) (|AbelianMonoidRing| |#1| (|NonNegativeInteger|))) (T |FractionFreeFastGaussian|)) 
((|qShiftC| (*1 *2 *3 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *3 (|Join| (|IntegralDomain|) (|GcdDomain|))) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|FractionFreeFastGaussian| *3 *5)) (|ofCategory| *5 (|AbelianMonoidRing| *3 *4)))) (|qShiftAction| (*1 *2 *2 *3 *3 *4) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *2 (|Join| (|IntegralDomain|) (|GcdDomain|))) (|isDomain| *1 (|FractionFreeFastGaussian| *2 *4)) (|ofCategory| *4 (|AbelianMonoidRing| *2 *3)))) (|DiffC| (*1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|GcdDomain|))) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|FractionFreeFastGaussian| *4 *5)) (|ofCategory| *5 (|AbelianMonoidRing| *4 *3)))) (|DiffAction| (*1 *2 *3 *3 *4) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *2 (|Join| (|IntegralDomain|) (|GcdDomain|))) (|isDomain| *1 (|FractionFreeFastGaussian| *2 *4)) (|ofCategory| *4 (|AbelianMonoidRing| *2 *3)))) (|ShiftC| (*1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|GcdDomain|))) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|FractionFreeFastGaussian| *4 *5)) (|ofCategory| *5 (|AbelianMonoidRing| *4 *3)))) (|ShiftAction| (*1 *2 *3 *3 *4) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *2 (|Join| (|IntegralDomain|) (|GcdDomain|))) (|isDomain| *1 (|FractionFreeFastGaussian| *2 *4)) (|ofCategory| *4 (|AbelianMonoidRing| *2 *3)))) (|generalCoefficient| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *3 (|Mapping| *2 (|NonNegativeInteger|) (|NonNegativeInteger|) *7)) (|isDomain| *4 (|Vector| *7)) (|isDomain| *5 (|NonNegativeInteger|)) (|isDomain| *6 (|Vector| (|SparseUnivariatePolynomial| *2))) (|ofCategory| *7 (|AbelianMonoidRing| *2 *5)) (|ofCategory| *2 (|Join| (|IntegralDomain|) (|GcdDomain|))) (|isDomain| *1 (|FractionFreeFastGaussian| *2 *7)))) (|generalInterpolation| (*1 *2 *3 *4 *5 *6 *6) (AND (|isDomain| *3 (|List| *7)) (|isDomain| *4 (|Mapping| *7 (|NonNegativeInteger|) (|NonNegativeInteger|) *8)) (|isDomain| *5 (|Vector| *8)) (|isDomain| *6 (|NonNegativeInteger|)) (|ofCategory| *7 (|Join| (|IntegralDomain|) (|GcdDomain|))) (|ofCategory| *8 (|AbelianMonoidRing| *7 *6)) (|isDomain| *2 (|Stream| (|Matrix| (|SparseUnivariatePolynomial| *7)))) (|isDomain| *1 (|FractionFreeFastGaussian| *7 *8)))) (|generalInterpolation| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *3 (|List| *7)) (|isDomain| *4 (|Mapping| *7 (|NonNegativeInteger|) (|NonNegativeInteger|) *8)) (|isDomain| *5 (|Vector| *8)) (|isDomain| *6 (|List| (|NonNegativeInteger|))) (|ofCategory| *7 (|Join| (|IntegralDomain|) (|GcdDomain|))) (|ofCategory| *8 (|AbelianMonoidRing| *7 (|NonNegativeInteger|))) (|isDomain| *2 (|Matrix| (|SparseUnivariatePolynomial| *7))) (|isDomain| *1 (|FractionFreeFastGaussian| *7 *8)))) (|interpolate| (*1 *2 *3 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| *5))) (|ofCategory| *5 (|Join| (|IntegralDomain|) (|GcdDomain|))) (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *2 (|Fraction| (|SparseUnivariatePolynomial| *5))) (|isDomain| *1 (|FractionFreeFastGaussian| *5 *6)) (|ofCategory| *6 (|AbelianMonoidRing| *5 *4)))) (|interpolate| (*1 *2 *3 *3 *4) (AND (|isDomain| *3 (|List| *5)) (|ofCategory| *5 (|Join| (|IntegralDomain|) (|GcdDomain|))) (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *2 (|Fraction| (|SparseUnivariatePolynomial| *5))) (|isDomain| *1 (|FractionFreeFastGaussian| *5 *6)) (|ofCategory| *6 (|AbelianMonoidRing| *5 *4)))) (|fffg| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|Mapping| *6 (|NonNegativeInteger|) (|Vector| (|SparseUnivariatePolynomial| *6)))) (|isDomain| *5 (|List| (|NonNegativeInteger|))) (|ofCategory| *6 (|Join| (|IntegralDomain|) (|GcdDomain|))) (|isDomain| *2 (|Matrix| (|SparseUnivariatePolynomial| *6))) (|isDomain| *1 (|FractionFreeFastGaussian| *6 *7)) (|ofCategory| *7 (|AbelianMonoidRing| *6 (|NonNegativeInteger|)))))) 
(CATEGORY |package| (SIGNATURE |fffg| ((|Matrix| (|SparseUnivariatePolynomial| |#1|)) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|Vector| (|SparseUnivariatePolynomial| |#1|))) (|List| (|NonNegativeInteger|)))) (SIGNATURE |interpolate| ((|Fraction| (|SparseUnivariatePolynomial| |#1|)) (|List| |#1|) (|List| |#1|) (|NonNegativeInteger|))) (SIGNATURE |interpolate| ((|Fraction| (|SparseUnivariatePolynomial| |#1|)) (|List| (|Fraction| |#1|)) (|List| (|Fraction| |#1|)) (|NonNegativeInteger|))) (SIGNATURE |generalInterpolation| ((|Matrix| (|SparseUnivariatePolynomial| |#1|)) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#2|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |generalInterpolation| ((|Stream| (|Matrix| (|SparseUnivariatePolynomial| |#1|))) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#2|) (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |generalCoefficient| (|#1| (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#2|) (|NonNegativeInteger|) (|Vector| (|SparseUnivariatePolynomial| |#1|)))) (SIGNATURE |ShiftAction| (|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|)) (SIGNATURE |ShiftC| ((|List| |#1|) (|NonNegativeInteger|))) (SIGNATURE |DiffAction| (|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|)) (SIGNATURE |DiffC| ((|List| |#1|) (|NonNegativeInteger|))) (SIGNATURE |qShiftAction| (|#1| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|)) (SIGNATURE |qShiftC| ((|List| |#1|) |#1| (|NonNegativeInteger|)))) 
((|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) 40)) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) 84)) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) 77)) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) 85)) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) 10)) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) 15))) 
(((|FiniteFieldFunctions| |#1|) (CATEGORY |package| (SIGNATURE |createZechTable| ((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |createMultiplicationTable| ((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |createMultiplicationMatrix| ((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))))) (SIGNATURE |sizeMultiplication| ((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))))) (SIGNATURE |createLowComplexityTable| ((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|))) (SIGNATURE |createLowComplexityNormalBasis| ((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)))) (|FiniteFieldCategory|)) (T |FiniteFieldFunctions|)) 
((|createLowComplexityNormalBasis| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Union| (|SparseUnivariatePolynomial| *4) (|Vector| (|List| (|Record| (|:| |value| *4) (|:| |index| (|SingleInteger|))))))) (|isDomain| *1 (|FiniteFieldFunctions| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))) (|createLowComplexityTable| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Vector| (|List| (|Record| (|:| |value| *4) (|:| |index| (|SingleInteger|)))))) (|isDomain| *1 (|FiniteFieldFunctions| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))) (|sizeMultiplication| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| (|List| (|Record| (|:| |value| *4) (|:| |index| (|SingleInteger|)))))) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FiniteFieldFunctions| *4)))) (|createMultiplicationMatrix| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| (|List| (|Record| (|:| |value| *4) (|:| |index| (|SingleInteger|)))))) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|FiniteFieldFunctions| *4)))) (|createMultiplicationTable| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Vector| (|List| (|Record| (|:| |value| *4) (|:| |index| (|SingleInteger|)))))) (|isDomain| *1 (|FiniteFieldFunctions| *4)))) (|createZechTable| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|PrimitiveArray| (|SingleInteger|))) (|isDomain| *1 (|FiniteFieldFunctions| *4))))) 
(CATEGORY |package| (SIGNATURE |createZechTable| ((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |createMultiplicationTable| ((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |createMultiplicationMatrix| ((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))))) (SIGNATURE |sizeMultiplication| ((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))))) (SIGNATURE |createLowComplexityTable| ((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|))) (SIGNATURE |createLowComplexityNormalBasis| ((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)))) 
((|coerce| ((|#1| |#3|) 84) ((|#3| |#1|) 68))) 
(((|FiniteFieldHomomorphisms| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |coerce| (|#3| |#1|)) (SIGNATURE |coerce| (|#1| |#3|))) (|FiniteAlgebraicExtensionField| |#2|) (|FiniteFieldCategory|) (|FiniteAlgebraicExtensionField| |#2|)) (T |FiniteFieldHomomorphisms|)) 
((|coerce| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) (|isDomain| *1 (|FiniteFieldHomomorphisms| *2 *4 *3)) (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))) (|coerce| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) (|isDomain| *1 (|FiniteFieldHomomorphisms| *3 *4 *2)) (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4))))) 
(CATEGORY |package| (SIGNATURE |coerce| (|#3| |#1|)) (SIGNATURE |coerce| (|#1| |#3|))) 
((|primitive?| (((|Boolean|) $) 50)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 21) (((|PositiveInteger|) $) 51)) (|nextItem| (((|Union| $ "failed") $) 16)) (|init| (($) 9)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 91)) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) 70) (((|NonNegativeInteger|) $) 59)) (|differentiate| (($ $ (|NonNegativeInteger|)) NIL) (($ $) 8)) (|createPrimitiveElement| (($) 44)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 33)) (|charthRoot| (((|Union| $ "failed") $) 39) (($ $) 38))) 
(((|FiniteFieldCategory&| |#1|) (CATEGORY |domain| (SIGNATURE |order| ((|PositiveInteger|) |#1|)) (SIGNATURE |discreteLog| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |primitive?| ((|Boolean|) |#1|)) (SIGNATURE |createPrimitiveElement| (|#1|)) (SIGNATURE |conditionP| ((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|))) (SIGNATURE |charthRoot| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |init| (|#1|)) (SIGNATURE |nextItem| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |discreteLog| ((|Union| (|NonNegativeInteger|) "failed") |#1| |#1|)) (SIGNATURE |order| ((|OnePointCompletion| (|PositiveInteger|)) |#1|)) (SIGNATURE |charthRoot| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)))) (|FiniteFieldCategory|)) (T |FiniteFieldCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |order| ((|PositiveInteger|) |#1|)) (SIGNATURE |discreteLog| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |primitive?| ((|Boolean|) |#1|)) (SIGNATURE |createPrimitiveElement| (|#1|)) (SIGNATURE |conditionP| ((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|))) (SIGNATURE |charthRoot| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |init| (|#1|)) (SIGNATURE |nextItem| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |discreteLog| ((|Union| (|NonNegativeInteger|) "failed") |#1| |#1|)) (SIGNATURE |order| ((|OnePointCompletion| (|PositiveInteger|)) |#1|)) (SIGNATURE |charthRoot| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) 90)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 73)) (|squareFree| (((|Factored| $) $) 72)) (|sizeLess?| (((|Boolean|) $ $) 58)) (|size| (((|NonNegativeInteger|)) 100)) (|sample| (($) 16 T CONST)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 84)) (|rem| (($ $ $) 54)) (|recip| (((|Union| $ "failed") $) 33)) (|random| (($) 103)) (|quo| (($ $ $) 55)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 50)) (|primitiveElement| (($) 88)) (|primitive?| (((|Boolean|) $) 87)) (|primeFrobenius| (($ $) 77) (($ $ (|NonNegativeInteger|)) 76)) (|prime?| (((|Boolean|) $) 71)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 79) (((|PositiveInteger|) $) 85)) (|one?| (((|Boolean|) $) 30)) (|nextItem| (((|Union| $ "failed") $) 99)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 51)) (|lookup| (((|PositiveInteger|) $) 102)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 70)) (|init| (($) 98 T CONST)) (|index| (($ (|PositiveInteger|)) 101)) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) 91)) (|factor| (((|Factored| $) $) 74)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 53) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 52)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 49)) (|euclideanSize| (((|NonNegativeInteger|) $) 57)) (|enumerate| (((|List| $)) 104)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 56)) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) 78) (((|NonNegativeInteger|) $) 86)) (|differentiate| (($ $ (|NonNegativeInteger|)) 96) (($ $) 94)) (|createPrimitiveElement| (($) 89)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 92)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42) (($ (|Fraction| (|Integer|))) 65)) (|charthRoot| (((|Union| $ "failed") $) 80) (($ $) 93)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 69)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $ (|NonNegativeInteger|)) 97) (($ $) 95)) (= (((|Boolean|) $ $) 6)) (/ (($ $ $) 64)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 68)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ (|Fraction| (|Integer|))) 67) (($ (|Fraction| (|Integer|)) $) 66))) 
(((|FiniteFieldCategory|) (|Category|)) (T |FiniteFieldCategory|)) 
((|charthRoot| (*1 *1 *1) (|ofCategory| *1 (|FiniteFieldCategory|))) (|conditionP| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|Matrix| *1)) (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|Vector| *1)))) (|factorsOfCyclicGroupSize| (*1 *2) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))))) (|tableForDiscreteLogarithm| (*1 *2 *3) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Table| (|PositiveInteger|) (|NonNegativeInteger|))))) (|createPrimitiveElement| (*1 *1) (|ofCategory| *1 (|FiniteFieldCategory|))) (|primitiveElement| (*1 *1) (|ofCategory| *1 (|FiniteFieldCategory|))) (|primitive?| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|Boolean|)))) (|discreteLog| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|order| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|PositiveInteger|)))) (|representationType| (*1 *2) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|Union| "prime" "polynomial" "normal" "cyclic"))))) 
(|Join| (|FieldOfPrimeCharacteristic|) (|Finite|) (|StepThrough|) (|DifferentialRing|) (CATEGORY |domain| (SIGNATURE |charthRoot| ($ $)) (SIGNATURE |conditionP| ((|Union| (|Vector| $) "failed") (|Matrix| $))) (SIGNATURE |factorsOfCyclicGroupSize| ((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|)))))) (SIGNATURE |tableForDiscreteLogarithm| ((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|))) (SIGNATURE |createPrimitiveElement| ($)) (SIGNATURE |primitiveElement| ($)) (SIGNATURE |primitive?| ((|Boolean|) $)) (SIGNATURE |discreteLog| ((|NonNegativeInteger|) $)) (SIGNATURE |order| ((|PositiveInteger|) $)) (SIGNATURE |representationType| ((|Union| "prime" "polynomial" "normal" "cyclic"))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DifferentialRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|FieldOfPrimeCharacteristic|) . T) ((|Finite|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| (|Fraction| (|Integer|))) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| (|Fraction| (|Integer|))) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightModule| (|Fraction| (|Integer|))) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|StepThrough|) . T) ((|UniqueFactorizationDomain|) . T)) 
((|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) 51)) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) 49))) 
(((|FunctionFieldIntegralBasis| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |integralBasis| ((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))))) (SIGNATURE |localIntegralBasis| ((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|))) (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $)))) (|UnivariatePolynomialCategory| |#1|) (|FramedAlgebra| |#1| |#2|)) (T |FunctionFieldIntegralBasis|)) 
((|localIntegralBasis| (*1 *2 *3) (AND (|ofCategory| *3 (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $))))) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Record| (|:| |basis| (|Matrix| *3)) (|:| |basisDen| *3) (|:| |basisInv| (|Matrix| *3)))) (|isDomain| *1 (|FunctionFieldIntegralBasis| *3 *4 *5)) (|ofCategory| *5 (|FramedAlgebra| *3 *4)))) (|integralBasis| (*1 *2) (AND (|ofCategory| *3 (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $))))) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Record| (|:| |basis| (|Matrix| *3)) (|:| |basisDen| *3) (|:| |basisInv| (|Matrix| *3)))) (|isDomain| *1 (|FunctionFieldIntegralBasis| *3 *4 *5)) (|ofCategory| *5 (|FramedAlgebra| *3 *4))))) 
(CATEGORY |package| (SIGNATURE |integralBasis| ((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))))) (SIGNATURE |localIntegralBasis| ((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|transcendent?| (((|Boolean|) $) NIL)) (|transcendenceDegree| (((|NonNegativeInteger|)) NIL)) (|trace| (((|PrimeField| |#1|) $) NIL) (($ $ (|PositiveInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeMultiplication| (((|NonNegativeInteger|)) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|size| (((|NonNegativeInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|PrimeField| |#1|) "failed") $) NIL)) (|retract| (((|PrimeField| |#1|) $) NIL)) (|represents| (($ (|Vector| (|PrimeField| |#1|))) NIL)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|primitiveElement| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|primitive?| (((|Boolean|) $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) NIL (OR (|has| (|PrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|PrimeField| |#1|) (|Finite|)))) (($ $) NIL (OR (|has| (|PrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|PrimeField| |#1|) (|Finite|))))) (|prime?| (((|Boolean|) $) NIL)) (|order| (((|PositiveInteger|) $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (((|OnePointCompletion| (|PositiveInteger|)) $) NIL (OR (|has| (|PrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|PrimeField| |#1|) (|Finite|))))) (|one?| (((|Boolean|) $) NIL)) (|normalElement| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|normal?| (((|Boolean|) $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|norm| (((|PrimeField| |#1|) $) NIL) (($ $ (|PositiveInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|nextItem| (((|Union| $ "failed") $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| (|PrimeField| |#1|)) $) NIL) (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|lookup| (((|PositiveInteger|) $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| (|PrimeField| |#1|)) $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|linearAssociatedLog| (((|SparseUnivariatePolynomial| (|PrimeField| |#1|)) $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (((|Union| (|SparseUnivariatePolynomial| (|PrimeField| |#1|)) "failed") $ $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| (|PrimeField| |#1|))) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|init| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)) CONST)) (|index| (($ (|PositiveInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|inGroundField?| (((|Boolean|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) NIL)) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) NIL)) (|generator| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|factor| (((|Factored| $) $) NIL)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) NIL) (((|PositiveInteger|)) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|enumerate| (((|List| $)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|discreteLog| (((|NonNegativeInteger|) $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (((|Union| (|NonNegativeInteger|) "failed") $ $) NIL (OR (|has| (|PrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|PrimeField| |#1|) (|Finite|))))) (|dimension| (((|CardinalNumber|)) NIL)) (|differentiate| (($ $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL) (((|PositiveInteger|) $) NIL)) (|definingPolynomial| (((|SparseUnivariatePolynomial| (|PrimeField| |#1|))) NIL)) (|createPrimitiveElement| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|createNormalElement| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|coordinates| (((|Vector| (|PrimeField| |#1|)) $) NIL) (((|Matrix| (|PrimeField| |#1|)) (|Vector| $)) NIL)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ (|PrimeField| |#1|)) NIL)) (|charthRoot| (($ $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (((|Union| $ "failed") $) NIL (OR (|has| (|PrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|PrimeField| |#1|) (|Finite|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|basis| (((|Vector| $)) NIL) (((|Vector| $) (|PositiveInteger|)) NIL)) (|associates?| (((|Boolean|) $ $) NIL)) (|algebraic?| (((|Boolean|) $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (|Frobenius| (($ $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (D (($ $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (= (((|Boolean|) $ $) NIL)) (/ (($ $ $) NIL) (($ $ (|PrimeField| |#1|)) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ $ (|PrimeField| |#1|)) NIL) (($ (|PrimeField| |#1|) $) NIL))) 
(((|FiniteFieldNormalBasis| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| (|PrimeField| |#1|)) (CATEGORY |package| (SIGNATURE |getMultiplicationTable| ((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|))))))) (SIGNATURE |getMultiplicationMatrix| ((|Matrix| (|PrimeField| |#1|)))) (SIGNATURE |sizeMultiplication| ((|NonNegativeInteger|))))) (|PositiveInteger|) (|PositiveInteger|)) (T |FiniteFieldNormalBasis|)) 
((|getMultiplicationTable| (*1 *2) (AND (|isDomain| *2 (|Vector| (|List| (|Record| (|:| |value| (|PrimeField| *3)) (|:| |index| (|SingleInteger|)))))) (|isDomain| *1 (|FiniteFieldNormalBasis| *3 *4)) (|ofType| *3 (|PositiveInteger|)) (|ofType| *4 (|PositiveInteger|)))) (|getMultiplicationMatrix| (*1 *2) (AND (|isDomain| *2 (|Matrix| (|PrimeField| *3))) (|isDomain| *1 (|FiniteFieldNormalBasis| *3 *4)) (|ofType| *3 (|PositiveInteger|)) (|ofType| *4 (|PositiveInteger|)))) (|sizeMultiplication| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FiniteFieldNormalBasis| *3 *4)) (|ofType| *3 (|PositiveInteger|)) (|ofType| *4 (|PositiveInteger|))))) 
(|Join| (|FiniteAlgebraicExtensionField| (|PrimeField| |#1|)) (CATEGORY |package| (SIGNATURE |getMultiplicationTable| ((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|))))))) (SIGNATURE |getMultiplicationMatrix| ((|Matrix| (|PrimeField| |#1|)))) (SIGNATURE |sizeMultiplication| ((|NonNegativeInteger|))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 74)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|transcendent?| (((|Boolean|) $) NIL)) (|transcendenceDegree| (((|NonNegativeInteger|)) NIL)) (|trace| ((|#1| $) 92) (($ $ (|PositiveInteger|)) 90 (|has| |#1| (|Finite|)))) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) 148 (|has| |#1| (|Finite|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeMultiplication| (((|NonNegativeInteger|)) 89)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|size| (((|NonNegativeInteger|)) 162 (|has| |#1| (|Finite|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 111)) (|retract| ((|#1| $) 91)) (|represents| (($ (|Vector| |#1|)) 57)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 187 (|has| |#1| (|Finite|)))) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) 158 (|has| |#1| (|Finite|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|primitiveElement| (($) 149 (|has| |#1| (|Finite|)))) (|primitive?| (((|Boolean|) $) NIL (|has| |#1| (|Finite|)))) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|)))) (($ $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|prime?| (((|Boolean|) $) NIL)) (|order| (((|PositiveInteger|) $) NIL (|has| |#1| (|Finite|))) (((|OnePointCompletion| (|PositiveInteger|)) $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|one?| (((|Boolean|) $) NIL)) (|normalElement| (($) 97 (|has| |#1| (|Finite|)))) (|normal?| (((|Boolean|) $) 175 (|has| |#1| (|Finite|)))) (|norm| ((|#1| $) 94) (($ $ (|PositiveInteger|)) 93 (|has| |#1| (|Finite|)))) (|nextItem| (((|Union| $ "failed") $) NIL (|has| |#1| (|Finite|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 188) (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|lookup| (((|PositiveInteger|) $) 133 (|has| |#1| (|Finite|)))) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) 73 (|has| |#1| (|Finite|)))) (|linearAssociatedLog| (((|SparseUnivariatePolynomial| |#1|) $) 70 (|has| |#1| (|Finite|))) (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) 82 (|has| |#1| (|Finite|)))) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) 69 (|has| |#1| (|Finite|)))) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 191)) (|init| (($) NIL (|has| |#1| (|Finite|)) CONST)) (|index| (($ (|PositiveInteger|)) 136 (|has| |#1| (|Finite|)))) (|inGroundField?| (((|Boolean|) $) 107)) (|hash| (((|SingleInteger|) $) NIL)) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) 83)) (|getMultiplicationMatrix| (((|Matrix| |#1|)) 87)) (|generator| (($) 96 (|has| |#1| (|Finite|)))) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) 150 (|has| |#1| (|Finite|)))) (|factor| (((|Factored| $) $) NIL)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) NIL) (((|PositiveInteger|)) 151)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|enumerate| (((|List| $)) NIL (|has| |#1| (|Finite|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|discreteLog| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|Finite|))) (((|Union| (|NonNegativeInteger|) "failed") $ $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|dimension| (((|CardinalNumber|)) NIL)) (|differentiate| (($ $) NIL (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL) (((|PositiveInteger|) $) 62)) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) 152)) (|createPrimitiveElement| (($) 132 (|has| |#1| (|Finite|)))) (|createNormalElement| (($) NIL (|has| |#1| (|Finite|)))) (|coordinates| (((|Vector| |#1|) $) 105) (((|Matrix| |#1|) (|Vector| $)) NIL)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (|has| |#1| (|Finite|)))) (|coerce| (((|OutputForm|) $) 123) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ |#1|) 56)) (|charthRoot| (($ $) NIL (|has| |#1| (|Finite|))) (((|Union| $ "failed") $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|characteristic| (((|NonNegativeInteger|)) 156)) (|basis| (((|Vector| $)) 172) (((|Vector| $) (|PositiveInteger|)) 100)) (|associates?| (((|Boolean|) $ $) NIL)) (|algebraic?| (((|Boolean|) $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) 30 T CONST)) (|One| (($) 22 T CONST)) (|Frobenius| (($ $) 106 (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) 98 (|has| |#1| (|Finite|)))) (D (($ $) NIL (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (= (((|Boolean|) $ $) 60)) (/ (($ $ $) 103) (($ $ |#1|) 104)) (- (($ $) 177) (($ $ $) 181)) (+ (($ $ $) 179)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) 137)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 185) (($ $ $) 142) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ $ |#1|) NIL) (($ |#1| $) 102))) 
(((|FiniteFieldNormalBasisExtensionByPolynomial| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| |#1|) (CATEGORY |package| (SIGNATURE |getMultiplicationTable| ((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))))) (SIGNATURE |getMultiplicationMatrix| ((|Matrix| |#1|))) (SIGNATURE |sizeMultiplication| ((|NonNegativeInteger|))))) (|FiniteFieldCategory|) (|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))))) (T |FiniteFieldNormalBasisExtensionByPolynomial|)) 
((|getMultiplicationTable| (*1 *2) (AND (|isDomain| *2 (|Vector| (|List| (|Record| (|:| |value| *3) (|:| |index| (|SingleInteger|)))))) (|isDomain| *1 (|FiniteFieldNormalBasisExtensionByPolynomial| *3 *4)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|Union| (|SparseUnivariatePolynomial| *3) *2)))) (|getMultiplicationMatrix| (*1 *2) (AND (|isDomain| *2 (|Matrix| *3)) (|isDomain| *1 (|FiniteFieldNormalBasisExtensionByPolynomial| *3 *4)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|Union| (|SparseUnivariatePolynomial| *3) (|Vector| (|List| (|Record| (|:| |value| *3) (|:| |index| (|SingleInteger|))))))))) (|sizeMultiplication| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FiniteFieldNormalBasisExtensionByPolynomial| *3 *4)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|Union| (|SparseUnivariatePolynomial| *3) (|Vector| (|List| (|Record| (|:| |value| *3) (|:| |index| (|SingleInteger|)))))))))) 
(|Join| (|FiniteAlgebraicExtensionField| |#1|) (CATEGORY |package| (SIGNATURE |getMultiplicationTable| ((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))))) (SIGNATURE |getMultiplicationMatrix| ((|Matrix| |#1|))) (SIGNATURE |sizeMultiplication| ((|NonNegativeInteger|))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|transcendent?| (((|Boolean|) $) NIL)) (|transcendenceDegree| (((|NonNegativeInteger|)) NIL)) (|trace| ((|#1| $) NIL) (($ $ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) NIL (|has| |#1| (|Finite|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeMultiplication| (((|NonNegativeInteger|)) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|size| (((|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL)) (|retract| ((|#1| $) NIL)) (|represents| (($ (|Vector| |#1|)) NIL)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL (|has| |#1| (|Finite|)))) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) NIL (|has| |#1| (|Finite|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|primitiveElement| (($) NIL (|has| |#1| (|Finite|)))) (|primitive?| (((|Boolean|) $) NIL (|has| |#1| (|Finite|)))) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|)))) (($ $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|prime?| (((|Boolean|) $) NIL)) (|order| (((|PositiveInteger|) $) NIL (|has| |#1| (|Finite|))) (((|OnePointCompletion| (|PositiveInteger|)) $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|one?| (((|Boolean|) $) NIL)) (|normalElement| (($) NIL (|has| |#1| (|Finite|)))) (|normal?| (((|Boolean|) $) NIL (|has| |#1| (|Finite|)))) (|norm| ((|#1| $) NIL) (($ $ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|nextItem| (((|Union| $ "failed") $) NIL (|has| |#1| (|Finite|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) NIL) (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|lookup| (((|PositiveInteger|) $) NIL (|has| |#1| (|Finite|)))) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) NIL (|has| |#1| (|Finite|)))) (|linearAssociatedLog| (((|SparseUnivariatePolynomial| |#1|) $) NIL (|has| |#1| (|Finite|))) (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) NIL (|has| |#1| (|Finite|)))) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) NIL (|has| |#1| (|Finite|)))) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|init| (($) NIL (|has| |#1| (|Finite|)) CONST)) (|index| (($ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|inGroundField?| (((|Boolean|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) NIL)) (|getMultiplicationMatrix| (((|Matrix| |#1|)) NIL)) (|generator| (($) NIL (|has| |#1| (|Finite|)))) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) NIL (|has| |#1| (|Finite|)))) (|factor| (((|Factored| $) $) NIL)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) NIL) (((|PositiveInteger|)) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|enumerate| (((|List| $)) NIL (|has| |#1| (|Finite|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|discreteLog| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|Finite|))) (((|Union| (|NonNegativeInteger|) "failed") $ $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|dimension| (((|CardinalNumber|)) NIL)) (|differentiate| (($ $) NIL (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL) (((|PositiveInteger|) $) NIL)) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) NIL)) (|createPrimitiveElement| (($) NIL (|has| |#1| (|Finite|)))) (|createNormalElement| (($) NIL (|has| |#1| (|Finite|)))) (|coordinates| (((|Vector| |#1|) $) NIL) (((|Matrix| |#1|) (|Vector| $)) NIL)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (|has| |#1| (|Finite|)))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ |#1|) NIL)) (|charthRoot| (($ $) NIL (|has| |#1| (|Finite|))) (((|Union| $ "failed") $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|basis| (((|Vector| $)) NIL) (((|Vector| $) (|PositiveInteger|)) NIL)) (|associates?| (((|Boolean|) $ $) NIL)) (|algebraic?| (((|Boolean|) $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (|Frobenius| (($ $) NIL (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (D (($ $) NIL (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (= (((|Boolean|) $ $) NIL)) (/ (($ $ $) NIL) (($ $ |#1|) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ $ |#1|) NIL) (($ |#1| $) NIL))) 
(((|FiniteFieldNormalBasisExtension| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| |#1|) (CATEGORY |package| (SIGNATURE |getMultiplicationTable| ((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))))) (SIGNATURE |getMultiplicationMatrix| ((|Matrix| |#1|))) (SIGNATURE |sizeMultiplication| ((|NonNegativeInteger|))))) (|FiniteFieldCategory|) (|PositiveInteger|)) (T |FiniteFieldNormalBasisExtension|)) 
((|getMultiplicationTable| (*1 *2) (AND (|isDomain| *2 (|Vector| (|List| (|Record| (|:| |value| *3) (|:| |index| (|SingleInteger|)))))) (|isDomain| *1 (|FiniteFieldNormalBasisExtension| *3 *4)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|PositiveInteger|)))) (|getMultiplicationMatrix| (*1 *2) (AND (|isDomain| *2 (|Matrix| *3)) (|isDomain| *1 (|FiniteFieldNormalBasisExtension| *3 *4)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|PositiveInteger|)))) (|sizeMultiplication| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FiniteFieldNormalBasisExtension| *3 *4)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|PositiveInteger|))))) 
(|Join| (|FiniteAlgebraicExtensionField| |#1|) (CATEGORY |package| (SIGNATURE |getMultiplicationTable| ((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))))) (SIGNATURE |getMultiplicationMatrix| ((|Matrix| |#1|))) (SIGNATURE |sizeMultiplication| ((|NonNegativeInteger|))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|transcendent?| (((|Boolean|) $) NIL)) (|transcendenceDegree| (((|NonNegativeInteger|)) NIL)) (|trace| (((|PrimeField| |#1|) $) NIL) (($ $ (|PositiveInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|size| (((|NonNegativeInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|PrimeField| |#1|) "failed") $) NIL)) (|retract| (((|PrimeField| |#1|) $) NIL)) (|represents| (($ (|Vector| (|PrimeField| |#1|))) NIL)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|primitiveElement| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|primitive?| (((|Boolean|) $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) NIL (OR (|has| (|PrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|PrimeField| |#1|) (|Finite|)))) (($ $) NIL (OR (|has| (|PrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|PrimeField| |#1|) (|Finite|))))) (|prime?| (((|Boolean|) $) NIL)) (|order| (((|PositiveInteger|) $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (((|OnePointCompletion| (|PositiveInteger|)) $) NIL (OR (|has| (|PrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|PrimeField| |#1|) (|Finite|))))) (|one?| (((|Boolean|) $) NIL)) (|normalElement| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|normal?| (((|Boolean|) $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|norm| (((|PrimeField| |#1|) $) NIL) (($ $ (|PositiveInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|nextItem| (((|Union| $ "failed") $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| (|PrimeField| |#1|)) $) NIL) (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|lookup| (((|PositiveInteger|) $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| (|PrimeField| |#1|)) $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|linearAssociatedLog| (((|SparseUnivariatePolynomial| (|PrimeField| |#1|)) $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (((|Union| (|SparseUnivariatePolynomial| (|PrimeField| |#1|)) "failed") $ $) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| (|PrimeField| |#1|))) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|init| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)) CONST)) (|index| (($ (|PositiveInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|inGroundField?| (((|Boolean|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|generator| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|factor| (((|Factored| $) $) NIL)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) NIL) (((|PositiveInteger|)) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|enumerate| (((|List| $)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|discreteLog| (((|NonNegativeInteger|) $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (((|Union| (|NonNegativeInteger|) "failed") $ $) NIL (OR (|has| (|PrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|PrimeField| |#1|) (|Finite|))))) (|dimension| (((|CardinalNumber|)) NIL)) (|differentiate| (($ $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL) (((|PositiveInteger|) $) NIL)) (|definingPolynomial| (((|SparseUnivariatePolynomial| (|PrimeField| |#1|))) NIL)) (|createPrimitiveElement| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|createNormalElement| (($) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|coordinates| (((|Vector| (|PrimeField| |#1|)) $) NIL) (((|Matrix| (|PrimeField| |#1|)) (|Vector| $)) NIL)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ (|PrimeField| |#1|)) NIL)) (|charthRoot| (($ $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (((|Union| $ "failed") $) NIL (OR (|has| (|PrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|PrimeField| |#1|) (|Finite|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|basis| (((|Vector| $)) NIL) (((|Vector| $) (|PositiveInteger|)) NIL)) (|associates?| (((|Boolean|) $ $) NIL)) (|algebraic?| (((|Boolean|) $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (|Frobenius| (($ $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (D (($ $) NIL (|has| (|PrimeField| |#1|) (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|PrimeField| |#1|) (|Finite|)))) (= (((|Boolean|) $ $) NIL)) (/ (($ $ $) NIL) (($ $ (|PrimeField| |#1|)) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ $ (|PrimeField| |#1|)) NIL) (($ (|PrimeField| |#1|) $) NIL))) 
(((|FiniteField| |#1| |#2|) (|FiniteAlgebraicExtensionField| (|PrimeField| |#1|)) (|PositiveInteger|) (|PositiveInteger|)) (T |FiniteField|)) 
NIL 
(|FiniteAlgebraicExtensionField| (|PrimeField| |#1|)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|transcendent?| (((|Boolean|) $) NIL)) (|transcendenceDegree| (((|NonNegativeInteger|)) NIL)) (|trace| ((|#1| $) NIL) (($ $ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) 119 (|has| |#1| (|Finite|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|size| (((|NonNegativeInteger|)) 138 (|has| |#1| (|Finite|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 91)) (|retract| ((|#1| $) 88)) (|represents| (($ (|Vector| |#1|)) 83)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 115 (|has| |#1| (|Finite|)))) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) 80 (|has| |#1| (|Finite|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|primitiveElement| (($) 39 (|has| |#1| (|Finite|)))) (|primitive?| (((|Boolean|) $) NIL (|has| |#1| (|Finite|)))) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|)))) (($ $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|prime?| (((|Boolean|) $) NIL)) (|order| (((|PositiveInteger|) $) NIL (|has| |#1| (|Finite|))) (((|OnePointCompletion| (|PositiveInteger|)) $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|one?| (((|Boolean|) $) NIL)) (|normalElement| (($) 120 (|has| |#1| (|Finite|)))) (|normal?| (((|Boolean|) $) 72 (|has| |#1| (|Finite|)))) (|norm| ((|#1| $) 38) (($ $ (|PositiveInteger|)) 40 (|has| |#1| (|Finite|)))) (|nextItem| (((|Union| $ "failed") $) NIL (|has| |#1| (|Finite|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 62) (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|lookup| (((|PositiveInteger|) $) 95 (|has| |#1| (|Finite|)))) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) NIL (|has| |#1| (|Finite|)))) (|linearAssociatedLog| (((|SparseUnivariatePolynomial| |#1|) $) NIL (|has| |#1| (|Finite|))) (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) NIL (|has| |#1| (|Finite|)))) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) NIL (|has| |#1| (|Finite|)))) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|init| (($) NIL (|has| |#1| (|Finite|)) CONST)) (|index| (($ (|PositiveInteger|)) 93 (|has| |#1| (|Finite|)))) (|inGroundField?| (((|Boolean|) $) 140)) (|hash| (((|SingleInteger|) $) NIL)) (|generator| (($) 35 (|has| |#1| (|Finite|)))) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) 113 (|has| |#1| (|Finite|)))) (|factor| (((|Factored| $) $) NIL)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) NIL) (((|PositiveInteger|)) 137)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|enumerate| (((|List| $)) NIL (|has| |#1| (|Finite|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|discreteLog| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|Finite|))) (((|Union| (|NonNegativeInteger|) "failed") $ $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|dimension| (((|CardinalNumber|)) NIL)) (|differentiate| (($ $) NIL (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL) (((|PositiveInteger|) $) 56)) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) 86)) (|createPrimitiveElement| (($) 125 (|has| |#1| (|Finite|)))) (|createNormalElement| (($) NIL (|has| |#1| (|Finite|)))) (|coordinates| (((|Vector| |#1|) $) 50) (((|Matrix| |#1|) (|Vector| $)) NIL)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (|has| |#1| (|Finite|)))) (|coerce| (((|OutputForm|) $) 136) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ |#1|) 85)) (|charthRoot| (($ $) NIL (|has| |#1| (|Finite|))) (((|Union| $ "failed") $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|characteristic| (((|NonNegativeInteger|)) 142)) (|basis| (((|Vector| $)) 107) (((|Vector| $) (|PositiveInteger|)) 46)) (|associates?| (((|Boolean|) $ $) NIL)) (|algebraic?| (((|Boolean|) $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) 109 T CONST)) (|One| (($) 31 T CONST)) (|Frobenius| (($ $) 65 (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (D (($ $) NIL (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (= (((|Boolean|) $ $) 105)) (/ (($ $ $) 97) (($ $ |#1|) 98)) (- (($ $) 78) (($ $ $) 103)) (+ (($ $ $) 101)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 41) (($ $ (|Integer|)) 128)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 76) (($ $ $) 53) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ $ |#1|) NIL) (($ |#1| $) 74))) 
(((|FiniteFieldExtensionByPolynomial| |#1| |#2|) (|FiniteAlgebraicExtensionField| |#1|) (|FiniteFieldCategory|) (|SparseUnivariatePolynomial| |#1|)) (T |FiniteFieldExtensionByPolynomial|)) 
NIL 
(|FiniteAlgebraicExtensionField| |#1|) 
((|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) 51))) 
(((|FiniteFieldPolynomialPackage2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rootOfIrreduciblePoly| (|#1| (|SparseUnivariatePolynomial| |#2|)))) (|Join| (|FieldOfPrimeCharacteristic|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |lookup| ((|PositiveInteger|) |#1|)) (SIGNATURE |basis| ((|Vector| |#1|) (|PositiveInteger|))) (SIGNATURE |Frobenius| (|#1| |#1|)))) (|FiniteFieldCategory|)) (T |FiniteFieldPolynomialPackage2|)) 
((|rootOfIrreduciblePoly| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|ofCategory| *2 (|Join| (|FieldOfPrimeCharacteristic|) (CATEGORY |package| (SIGNATURE |coerce| (*2 *4)) (SIGNATURE |lookup| ((|PositiveInteger|) *2)) (SIGNATURE |basis| ((|Vector| *2) (|PositiveInteger|))) (SIGNATURE |Frobenius| (*2 *2))))) (|isDomain| *1 (|FiniteFieldPolynomialPackage2| *2 *4))))) 
(CATEGORY |package| (SIGNATURE |rootOfIrreduciblePoly| (|#1| (|SparseUnivariatePolynomial| |#2|)))) 
((|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) 36)) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) 109) (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) 108)) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) 81)) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) 71)) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) 73)) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) 69)) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) 85)) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) 97)) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) 100)) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) 99)) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) 98)) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) 94)) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) 62)) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) 103)) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) 106)) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) 105)) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) 104)) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) 101))) 
(((|FiniteFieldPolynomialPackage| |#1|) (CATEGORY |package| (SIGNATURE |primitive?| ((|Boolean|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |normal?| ((|Boolean|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |numberOfIrreduciblePoly| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |numberOfPrimitivePoly| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |numberOfNormalPoly| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |createIrreduciblePoly| ((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|))) (SIGNATURE |createPrimitivePoly| ((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|))) (SIGNATURE |createNormalPoly| ((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|))) (SIGNATURE |createNormalPrimitivePoly| ((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|))) (SIGNATURE |createPrimitiveNormalPoly| ((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|))) (SIGNATURE |nextIrreduciblePoly| ((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |nextPrimitivePoly| ((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |nextNormalPoly| ((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |nextNormalPrimitivePoly| ((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |nextPrimitiveNormalPoly| ((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |random| ((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|))) (SIGNATURE |random| ((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |leastAffineMultiple| ((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |reducedQPowers| ((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)))) (|FiniteFieldCategory|)) (T |FiniteFieldPolynomialPackage|)) 
((|reducedQPowers| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|PrimitiveArray| (|SparseUnivariatePolynomial| *4))) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4)) (|isDomain| *3 (|SparseUnivariatePolynomial| *4)))) (|leastAffineMultiple| (*1 *2 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3)))) (|random| (*1 *2 *3 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))) (|random| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))) (|nextPrimitiveNormalPoly| (*1 *2 *2) (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3)))) (|nextNormalPrimitivePoly| (*1 *2 *2) (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3)))) (|nextNormalPoly| (*1 *2 *2) (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3)))) (|nextPrimitivePoly| (*1 *2 *2) (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3)))) (|nextIrreduciblePoly| (*1 *2 *2) (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3)))) (|createPrimitiveNormalPoly| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))) (|createNormalPrimitivePoly| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))) (|createNormalPoly| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))) (|createPrimitivePoly| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))) (|createIrreduciblePoly| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))) (|numberOfNormalPoly| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3)) (|ofCategory| *3 (|FiniteFieldCategory|)))) (|numberOfPrimitivePoly| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3)) (|ofCategory| *3 (|FiniteFieldCategory|)))) (|numberOfIrreduciblePoly| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3)) (|ofCategory| *3 (|FiniteFieldCategory|)))) (|normal?| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4)))) (|primitive?| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4))))) 
(CATEGORY |package| (SIGNATURE |primitive?| ((|Boolean|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |normal?| ((|Boolean|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |numberOfIrreduciblePoly| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |numberOfPrimitivePoly| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |numberOfNormalPoly| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |createIrreduciblePoly| ((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|))) (SIGNATURE |createPrimitivePoly| ((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|))) (SIGNATURE |createNormalPoly| ((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|))) (SIGNATURE |createNormalPrimitivePoly| ((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|))) (SIGNATURE |createPrimitiveNormalPoly| ((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|))) (SIGNATURE |nextIrreduciblePoly| ((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |nextPrimitivePoly| ((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |nextNormalPoly| ((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |nextNormalPrimitivePoly| ((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |nextPrimitiveNormalPoly| ((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |random| ((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|))) (SIGNATURE |random| ((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |leastAffineMultiple| ((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |reducedQPowers| ((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)))) 
((|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) 33))) 
(((|FiniteFieldSolveLinearPolynomialEquation| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquation| ((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|))) (|FiniteFieldCategory|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| |#2|)) (T |FiniteFieldSolveLinearPolynomialEquation|)) 
((|solveLinearPolynomialEquation| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *1 (|FiniteFieldSolveLinearPolynomialEquation| *4 *5 *3))))) 
(CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquation| ((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|))) 
((|Yun| (((|Factored| |#2|) |#2|) 46)) (|Musser| (((|Factored| |#2|) |#2|) 36))) 
(((|FiniteFieldSquareFreeDecomposition| |#1| |#2|) (CATEGORY |package| (SIGNATURE |Musser| ((|Factored| |#2|) |#2|)) (SIGNATURE |Yun| ((|Factored| |#2|) |#2|))) (|FiniteFieldCategory|) (|UnivariatePolynomialCategory| |#1|)) (T |FiniteFieldSquareFreeDecomposition|)) 
((|Yun| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|FiniteFieldSquareFreeDecomposition| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|Musser| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|FiniteFieldSquareFreeDecomposition| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |Musser| ((|Factored| |#2|) |#2|)) (SIGNATURE |Yun| ((|Factored| |#2|) |#2|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|transcendent?| (((|Boolean|) $) NIL)) (|transcendenceDegree| (((|NonNegativeInteger|)) NIL)) (|trace| ((|#1| $) NIL) (($ $ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) NIL (|has| |#1| (|Finite|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|size| (((|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL)) (|retract| ((|#1| $) NIL)) (|represents| (($ (|Vector| |#1|)) NIL)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL (|has| |#1| (|Finite|)))) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) NIL (|has| |#1| (|Finite|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|primitiveElement| (($) NIL (|has| |#1| (|Finite|)))) (|primitive?| (((|Boolean|) $) NIL (|has| |#1| (|Finite|)))) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|)))) (($ $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|prime?| (((|Boolean|) $) NIL)) (|order| (((|PositiveInteger|) $) NIL (|has| |#1| (|Finite|))) (((|OnePointCompletion| (|PositiveInteger|)) $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|one?| (((|Boolean|) $) NIL)) (|normalElement| (($) NIL (|has| |#1| (|Finite|)))) (|normal?| (((|Boolean|) $) NIL (|has| |#1| (|Finite|)))) (|norm| ((|#1| $) NIL) (($ $ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|nextItem| (((|Union| $ "failed") $) NIL (|has| |#1| (|Finite|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) NIL) (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|lookup| (((|PositiveInteger|) $) NIL (|has| |#1| (|Finite|)))) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) NIL (|has| |#1| (|Finite|)))) (|linearAssociatedLog| (((|SparseUnivariatePolynomial| |#1|) $) NIL (|has| |#1| (|Finite|))) (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) NIL (|has| |#1| (|Finite|)))) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) NIL (|has| |#1| (|Finite|)))) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|init| (($) NIL (|has| |#1| (|Finite|)) CONST)) (|index| (($ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|inGroundField?| (((|Boolean|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|generator| (($) NIL (|has| |#1| (|Finite|)))) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) NIL (|has| |#1| (|Finite|)))) (|factor| (((|Factored| $) $) NIL)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) NIL) (((|PositiveInteger|)) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|enumerate| (((|List| $)) NIL (|has| |#1| (|Finite|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|discreteLog| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|Finite|))) (((|Union| (|NonNegativeInteger|) "failed") $ $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|dimension| (((|CardinalNumber|)) NIL)) (|differentiate| (($ $) NIL (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL) (((|PositiveInteger|) $) NIL)) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) NIL)) (|createPrimitiveElement| (($) NIL (|has| |#1| (|Finite|)))) (|createNormalElement| (($) NIL (|has| |#1| (|Finite|)))) (|coordinates| (((|Vector| |#1|) $) NIL) (((|Matrix| |#1|) (|Vector| $)) NIL)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (|has| |#1| (|Finite|)))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ |#1|) NIL)) (|charthRoot| (($ $) NIL (|has| |#1| (|Finite|))) (((|Union| $ "failed") $) NIL (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|basis| (((|Vector| $)) NIL) (((|Vector| $) (|PositiveInteger|)) NIL)) (|associates?| (((|Boolean|) $ $) NIL)) (|algebraic?| (((|Boolean|) $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (|Frobenius| (($ $) NIL (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (D (($ $) NIL (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (= (((|Boolean|) $ $) NIL)) (/ (($ $ $) NIL) (($ $ |#1|) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ $ |#1|) NIL) (($ |#1| $) NIL))) 
(((|FiniteFieldExtension| |#1| |#2|) (|FiniteAlgebraicExtensionField| |#1|) (|FiniteFieldCategory|) (|PositiveInteger|)) (T |FiniteFieldExtension|)) 
NIL 
(|FiniteAlgebraicExtensionField| |#1|) 
((|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) 31)) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) 42)) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) 38))) 
(((|FGLMIfCanPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |zeroDimensional?| ((|Boolean|) (|List| (|Polynomial| |#1|)))) (SIGNATURE |fglmIfCan| ((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|)))) (SIGNATURE |groebner| ((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))))) (|GcdDomain|) (|List| (|Symbol|))) (T |FGLMIfCanPackage|)) 
((|groebner| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|Polynomial| *3))) (|ofCategory| *3 (|GcdDomain|)) (|isDomain| *1 (|FGLMIfCanPackage| *3 *4)) (|ofType| *4 (|List| (|Symbol|))))) (|fglmIfCan| (*1 *2 *2) (|partial| AND (|isDomain| *2 (|List| (|Polynomial| *3))) (|ofCategory| *3 (|GcdDomain|)) (|isDomain| *1 (|FGLMIfCanPackage| *3 *4)) (|ofType| *4 (|List| (|Symbol|))))) (|zeroDimensional?| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Polynomial| *4))) (|ofCategory| *4 (|GcdDomain|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FGLMIfCanPackage| *4 *5)) (|ofType| *5 (|List| (|Symbol|)))))) 
(CATEGORY |package| (SIGNATURE |zeroDimensional?| ((|Boolean|) (|List| (|Polynomial| |#1|)))) (SIGNATURE |fglmIfCan| ((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|)))) (SIGNATURE |groebner| ((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))))) 
((~= (((|Boolean|) $ $) NIL)) (|size| (((|NonNegativeInteger|) $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL)) (|retract| ((|#1| $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|one?| (((|Boolean|) $) 14)) (|nthFactor| ((|#1| $ (|Integer|)) NIL)) (|nthExpon| (((|Integer|) $ (|Integer|)) NIL)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 32)) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) 24)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 26)) (|hash| (((|SingleInteger|) $) NIL)) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) 28)) (|conjugate| (($ $ $) NIL)) (|commutator| (($ $ $) NIL)) (|coerce| (((|OutputForm|) $) 38) (($ |#1|) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|One| (($) 9 T CONST)) (= (((|Boolean|) $ $) NIL)) (/ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL) (($ |#1| (|Integer|)) 17)) (* (($ $ $) 43) (($ |#1| $) 21) (($ $ |#1|) 19))) 
(((|FreeGroup| |#1|) (|Join| (|Group|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE * ($ |#1| $)) (SIGNATURE * ($ $ |#1|)) (SIGNATURE ** ($ |#1| (|Integer|))) (SIGNATURE |size| ((|NonNegativeInteger|) $)) (SIGNATURE |nthExpon| ((|Integer|) $ (|Integer|))) (SIGNATURE |nthFactor| (|#1| $ (|Integer|))) (SIGNATURE |mapExpon| ($ (|Mapping| (|Integer|) (|Integer|)) $)) (SIGNATURE |mapGen| ($ (|Mapping| |#1| |#1|) $)) (SIGNATURE |factors| ((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $)))) (|SetCategory|)) (T |FreeGroup|)) 
((* (*1 *1 *2 *1) (AND (|isDomain| *1 (|FreeGroup| *2)) (|ofCategory| *2 (|SetCategory|)))) (* (*1 *1 *1 *2) (AND (|isDomain| *1 (|FreeGroup| *2)) (|ofCategory| *2 (|SetCategory|)))) (** (*1 *1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|FreeGroup| *2)) (|ofCategory| *2 (|SetCategory|)))) (|size| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FreeGroup| *3)) (|ofCategory| *3 (|SetCategory|)))) (|nthExpon| (*1 *2 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|FreeGroup| *3)) (|ofCategory| *3 (|SetCategory|)))) (|nthFactor| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|FreeGroup| *2)) (|ofCategory| *2 (|SetCategory|)))) (|mapExpon| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Integer|) (|Integer|))) (|isDomain| *1 (|FreeGroup| *3)) (|ofCategory| *3 (|SetCategory|)))) (|mapGen| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|FreeGroup| *3)))) (|factors| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| (|Integer|))))) (|isDomain| *1 (|FreeGroup| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(|Join| (|Group|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE * ($ |#1| $)) (SIGNATURE * ($ $ |#1|)) (SIGNATURE ** ($ |#1| (|Integer|))) (SIGNATURE |size| ((|NonNegativeInteger|) $)) (SIGNATURE |nthExpon| ((|Integer|) $ (|Integer|))) (SIGNATURE |nthFactor| (|#1| $ (|Integer|))) (SIGNATURE |mapExpon| ($ (|Mapping| (|Integer|) (|Integer|)) $)) (SIGNATURE |mapGen| ($ (|Mapping| |#1| |#1|) $)) (SIGNATURE |factors| ((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $)))) 
((|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 13)) (|unitCanonical| (($ $) 14)) (|squareFree| (((|Factored| $) $) 29)) (|prime?| (((|Boolean|) $) 25)) (|inv| (($ $) 18)) (|gcd| (($ $ $) 22) (($ (|List| $)) NIL)) (|factor| (((|Factored| $) $) 30)) (|exquo| (((|Union| $ "failed") $ $) 21)) (|euclideanSize| (((|NonNegativeInteger|) $) 24)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 34)) (|associates?| (((|Boolean|) $ $) 15)) (/ (($ $ $) 32))) 
(((|Field&| |#1|) (CATEGORY |domain| (SIGNATURE / (|#1| |#1| |#1|)) (SIGNATURE |inv| (|#1| |#1|)) (SIGNATURE |prime?| ((|Boolean|) |#1|)) (SIGNATURE |squareFree| ((|Factored| |#1|) |#1|)) (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) (SIGNATURE |divide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |euclideanSize| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |gcd| (|#1| (|List| |#1|))) (SIGNATURE |gcd| (|#1| |#1| |#1|)) (SIGNATURE |associates?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |unitCanonical| (|#1| |#1|)) (SIGNATURE |unitNormal| ((|Record| (|:| |unit| |#1|) (|:| |canonical| |#1|) (|:| |associate| |#1|)) |#1|)) (SIGNATURE |exquo| ((|Union| |#1| "failed") |#1| |#1|))) (|Field|)) (T |Field&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE / (|#1| |#1| |#1|)) (SIGNATURE |inv| (|#1| |#1|)) (SIGNATURE |prime?| ((|Boolean|) |#1|)) (SIGNATURE |squareFree| ((|Factored| |#1|) |#1|)) (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) (SIGNATURE |divide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |euclideanSize| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |gcd| (|#1| (|List| |#1|))) (SIGNATURE |gcd| (|#1| |#1| |#1|)) (SIGNATURE |associates?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |unitCanonical| (|#1| |#1|)) (SIGNATURE |unitNormal| ((|Record| (|:| |unit| |#1|) (|:| |canonical| |#1|) (|:| |associate| |#1|)) |#1|)) (SIGNATURE |exquo| ((|Union| |#1| "failed") |#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 73)) (|squareFree| (((|Factored| $) $) 72)) (|sizeLess?| (((|Boolean|) $ $) 58)) (|sample| (($) 16 T CONST)) (|rem| (($ $ $) 54)) (|recip| (((|Union| $ "failed") $) 33)) (|quo| (($ $ $) 55)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 50)) (|prime?| (((|Boolean|) $) 71)) (|one?| (((|Boolean|) $) 30)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 51)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 70)) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|factor| (((|Factored| $) $) 74)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 53) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 52)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 49)) (|euclideanSize| (((|NonNegativeInteger|) $) 57)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 56)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42) (($ (|Fraction| (|Integer|))) 65)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 69)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (/ (($ $ $) 64)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 68)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ (|Fraction| (|Integer|))) 67) (($ (|Fraction| (|Integer|)) $) 66))) 
(((|Field|) (|Category|)) (T |Field|)) 
((/ (*1 *1 *1 *1) (|ofCategory| *1 (|Field|)))) 
(|Join| (|EuclideanDomain|) (|UniqueFactorizationDomain|) (|DivisionRing|) (CATEGORY |domain| (SIGNATURE / ($ $ $)) (ATTRIBUTE |canonicalUnitNormal|) (ATTRIBUTE |canonicalsClosed|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| (|Fraction| (|Integer|))) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| (|Fraction| (|Integer|))) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightModule| (|Fraction| (|Integer|))) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|UniqueFactorizationDomain|) . T)) 
((~= (((|Boolean|) $ $) 7)) (|write!| ((|#2| $ |#2|) 13)) (|reopen!| (($ $ (|String|)) 18)) (|read!| ((|#2| $) 14)) (|open| (($ |#1|) 20) (($ |#1| (|String|)) 19)) (|name| ((|#1| $) 16)) (|latex| (((|String|) $) 9)) (|iomode| (((|String|) $) 15)) (|hash| (((|SingleInteger|) $) 10)) (|flush| (((|Void|) $) 12)) (|coerce| (((|OutputForm|) $) 11)) (|close!| (($ $) 17)) (= (((|Boolean|) $ $) 6))) 
(((|FileCategory| |#1| |#2|) (|Category|) (|SetCategory|) (|SetCategory|)) (T |FileCategory|)) 
((|open| (*1 *1 *2) (AND (|ofCategory| *1 (|FileCategory| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|open| (*1 *1 *2 *3) (AND (|isDomain| *3 (|String|)) (|ofCategory| *1 (|FileCategory| *2 *4)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)))) (|reopen!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|String|)) (|ofCategory| *1 (|FileCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)))) (|close!| (*1 *1 *1) (AND (|ofCategory| *1 (|FileCategory| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|name| (*1 *2 *1) (AND (|ofCategory| *1 (|FileCategory| *2 *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)))) (|iomode| (*1 *2 *1) (AND (|ofCategory| *1 (|FileCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|String|)))) (|read!| (*1 *2 *1) (AND (|ofCategory| *1 (|FileCategory| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)))) (|write!| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|FileCategory| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)))) (|flush| (*1 *2 *1) (AND (|ofCategory| *1 (|FileCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Void|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |open| ($ |t#1|)) (SIGNATURE |open| ($ |t#1| (|String|))) (SIGNATURE |reopen!| ($ $ (|String|))) (SIGNATURE |close!| ($ $)) (SIGNATURE |name| (|t#1| $)) (SIGNATURE |iomode| ((|String|) $)) (SIGNATURE |read!| (|t#2| $)) (SIGNATURE |write!| (|t#2| $ |t#2|)) (SIGNATURE |flush| ((|Void|) $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|write!| ((|#1| $ |#1|) 29)) (|reopen!| (($ $ (|String|)) 22)) (|readIfCan!| (((|Union| |#1| "failed") $) 28)) (|read!| ((|#1| $) 26)) (|open| (($ (|FileName|)) 21) (($ (|FileName|) (|String|)) 20)) (|name| (((|FileName|) $) 24)) (|latex| (((|String|) $) NIL)) (|iomode| (((|String|) $) 25)) (|hash| (((|SingleInteger|) $) NIL)) (|flush| (((|Void|) $) 31)) (|coerce| (((|OutputForm|) $) 19)) (|close!| (($ $) 23)) (= (((|Boolean|) $ $) 18))) 
(((|File| |#1|) (|Join| (|FileCategory| (|FileName|) |#1|) (CATEGORY |domain| (SIGNATURE |readIfCan!| ((|Union| |#1| "failed") $)))) (|SetCategory|)) (T |File|)) 
((|readIfCan!| (*1 *2 *1) (|partial| AND (|isDomain| *1 (|File| *2)) (|ofCategory| *2 (|SetCategory|))))) 
(|Join| (|FileCategory| (|FileName|) |#1|) (CATEGORY |domain| (SIGNATURE |readIfCan!| ((|Union| |#1| "failed") $)))) 
((|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) 62)) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) 120)) (|rightTrace| ((|#2| $) 32)) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) 124)) (|rightRecip| (((|Union| $ "failed") $) 76)) (|rightNorm| ((|#2| $) 35)) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) 84)) (|rightDiscriminant| ((|#2| (|Vector| $)) 107)) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) 28)) (|rightAlternative?| (((|Boolean|)) 101)) (|represents| (($ (|Vector| |#2|) (|Vector| $)) 114)) (|recip| (((|Union| $ "failed") $) 80)) (|noncommutativeJordanAlgebra?| (((|Boolean|)) 96)) (|lieAlgebra?| (((|Boolean|)) 91)) (|lieAdmissible?| (((|Boolean|)) 54)) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) 118)) (|leftTrace| ((|#2| $) 31)) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) 123)) (|leftRecip| (((|Union| $ "failed") $) 74)) (|leftNorm| ((|#2| $) 34)) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) 83)) (|leftDiscriminant| ((|#2| (|Vector| $)) 105)) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) 26)) (|leftAlternative?| (((|Boolean|)) 100)) (|jordanAlgebra?| (((|Boolean|)) 93)) (|jordanAdmissible?| (((|Boolean|)) 52)) (|jacobiIdentity?| (((|Boolean|)) 88)) (|flexible?| (((|Boolean|)) 102)) (|coordinates| (((|Vector| |#2|) $ (|Vector| $)) NIL) (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) 112)) (|commutative?| (((|Boolean|)) 98)) (|associatorDependence| (((|List| (|Vector| |#2|))) 87)) (|associative?| (((|Boolean|)) 99)) (|antiCommutative?| (((|Boolean|)) 97)) (|antiAssociative?| (((|Boolean|)) 46)) (|alternative?| (((|Boolean|)) 103))) 
(((|FiniteRankNonAssociativeAlgebra&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |rightMinimalPolynomial| ((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |leftMinimalPolynomial| ((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |associatorDependence| ((|List| (|Vector| |#2|)))) (SIGNATURE |rightRecip| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |leftRecip| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |recip| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |lieAlgebra?| ((|Boolean|))) (SIGNATURE |jordanAlgebra?| ((|Boolean|))) (SIGNATURE |noncommutativeJordanAlgebra?| ((|Boolean|))) (SIGNATURE |jordanAdmissible?| ((|Boolean|))) (SIGNATURE |lieAdmissible?| ((|Boolean|))) (SIGNATURE |jacobiIdentity?| ((|Boolean|))) (SIGNATURE |alternative?| ((|Boolean|))) (SIGNATURE |flexible?| ((|Boolean|))) (SIGNATURE |rightAlternative?| ((|Boolean|))) (SIGNATURE |leftAlternative?| ((|Boolean|))) (SIGNATURE |antiAssociative?| ((|Boolean|))) (SIGNATURE |associative?| ((|Boolean|))) (SIGNATURE |antiCommutative?| ((|Boolean|))) (SIGNATURE |commutative?| ((|Boolean|))) (SIGNATURE |rightCharacteristicPolynomial| ((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |leftCharacteristicPolynomial| ((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |rightTraceMatrix| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |leftTraceMatrix| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |rightDiscriminant| (|#2| (|Vector| |#1|))) (SIGNATURE |leftDiscriminant| (|#2| (|Vector| |#1|))) (SIGNATURE |represents| (|#1| (|Vector| |#2|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Matrix| |#2|) (|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#2|) |#1| (|Vector| |#1|))) (SIGNATURE |rightNorm| (|#2| |#1|)) (SIGNATURE |leftNorm| (|#2| |#1|)) (SIGNATURE |rightTrace| (|#2| |#1|)) (SIGNATURE |leftTrace| (|#2| |#1|)) (SIGNATURE |rightRegularRepresentation| ((|Matrix| |#2|) |#1| (|Vector| |#1|))) (SIGNATURE |leftRegularRepresentation| ((|Matrix| |#2|) |#1| (|Vector| |#1|))) (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| |#2|)) (|Vector| |#1|)))) (|FiniteRankNonAssociativeAlgebra| |#2|) (|CommutativeRing|)) (T |FiniteRankNonAssociativeAlgebra&|)) 
((|commutative?| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4)))) (|antiCommutative?| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4)))) (|associative?| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4)))) (|antiAssociative?| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4)))) (|leftAlternative?| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4)))) (|rightAlternative?| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4)))) (|flexible?| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4)))) (|alternative?| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4)))) (|jacobiIdentity?| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4)))) (|lieAdmissible?| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4)))) (|jordanAdmissible?| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4)))) (|noncommutativeJordanAlgebra?| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4)))) (|jordanAlgebra?| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4)))) (|lieAlgebra?| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4)))) (|associatorDependence| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|List| (|Vector| *4))) (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4))))) 
(CATEGORY |domain| (SIGNATURE |rightMinimalPolynomial| ((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |leftMinimalPolynomial| ((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |associatorDependence| ((|List| (|Vector| |#2|)))) (SIGNATURE |rightRecip| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |leftRecip| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |recip| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |lieAlgebra?| ((|Boolean|))) (SIGNATURE |jordanAlgebra?| ((|Boolean|))) (SIGNATURE |noncommutativeJordanAlgebra?| ((|Boolean|))) (SIGNATURE |jordanAdmissible?| ((|Boolean|))) (SIGNATURE |lieAdmissible?| ((|Boolean|))) (SIGNATURE |jacobiIdentity?| ((|Boolean|))) (SIGNATURE |alternative?| ((|Boolean|))) (SIGNATURE |flexible?| ((|Boolean|))) (SIGNATURE |rightAlternative?| ((|Boolean|))) (SIGNATURE |leftAlternative?| ((|Boolean|))) (SIGNATURE |antiAssociative?| ((|Boolean|))) (SIGNATURE |associative?| ((|Boolean|))) (SIGNATURE |antiCommutative?| ((|Boolean|))) (SIGNATURE |commutative?| ((|Boolean|))) (SIGNATURE |rightCharacteristicPolynomial| ((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |leftCharacteristicPolynomial| ((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |rightTraceMatrix| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |leftTraceMatrix| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |rightDiscriminant| (|#2| (|Vector| |#1|))) (SIGNATURE |leftDiscriminant| (|#2| (|Vector| |#1|))) (SIGNATURE |represents| (|#1| (|Vector| |#2|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Matrix| |#2|) (|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#2|) |#1| (|Vector| |#1|))) (SIGNATURE |rightNorm| (|#2| |#1|)) (SIGNATURE |leftNorm| (|#2| |#1|)) (SIGNATURE |rightTrace| (|#2| |#1|)) (SIGNATURE |leftTrace| (|#2| |#1|)) (SIGNATURE |rightRegularRepresentation| ((|Matrix| |#2|) |#1| (|Vector| |#1|))) (SIGNATURE |leftRegularRepresentation| ((|Matrix| |#2|) |#1| (|Vector| |#1|))) (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| |#2|)) (|Vector| |#1|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unit| (((|Union| $ "failed")) 35 (|has| |#1| (|IntegralDomain|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) 76)) (|someBasis| (((|Vector| $)) 79)) (|sample| (($) 16 T CONST)) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) 38 (|has| |#1| (|IntegralDomain|)))) (|rightUnit| (((|Union| $ "failed")) 36 (|has| |#1| (|IntegralDomain|)))) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) 63)) (|rightTrace| ((|#1| $) 72)) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 74)) (|rightRecip| (((|Union| $ "failed") $) 43 (|has| |#1| (|IntegralDomain|)))) (|rightPower| (($ $ (|PositiveInteger|)) 27)) (|rightNorm| ((|#1| $) 70)) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 40 (|has| |#1| (|IntegralDomain|)))) (|rightDiscriminant| ((|#1| (|Vector| $)) 65)) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 61)) (|rightAlternative?| (((|Boolean|)) 55)) (|represents| (($ (|Vector| |#1|) (|Vector| $)) 67)) (|recip| (((|Union| $ "failed") $) 45 (|has| |#1| (|IntegralDomain|)))) (|rank| (((|PositiveInteger|)) 78)) (|powerAssociative?| (((|Boolean|)) 52)) (|plenaryPower| (($ $ (|PositiveInteger|)) 32)) (|noncommutativeJordanAlgebra?| (((|Boolean|)) 48)) (|lieAlgebra?| (((|Boolean|)) 46)) (|lieAdmissible?| (((|Boolean|)) 50)) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) 39 (|has| |#1| (|IntegralDomain|)))) (|leftUnit| (((|Union| $ "failed")) 37 (|has| |#1| (|IntegralDomain|)))) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) 64)) (|leftTrace| ((|#1| $) 73)) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 75)) (|leftRecip| (((|Union| $ "failed") $) 44 (|has| |#1| (|IntegralDomain|)))) (|leftPower| (($ $ (|PositiveInteger|)) 28)) (|leftNorm| ((|#1| $) 71)) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 41 (|has| |#1| (|IntegralDomain|)))) (|leftDiscriminant| ((|#1| (|Vector| $)) 66)) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 62)) (|leftAlternative?| (((|Boolean|)) 56)) (|latex| (((|String|) $) 9)) (|jordanAlgebra?| (((|Boolean|)) 47)) (|jordanAdmissible?| (((|Boolean|)) 49)) (|jacobiIdentity?| (((|Boolean|)) 51)) (|hash| (((|SingleInteger|) $) 10)) (|flexible?| (((|Boolean|)) 54)) (|coordinates| (((|Vector| |#1|) $ (|Vector| $)) 69) (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) 68)) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) 77)) (|commutator| (($ $ $) 24)) (|commutative?| (((|Boolean|)) 60)) (|coerce| (((|OutputForm|) $) 11)) (|associatorDependence| (((|List| (|Vector| |#1|))) 42 (|has| |#1| (|IntegralDomain|)))) (|associator| (($ $ $ $) 25)) (|associative?| (((|Boolean|)) 58)) (|antiCommutator| (($ $ $) 23)) (|antiCommutative?| (((|Boolean|)) 59)) (|antiAssociative?| (((|Boolean|)) 57)) (|alternative?| (((|Boolean|)) 53)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 29)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 26) (($ $ |#1|) 34) (($ |#1| $) 33))) 
(((|FiniteRankNonAssociativeAlgebra| |#1|) (|Category|) (|CommutativeRing|)) (T |FiniteRankNonAssociativeAlgebra|)) 
((|someBasis| (*1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)))) (|rank| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|PositiveInteger|)))) (|conditionsForIdempotents| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|List| (|Polynomial| *4))))) (|structuralConstants| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Vector| (|Matrix| *4))))) (|leftRegularRepresentation| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|rightRegularRepresentation| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|leftTrace| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|rightTrace| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|leftNorm| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|rightNorm| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|coordinates| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *4)))) (|coordinates| (*1 *2 *3 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|represents| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|Vector| *1)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)))) (|leftDiscriminant| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|rightDiscriminant| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|leftTraceMatrix| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|rightTraceMatrix| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|leftCharacteristicPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|rightCharacteristicPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|commutative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|antiCommutative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|associative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|antiAssociative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|leftAlternative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|rightAlternative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|flexible?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|alternative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|powerAssociative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|jacobiIdentity?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|lieAdmissible?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|jordanAdmissible?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|noncommutativeJordanAlgebra?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|jordanAlgebra?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|lieAlgebra?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|recip| (*1 *1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|IntegralDomain|)))) (|leftRecip| (*1 *1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|IntegralDomain|)))) (|rightRecip| (*1 *1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|IntegralDomain|)))) (|associatorDependence| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| (|Vector| *3))))) (|leftMinimalPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|rightMinimalPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|leftUnits| (*1 *2) (|partial| AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Record| (|:| |particular| *1) (|:| |basis| (|List| *1)))) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)))) (|rightUnits| (*1 *2) (|partial| AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Record| (|:| |particular| *1) (|:| |basis| (|List| *1)))) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)))) (|leftUnit| (*1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|CommutativeRing|)))) (|rightUnit| (*1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|CommutativeRing|)))) (|unit| (*1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|CommutativeRing|))))) 
(|Join| (|NonAssociativeAlgebra| |t#1|) (CATEGORY |domain| (SIGNATURE |someBasis| ((|Vector| $))) (SIGNATURE |rank| ((|PositiveInteger|))) (SIGNATURE |conditionsForIdempotents| ((|List| (|Polynomial| |t#1|)) (|Vector| $))) (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| |t#1|)) (|Vector| $))) (SIGNATURE |leftRegularRepresentation| ((|Matrix| |t#1|) $ (|Vector| $))) (SIGNATURE |rightRegularRepresentation| ((|Matrix| |t#1|) $ (|Vector| $))) (SIGNATURE |leftTrace| (|t#1| $)) (SIGNATURE |rightTrace| (|t#1| $)) (SIGNATURE |leftNorm| (|t#1| $)) (SIGNATURE |rightNorm| (|t#1| $)) (SIGNATURE |coordinates| ((|Vector| |t#1|) $ (|Vector| $))) (SIGNATURE |coordinates| ((|Matrix| |t#1|) (|Vector| $) (|Vector| $))) (SIGNATURE |represents| ($ (|Vector| |t#1|) (|Vector| $))) (SIGNATURE |leftDiscriminant| (|t#1| (|Vector| $))) (SIGNATURE |rightDiscriminant| (|t#1| (|Vector| $))) (SIGNATURE |leftTraceMatrix| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |rightTraceMatrix| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |leftCharacteristicPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |rightCharacteristicPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |commutative?| ((|Boolean|))) (SIGNATURE |antiCommutative?| ((|Boolean|))) (SIGNATURE |associative?| ((|Boolean|))) (SIGNATURE |antiAssociative?| ((|Boolean|))) (SIGNATURE |leftAlternative?| ((|Boolean|))) (SIGNATURE |rightAlternative?| ((|Boolean|))) (SIGNATURE |flexible?| ((|Boolean|))) (SIGNATURE |alternative?| ((|Boolean|))) (SIGNATURE |powerAssociative?| ((|Boolean|))) (SIGNATURE |jacobiIdentity?| ((|Boolean|))) (SIGNATURE |lieAdmissible?| ((|Boolean|))) (SIGNATURE |jordanAdmissible?| ((|Boolean|))) (SIGNATURE |noncommutativeJordanAlgebra?| ((|Boolean|))) (SIGNATURE |jordanAlgebra?| ((|Boolean|))) (SIGNATURE |lieAlgebra?| ((|Boolean|))) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |recip| ((|Union| $ "failed") $)) (SIGNATURE |leftRecip| ((|Union| $ "failed") $)) (SIGNATURE |rightRecip| ((|Union| $ "failed") $)) (SIGNATURE |associatorDependence| ((|List| (|Vector| |t#1|)))) (SIGNATURE |leftMinimalPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |rightMinimalPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |leftUnits| ((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed"))) (SIGNATURE |rightUnits| ((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed"))) (SIGNATURE |leftUnit| ((|Union| $ "failed"))) (SIGNATURE |rightUnit| ((|Union| $ "failed"))) (SIGNATURE |unit| ((|Union| $ "failed"))) (ATTRIBUTE |unitsKnown|)) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| |#1|) . T) ((|Module| |#1|) . T) ((|Monad|) . T) ((|NonAssociativeAlgebra| |#1|) . T) ((|NonAssociativeRng|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T)) 
((|random| (($) 13)) (|enumerate| (((|List| $)) 15))) 
(((|Finite&| |#1|) (CATEGORY |domain| (SIGNATURE |enumerate| ((|List| |#1|))) (SIGNATURE |random| (|#1|))) (|Finite|)) (T |Finite&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |enumerate| ((|List| |#1|))) (SIGNATURE |random| (|#1|))) 
((~= (((|Boolean|) $ $) 7)) (|size| (((|NonNegativeInteger|)) 16)) (|random| (($) 13)) (|lookup| (((|PositiveInteger|) $) 14)) (|latex| (((|String|) $) 9)) (|index| (($ (|PositiveInteger|)) 15)) (|hash| (((|SingleInteger|) $) 10)) (|enumerate| (((|List| $)) 12)) (|coerce| (((|OutputForm|) $) 11)) (= (((|Boolean|) $ $) 6))) 
(((|Finite|) (|Category|)) (T |Finite|)) 
((|size| (*1 *2) (AND (|ofCategory| *1 (|Finite|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|index| (*1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|Finite|)))) (|lookup| (*1 *2 *1) (AND (|ofCategory| *1 (|Finite|)) (|isDomain| *2 (|PositiveInteger|)))) (|random| (*1 *1) (|ofCategory| *1 (|Finite|))) (|enumerate| (*1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|Finite|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |size| ((|NonNegativeInteger|))) (SIGNATURE |index| ($ (|PositiveInteger|))) (SIGNATURE |lookup| ((|PositiveInteger|) $)) (SIGNATURE |random| ($)) (SIGNATURE |enumerate| ((|List| $))))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((|traceMatrix| (((|Matrix| |#2|) (|Vector| $)) 40)) (|represents| (($ (|Vector| |#2|) (|Vector| $)) 35)) (|regularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) 43)) (|discriminant| ((|#2| (|Vector| $)) 13)) (|coordinates| (((|Vector| |#2|) $ (|Vector| $)) NIL) (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) 25))) 
(((|FiniteRankAlgebra&| |#1| |#2| |#3|) (CATEGORY |domain| (SIGNATURE |traceMatrix| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |discriminant| (|#2| (|Vector| |#1|))) (SIGNATURE |represents| (|#1| (|Vector| |#2|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Matrix| |#2|) (|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#2|) |#1| (|Vector| |#1|))) (SIGNATURE |regularRepresentation| ((|Matrix| |#2|) |#1| (|Vector| |#1|)))) (|FiniteRankAlgebra| |#2| |#3|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#2|)) (T |FiniteRankAlgebra&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |traceMatrix| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |discriminant| (|#2| (|Vector| |#1|))) (SIGNATURE |represents| (|#1| (|Vector| |#2|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Matrix| |#2|) (|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#2|) |#1| (|Vector| |#1|))) (SIGNATURE |regularRepresentation| ((|Matrix| |#2|) |#1| (|Vector| |#1|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) 44)) (|trace| ((|#1| $) 50)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|represents| (($ (|Vector| |#1|) (|Vector| $)) 46)) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 51)) (|recip| (((|Union| $ "failed") $) 33)) (|rank| (((|PositiveInteger|)) 52)) (|one?| (((|Boolean|) $) 30)) (|norm| ((|#1| $) 49)) (|minimalPolynomial| ((|#2| $) 42 (|has| |#1| (|Field|)))) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|discriminant| ((|#1| (|Vector| $)) 45)) (|coordinates| (((|Vector| |#1|) $ (|Vector| $)) 48) (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) 47)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ |#1|) 36)) (|charthRoot| (((|Union| $ "failed") $) 41 (|has| |#1| (|CharacteristicNonZero|)))) (|characteristicPolynomial| ((|#2| $) 43)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 38) (($ |#1| $) 37))) 
(((|FiniteRankAlgebra| |#1| |#2|) (|Category|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |t#1|)) (T |FiniteRankAlgebra|)) 
((|rank| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankAlgebra| *3 *4)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|PositiveInteger|)))) (|regularRepresentation| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankAlgebra| *4 *5)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Matrix| *4)))) (|trace| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankAlgebra| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|norm| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankAlgebra| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|coordinates| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankAlgebra| *4 *5)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Vector| *4)))) (|coordinates| (*1 *2 *3 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankAlgebra| *4 *5)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Matrix| *4)))) (|represents| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|Vector| *1)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *1 (|FiniteRankAlgebra| *4 *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)))) (|discriminant| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankAlgebra| *2 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|traceMatrix| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankAlgebra| *4 *5)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Matrix| *4)))) (|characteristicPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankAlgebra| *3 *2)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|minimalPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankAlgebra| *3 *2)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|Field|)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(|Join| (|Algebra| |t#1|) (CATEGORY |domain| (SIGNATURE |rank| ((|PositiveInteger|))) (SIGNATURE |regularRepresentation| ((|Matrix| |t#1|) $ (|Vector| $))) (SIGNATURE |trace| (|t#1| $)) (SIGNATURE |norm| (|t#1| $)) (SIGNATURE |coordinates| ((|Vector| |t#1|) $ (|Vector| $))) (SIGNATURE |coordinates| ((|Matrix| |t#1|) (|Vector| $) (|Vector| $))) (SIGNATURE |represents| ($ (|Vector| |t#1|) (|Vector| $))) (SIGNATURE |discriminant| (|t#1| (|Vector| $))) (SIGNATURE |traceMatrix| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |characteristicPolynomial| (|t#2| $)) (IF (|has| |t#1| (|Field|)) (SIGNATURE |minimalPolynomial| (|t#2| $)) |noBranch|) (IF (|has| |t#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |noBranch|) (IF (|has| |t#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) 23)) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) 15)) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) 21))) 
(((|FiniteLinearAggregateFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#3| |#1|) |#2|)) (SIGNATURE |reduce| (|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|)) (SIGNATURE |scan| (|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|))) (|Type|) (|FiniteLinearAggregate| |#1|) (|Type|) (|FiniteLinearAggregate| |#3|)) (T |FiniteLinearAggregateFunctions2|)) 
((|scan| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *5 *6 *5)) (|ofCategory| *6 (|Type|)) (|ofCategory| *5 (|Type|)) (|ofCategory| *2 (|FiniteLinearAggregate| *5)) (|isDomain| *1 (|FiniteLinearAggregateFunctions2| *6 *4 *5 *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *6)))) (|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) (|ofCategory| *5 (|Type|)) (|ofCategory| *2 (|Type|)) (|isDomain| *1 (|FiniteLinearAggregateFunctions2| *5 *4 *2 *6)) (|ofCategory| *4 (|FiniteLinearAggregate| *5)) (|ofCategory| *6 (|FiniteLinearAggregate| *2)))) (|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|)) (|ofCategory| *2 (|FiniteLinearAggregate| *6)) (|isDomain| *1 (|FiniteLinearAggregateFunctions2| *5 *4 *6 *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *5))))) 
(CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#3| |#1|) |#2|)) (SIGNATURE |reduce| (|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|)) (SIGNATURE |scan| (|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|))) 
((|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) NIL) (((|Boolean|) $) 18)) (|sort!| (($ (|Mapping| (|Boolean|) |#2| |#2|) $) NIL) (($ $) 28)) (|sort| (($ (|Mapping| (|Boolean|) |#2| |#2|) $) 27) (($ $) 22)) (|reverse| (($ $) 25)) (|position| (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) NIL) (((|Integer|) |#2| $) 11) (((|Integer|) |#2| $ (|Integer|)) NIL)) (|merge| (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) NIL) (($ $ $) 20))) 
(((|FiniteLinearAggregate&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |sort!| (|#1| |#1|)) (SIGNATURE |sort!| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1|)) (SIGNATURE |sorted?| ((|Boolean|) |#1|)) (SIGNATURE |sort| (|#1| |#1|)) (SIGNATURE |merge| (|#1| |#1| |#1|)) (SIGNATURE |position| ((|Integer|) |#2| |#1| (|Integer|))) (SIGNATURE |position| ((|Integer|) |#2| |#1|)) (SIGNATURE |position| ((|Integer|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |sorted?| ((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) |#1|)) (SIGNATURE |sort| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1|)) (SIGNATURE |reverse| (|#1| |#1|)) (SIGNATURE |merge| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1| |#1|))) (|FiniteLinearAggregate| |#2|) (|Type|)) (T |FiniteLinearAggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |sort!| (|#1| |#1|)) (SIGNATURE |sort!| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1|)) (SIGNATURE |sorted?| ((|Boolean|) |#1|)) (SIGNATURE |sort| (|#1| |#1|)) (SIGNATURE |merge| (|#1| |#1| |#1|)) (SIGNATURE |position| ((|Integer|) |#2| |#1| (|Integer|))) (SIGNATURE |position| ((|Integer|) |#2| |#1|)) (SIGNATURE |position| ((|Integer|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |sorted?| ((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) |#1|)) (SIGNATURE |sort| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1|)) (SIGNATURE |reverse| (|#1| |#1|)) (SIGNATURE |merge| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1| |#1|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) 91) (((|Boolean|) $) 85 (|has| |#1| (|OrderedSet|)))) (|sort!| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) 82 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $) 81 (AND (|has| |#1| (|OrderedSet|)) (|has| $ (ATTRIBUTE |shallowlyMutable|))))) (|sort| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) 92) (($ $) 86 (|has| |#1| (|OrderedSet|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setelt| ((|#1| $ (|Integer|) |#1|) 49 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) 53 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 70 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) 7 T CONST)) (|reverse!| (($ $) 83 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) 93)) (|removeDuplicates| (($ $) 73 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove| (($ |#1| $) 72 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#1|) $) 69 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 71 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 68 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 67 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| ((|#1| $ (|Integer|) |#1|) 50 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#1| $ (|Integer|)) 48)) (|position| (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) 90) (((|Integer|) |#1| $) 89 (|has| |#1| (|SetCategory|))) (((|Integer|) |#1| $ (|Integer|)) 88 (|has| |#1| (|SetCategory|)))) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|new| (($ (|NonNegativeInteger|) |#1|) 64)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|minIndex| (((|Integer|) $) 40 (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) 80 (|has| |#1| (|OrderedSet|)))) (|merge| (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) 94) (($ $ $) 87 (|has| |#1| (|OrderedSet|)))) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|maxIndex| (((|Integer|) $) 41 (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) 79 (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35) (($ (|Mapping| |#1| |#1| |#1|) $ $) 59)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|insert| (($ |#1| $ (|Integer|)) 55) (($ $ $ (|Integer|)) 54)) (|indices| (((|List| (|Integer|)) $) 43)) (|index?| (((|Boolean|) (|Integer|) $) 44)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|first| ((|#1| $) 39 (|has| (|Integer|) (|OrderedSet|)))) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) 66)) (|fill!| (($ $ |#1|) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|entry?| (((|Boolean|) |#1| $) 42 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|entries| (((|List| |#1|) $) 45)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| ((|#1| $ (|Integer|) |#1|) 47) ((|#1| $ (|Integer|)) 46) (($ $ (|UniversalSegment| (|Integer|))) 58)) (|delete| (($ $ (|Integer|)) 57) (($ $ (|UniversalSegment| (|Integer|))) 56)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copyInto!| (($ $ $ (|Integer|)) 84 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) 13)) (|convert| (((|InputForm|) $) 74 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 65)) (|concat| (($ $ |#1|) 63) (($ |#1| $) 62) (($ $ $) 61) (($ (|List| $)) 60)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (>= (((|Boolean|) $ $) 77 (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) 76 (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (<= (((|Boolean|) $ $) 78 (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) 75 (|has| |#1| (|OrderedSet|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|FiniteLinearAggregate| |#1|) (|Category|) (|Type|)) (T |FiniteLinearAggregate|)) 
((|merge| (*1 *1 *2 *1 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3 *3)) (|ofCategory| *1 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|reverse| (*1 *1 *1) (AND (|ofCategory| *1 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|sort| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3 *3)) (|ofCategory| *1 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|sorted?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4)) (|ofCategory| *1 (|FiniteLinearAggregate| *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|position| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|ofCategory| *1 (|FiniteLinearAggregate| *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Integer|)))) (|position| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Integer|)))) (|position| (*1 *2 *3 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|SetCategory|)))) (|merge| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|OrderedSet|)))) (|sort| (*1 *1 *1) (AND (|ofCategory| *1 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|OrderedSet|)))) (|sorted?| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|copyInto!| (*1 *1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|reverse!| (*1 *1 *1) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|sort!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3 *3)) (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|sort!| (*1 *1 *1) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|OrderedSet|))))) 
(|Join| (|LinearAggregate| |t#1|) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (SIGNATURE |merge| ($ (|Mapping| (|Boolean|) |t#1| |t#1|) $ $)) (SIGNATURE |reverse| ($ $)) (SIGNATURE |sort| ($ (|Mapping| (|Boolean|) |t#1| |t#1|) $)) (SIGNATURE |sorted?| ((|Boolean|) (|Mapping| (|Boolean|) |t#1| |t#1|) $)) (SIGNATURE |position| ((|Integer|) (|Mapping| (|Boolean|) |t#1|) $)) (IF (|has| |t#1| (|SetCategory|)) (PROGN (SIGNATURE |position| ((|Integer|) |t#1| $)) (SIGNATURE |position| ((|Integer|) |t#1| $ (|Integer|)))) |noBranch|) (IF (|has| |t#1| (|OrderedSet|)) (PROGN (ATTRIBUTE (|OrderedSet|)) (SIGNATURE |merge| ($ $ $)) (SIGNATURE |sort| ($ $)) (SIGNATURE |sorted?| ((|Boolean|) $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |shallowlyMutable|)) (PROGN (SIGNATURE |copyInto!| ($ $ $ (|Integer|))) (SIGNATURE |reverse!| ($ $)) (SIGNATURE |sort!| ($ (|Mapping| (|Boolean|) |t#1| |t#1|) $)) (IF (|has| |t#1| (|OrderedSet|)) (SIGNATURE |sort!| ($ $)) |noBranch|)) |noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| (|Integer|) |#1|) . T) ((|EltableAggregate| (|Integer|) |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| (|Integer|) |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|LinearAggregate| |#1|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|SetCategory|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|Type|) . T)) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|varList| (((|List| |#1|) $) 29)) (|trunc| (($ $ (|NonNegativeInteger|)) 30)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) 33)) (|mirror| (($ $) 31)) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) 34)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|eval| (($ $ |#1| $) 28) (($ $ (|List| |#1|) (|List| $)) 27)) (|degree| (((|NonNegativeInteger|) $) 35)) (|construct| (($ $ $) 26)) (|coerce| (((|OutputForm|) $) 11) (($ |#1|) 38) (((|XDistributedPolynomial| |#1| |#2|) $) 37) (((|XRecursivePolynomial| |#1| |#2|) $) 36)) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) 39)) (|Zero| (($) 17 T CONST)) (|LiePoly| (($ (|LyndonWord| |#1|)) 32)) (= (((|Boolean|) $ $) 6)) (/ (($ $ |#2|) 25 (|has| |#2| (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ |#2| $) 22) (($ $ |#2|) 24))) 
(((|FreeLieAlgebra| |#1| |#2|) (|Category|) (|OrderedSet|) (|CommutativeRing|)) (T |FreeLieAlgebra|)) 
((|coef| (*1 *2 *3 *1) (AND (|isDomain| *3 (|XRecursivePolynomial| *4 *2)) (|ofCategory| *1 (|FreeLieAlgebra| *4 *2)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|CommutativeRing|)))) (|coerce| (*1 *1 *2) (AND (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|)))) (|coerce| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|XDistributedPolynomial| *3 *4)))) (|coerce| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|XRecursivePolynomial| *3 *4)))) (|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|lquo| (*1 *2 *2 *1) (AND (|isDomain| *2 (|XRecursivePolynomial| *3 *4)) (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)))) (|rquo| (*1 *2 *2 *1) (AND (|isDomain| *2 (|XRecursivePolynomial| *3 *4)) (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)))) (|LiePoly| (*1 *1 *2) (AND (|isDomain| *2 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)) (|ofCategory| *4 (|CommutativeRing|)))) (|mirror| (*1 *1 *1) (AND (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|)))) (|trunc| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)))) (|varList| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|List| *3)))) (|eval| (*1 *1 *1 *2 *1) (AND (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|)))) (|eval| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *4)) (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|FreeLieAlgebra| *4 *5)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|CommutativeRing|))))) 
(|Join| (|LieAlgebra| |t#2|) (CATEGORY |domain| (SIGNATURE |coef| (|t#2| (|XRecursivePolynomial| |t#1| |t#2|) $)) (SIGNATURE |coerce| ($ |t#1|)) (SIGNATURE |coerce| ((|XDistributedPolynomial| |t#1| |t#2|) $)) (SIGNATURE |coerce| ((|XRecursivePolynomial| |t#1| |t#2|) $)) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |lquo| ((|XRecursivePolynomial| |t#1| |t#2|) (|XRecursivePolynomial| |t#1| |t#2|) $)) (SIGNATURE |rquo| ((|XRecursivePolynomial| |t#1| |t#2|) (|XRecursivePolynomial| |t#1| |t#2|) $)) (SIGNATURE |LiePoly| ($ (|LyndonWord| |t#1|))) (SIGNATURE |mirror| ($ $)) (SIGNATURE |trunc| ($ $ (|NonNegativeInteger|))) (SIGNATURE |varList| ((|List| |t#1|) $)) (SIGNATURE |eval| ($ $ |t#1| $)) (SIGNATURE |eval| ($ $ (|List| |t#1|) (|List| $))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#2| |#2|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| |#2|) . T) ((|LieAlgebra| |#2|) . T) ((|Module| |#2|) . T) ((|RightModule| |#2|) . T) ((|SetCategory|) . T)) 
((|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) 22)) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) 12)) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) 21))) 
(((|FiniteLinearAggregateSort| |#1| |#2|) (CATEGORY |package| (SIGNATURE |quickSort| (|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|)) (SIGNATURE |heapSort| (|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|)) (SIGNATURE |shellSort| (|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|))) (|Type|) (|Join| (|FiniteLinearAggregate| |#1|) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|)))) (T |FiniteLinearAggregateSort|)) 
((|shellSort| (*1 *2 *3 *2) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *1 (|FiniteLinearAggregateSort| *4 *2)) (|ofCategory| *2 (|Join| (|FiniteLinearAggregate| *4) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|)))))) (|heapSort| (*1 *2 *3 *2) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *1 (|FiniteLinearAggregateSort| *4 *2)) (|ofCategory| *2 (|Join| (|FiniteLinearAggregate| *4) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|)))))) (|quickSort| (*1 *2 *3 *2) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *1 (|FiniteLinearAggregateSort| *4 *2)) (|ofCategory| *2 (|Join| (|FiniteLinearAggregate| *4) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|))))))) 
(CATEGORY |package| (SIGNATURE |quickSort| (|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|)) (SIGNATURE |heapSort| (|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|)) (SIGNATURE |shellSort| (|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|))) 
((|reducedSystem| (((|Matrix| |#2|) (|Matrix| $)) NIL) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| $) (|Vector| $)) NIL) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) 19) (((|Matrix| (|Integer|)) (|Matrix| $)) 13))) 
(((|FullyLinearlyExplicitRingOver&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |reducedSystem| ((|Matrix| (|Integer|)) (|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Matrix| |#2|) (|Matrix| |#1|)))) (|FullyLinearlyExplicitRingOver| |#2|) (|Ring|)) (T |FullyLinearlyExplicitRingOver&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |reducedSystem| ((|Matrix| (|Integer|)) (|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Matrix| |#2|) (|Matrix| |#1|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|reducedSystem| (((|Matrix| |#1|) (|Matrix| $)) 35) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) 34) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) 38 (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Matrix| (|Integer|)) (|Matrix| $)) 37 (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))))) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|FullyLinearlyExplicitRingOver| |#1|) (|Category|) (|Ring|)) (T |FullyLinearlyExplicitRingOver|)) 
NIL 
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NIL)) (|fractionPart| (($ $) 53)) (|floor| (($ $) 108)) (|float| (($ (|Integer|) (|Integer|)) 106) (($ (|Integer|) (|Integer|) (|PositiveInteger|)) 107)) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|exponent| (((|Integer|) $) 19)) (|exp1| (($) 93)) (|exp| (($ $) 78)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|digits| (((|PositiveInteger|)) 99) (((|PositiveInteger|) (|PositiveInteger|)) 100 (|has| $ (ATTRIBUTE |arbitraryPrecision|)))) (|differentiate| (($ $ (|NonNegativeInteger|)) NIL) (($ $) 114)) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) 47 (|has| $ (ATTRIBUTE |arbitraryPrecision|)))) (|csch| (($ $) NIL)) (|csc| 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(((|Float|) (|Join| (|FloatingPointSystem|) (|DifferentialRing|) (|ConvertibleTo| (|String|)) (|OpenMath|) (|CoercibleTo| (|DoubleFloat|)) (|TranscendentalFunctionCategory|) (|ConvertibleTo| (|InputForm|)) (CATEGORY |domain| (SIGNATURE / ($ $ (|Integer|))) (SIGNATURE ** ($ $ $)) (SIGNATURE |normalize| ($ $)) (SIGNATURE |relerror| ((|Integer|) $ $)) (SIGNATURE |shift| ($ $ (|Integer|))) (SIGNATURE |rationalApproximation| ((|Fraction| (|Integer|)) $ (|NonNegativeInteger|))) (SIGNATURE |rationalApproximation| ((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |log2| ($)) (SIGNATURE |log10| ($)) (SIGNATURE |exp1| ($)) (SIGNATURE |atan| ($ $ $)) (SIGNATURE |log2| ($ $)) (SIGNATURE |log10| ($ $)) (SIGNATURE |convert| ($ (|DoubleFloat|))) (SIGNATURE |outputFloating| ((|Void|))) (SIGNATURE |outputFloating| ((|Void|) (|NonNegativeInteger|))) (SIGNATURE |outputFixed| ((|Void|))) (SIGNATURE |outputFixed| ((|Void|) (|NonNegativeInteger|))) (SIGNATURE |outputGeneral| ((|Void|))) (SIGNATURE |outputGeneral| ((|Void|) (|NonNegativeInteger|))) (SIGNATURE |outputSpacing| ((|Void|) (|NonNegativeInteger|))) (ATTRIBUTE |arbitraryPrecision|) (ATTRIBUTE |arbitraryExponent|)))) (T |Float|)) 
((** (*1 *1 *1 *1) (|isDomain| *1 (|Float|))) (/ (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Float|)))) (|normalize| (*1 *1 *1) (|isDomain| *1 (|Float|))) (|relerror| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Float|)))) (|shift| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Float|)))) (|rationalApproximation| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|Float|)))) (|rationalApproximation| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|Float|)))) (|log2| (*1 *1) (|isDomain| *1 (|Float|))) (|log10| (*1 *1) (|isDomain| *1 (|Float|))) (|exp1| (*1 *1) (|isDomain| *1 (|Float|))) (|atan| (*1 *1 *1 *1) (|isDomain| *1 (|Float|))) (|log2| (*1 *1 *1) (|isDomain| *1 (|Float|))) (|log10| (*1 *1 *1) (|isDomain| *1 (|Float|))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|Float|)))) (|outputFloating| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Float|)))) (|outputFloating| (*1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Float|)))) (|outputFixed| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Float|)))) (|outputFixed| (*1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Float|)))) (|outputGeneral| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Float|)))) (|outputGeneral| (*1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Float|)))) (|outputSpacing| (*1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Float|))))) 
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(((|FloatingRealPackage| |#1|) (CATEGORY |package| (SIGNATURE |solve| ((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|)) (SIGNATURE |solve| ((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|)) (SIGNATURE |solve| ((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|)) (SIGNATURE |solve| ((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|)) (SIGNATURE |realRoots| ((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|)) (SIGNATURE |realRoots| ((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|))) (|Join| (|OrderedRing|) (|Field|))) (T |FloatingRealPackage|)) 
((|realRoots| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|Polynomial| (|Integer|)))) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|FloatingRealPackage| *4)) (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|))))) (|realRoots| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|List| *5))) (|isDomain| *1 (|FloatingRealPackage| *5)) (|ofCategory| *5 (|Join| (|OrderedRing|) (|Field|))))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|Equation| (|Polynomial| *4)))) (|isDomain| *1 (|FloatingRealPackage| *4)) (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|))))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|Polynomial| (|Integer|)))) (|isDomain| *2 (|List| (|Equation| (|Polynomial| *4)))) (|isDomain| *1 (|FloatingRealPackage| *4)) (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|))))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|)))))) (|isDomain| *2 (|List| (|List| (|Equation| (|Polynomial| *4))))) (|isDomain| *1 (|FloatingRealPackage| *4)) (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|))))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|List| (|Equation| (|Polynomial| *4))))) (|isDomain| *1 (|FloatingRealPackage| *4)) (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|)))))) 
(CATEGORY |package| (SIGNATURE |solve| ((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|)) (SIGNATURE |solve| ((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|)) (SIGNATURE |solve| ((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|)) (SIGNATURE |solve| ((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|)) (SIGNATURE |realRoots| ((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|)) (SIGNATURE |realRoots| ((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|))) 
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(((|FreeModule1| |#1| |#2|) (|Join| (|FreeModuleCat| |#1| |#2|) (CATEGORY |domain| (SIGNATURE * ($ |#2| |#1|)))) (|Ring|) (|OrderedSet|)) (T |FreeModule1|)) 
((* (*1 *1 *2 *3) (AND (|isDomain| *1 (|FreeModule1| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedSet|))))) 
(|Join| (|FreeModuleCat| |#1| |#2|) (CATEGORY |domain| (SIGNATURE * ($ |#2| |#1|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) 41)) (|retract| ((|#2| $) 40)) (|reductum| (($ $) 27)) (|numberOfMonomials| (((|NonNegativeInteger|) $) 31)) (|monomials| (((|List| $) $) 32)) (|monomial?| (((|Boolean|) $) 35)) (|monom| (($ |#2| |#1|) 36)) (|map| (($ (|Mapping| |#1| |#1|) $) 37)) (|listOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) 34)) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) 28)) (|leadingMonomial| ((|#2| $) 30)) (|leadingCoefficient| ((|#1| $) 29)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11) (($ |#2|) 42)) (|coefficients| (((|List| |#1|) $) 33)) (|coefficient| ((|#1| $ |#2|) 38)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ |#1| $) 22) (($ $ |#1|) 24) (($ |#1| |#2|) 39))) 
(((|FreeModuleCat| |#1| |#2|) (|Category|) (|Ring|) (|SetCategory|)) (T |FreeModuleCat|)) 
((* (*1 *1 *2 *3) (AND (|ofCategory| *1 (|FreeModuleCat| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|SetCategory|)))) (|coefficient| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|FreeModuleCat| *2 *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|Ring|)))) (|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|FreeModuleCat| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|SetCategory|)))) (|monom| (*1 *1 *2 *3) (AND (|ofCategory| *1 (|FreeModuleCat| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|SetCategory|)))) (|monomial?| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeModuleCat| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|listOfTerms| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeModuleCat| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|List| (|Record| (|:| |k| *4) (|:| |c| *3)))))) (|coefficients| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeModuleCat| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|List| *3)))) (|monomials| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|FreeModuleCat| *3 *4)))) (|numberOfMonomials| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeModuleCat| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|leadingMonomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeModuleCat| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|SetCategory|)))) (|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeModuleCat| *2 *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|Ring|)))) (|leadingTerm| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeModuleCat| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Record| (|:| |k| *4) (|:| |c| *3))))) (|reductum| (*1 *1 *1) (AND (|ofCategory| *1 (|FreeModuleCat| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|SetCategory|))))) 
(|Join| (|BiModule| |t#1| |t#1|) (|RetractableTo| |t#2|) (CATEGORY |domain| (SIGNATURE * ($ |t#1| |t#2|)) (SIGNATURE |coefficient| (|t#1| $ |t#2|)) (SIGNATURE |map| ($ (|Mapping| |t#1| |t#1|) $)) (SIGNATURE |monom| ($ |t#2| |t#1|)) (SIGNATURE |monomial?| ((|Boolean|) $)) (SIGNATURE |listOfTerms| ((|List| (|Record| (|:| |k| |t#2|) (|:| |c| |t#1|))) $)) (SIGNATURE |coefficients| ((|List| |t#1|) $)) (SIGNATURE |monomials| ((|List| $) $)) (SIGNATURE |numberOfMonomials| ((|NonNegativeInteger|) $)) (SIGNATURE |leadingMonomial| (|t#2| $)) (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |leadingTerm| ((|Record| (|:| |k| |t#2|) (|:| |c| |t#1|)) $)) (SIGNATURE |reductum| ($ $)) (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Module| |t#1|)) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| |#1|) . T) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|RetractableTo| |#2|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T)) 
((|outputAsFortran| (((|Void|) $) 7)) (|coerce| (((|OutputForm|) $) 8) (($ (|Matrix| (|MachineFloat|))) 12) (($ (|List| (|FortranCode|))) 11) (($ (|FortranCode|)) 10) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 9))) 
(((|FortranMatrixCategory|) (|Category|)) (T |FortranMatrixCategory|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Matrix| (|MachineFloat|))) (|ofCategory| *1 (|FortranMatrixCategory|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|FortranCode|))) (|ofCategory| *1 (|FortranMatrixCategory|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|FortranCode|)) (|ofCategory| *1 (|FortranMatrixCategory|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) (|ofCategory| *1 (|FortranMatrixCategory|))))) 
(|Join| (|FortranProgramCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Matrix| (|MachineFloat|)))) (SIGNATURE |coerce| ($ (|List| (|FortranCode|)))) (SIGNATURE |coerce| ($ (|FortranCode|))) (SIGNATURE |coerce| ($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|)))))))) 
(((|CoercibleTo| (|OutputForm|)) . T) ((|FortranProgramCategory|) . T) ((|Type|) . T)) 
((|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) 19) (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) 17) (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) 15) (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) 13) (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) 11) (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) 9)) (|retract| (($ (|Matrix| (|Expression| (|Float|)))) 20) (($ (|Matrix| (|Expression| (|Integer|)))) 18) (($ (|Matrix| (|Polynomial| (|Float|)))) 16) (($ (|Matrix| (|Polynomial| (|Integer|)))) 14) (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) 12) (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) 10)) (|outputAsFortran| (((|Void|) $) 7)) (|coerce| (((|OutputForm|) $) 8) (($ (|List| (|FortranCode|))) 23) (($ (|FortranCode|)) 22) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 21))) 
(((|FortranMatrixFunctionCategory|) (|Category|)) (T |FortranMatrixFunctionCategory|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|FortranCode|))) (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|FortranCode|)) (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Matrix| (|Expression| (|Float|)))) (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Matrix| (|Expression| (|Float|)))) (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Matrix| (|Expression| (|Integer|)))) (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Matrix| (|Expression| (|Integer|)))) (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Matrix| (|Polynomial| (|Float|)))) (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Matrix| (|Polynomial| (|Float|)))) (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Matrix| (|Polynomial| (|Integer|)))) (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Matrix| (|Polynomial| (|Integer|)))) (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) (|ofCategory| *1 (|FortranMatrixFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) (|ofCategory| *1 (|FortranMatrixFunctionCategory|))))) 
(|Join| (|FortranProgramCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|List| (|FortranCode|)))) (SIGNATURE |coerce| ($ (|FortranCode|))) (SIGNATURE |coerce| ($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|)))))) (SIGNATURE |retract| ($ (|Matrix| (|Expression| (|Float|))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Matrix| (|Expression| (|Float|))))) (SIGNATURE |retract| ($ (|Matrix| (|Expression| (|Integer|))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|))))) (SIGNATURE |retract| ($ (|Matrix| (|Polynomial| (|Float|))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|))))) (SIGNATURE |retract| ($ (|Matrix| (|Polynomial| (|Integer|))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|))))) (SIGNATURE |retract| ($ (|Matrix| (|Fraction| (|Polynomial| (|Float|)))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|)))))) (SIGNATURE |retract| ($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|)))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|)))))))) 
(((|CoercibleTo| (|OutputForm|)) . T) ((|FortranProgramCategory|) . T) ((|Type|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|reductum| (($ $) NIL)) (|monomial| (($ |#1| |#2|) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|leadingSupport| ((|#2| $) NIL)) (|leadingCoefficient| ((|#1| $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 27)) (|Zero| (($) 12 T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ |#1| $) 16) (($ $ |#1|) 18))) 
(((|FreeModule| |#1| |#2|) (|Join| (|BiModule| |#1| |#1|) (|IndexedDirectProductCategory| |#1| |#2|) (CATEGORY |package| (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Module| |#1|)) |noBranch|))) (|Ring|) (|OrderedSet|)) (T |FreeModule|)) 
NIL 
(|Join| (|BiModule| |#1| |#1|) (|IndexedDirectProductCategory| |#1| |#2|) (CATEGORY |package| (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Module| |#1|)) |noBranch|))) 
((~= (((|Boolean|) $ $) NIL)) (|size| (((|NonNegativeInteger|) $) 56)) (|sample| (($) NIL T CONST)) (|rquo| (((|Union| $ "failed") $ $) 58)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL)) (|retract| ((|#1| $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) 52)) (|one?| (((|Boolean|) $) 14)) (|nthFactor| ((|#1| $ (|Integer|)) NIL)) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) NIL)) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 37)) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) 34)) (|lquo| (((|Union| $ "failed") $ $) 49)) (|latex| (((|String|) $) NIL)) (|hcrf| (($ $ $) 25)) (|hclf| (($ $ $) 23)) (|hash| (((|SingleInteger|) $) NIL)) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) 31)) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) 55)) (|coerce| (((|OutputForm|) $) 21) (($ |#1|) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|One| (($) 9 T CONST)) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) 41)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) 60 (|has| |#1| (|OrderedSet|)))) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ |#1| (|NonNegativeInteger|)) 40)) (* (($ $ $) 47) (($ |#1| $) 29) (($ $ |#1|) 27))) 
(((|FreeMonoid| |#1|) (|Join| (|Monoid|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE * ($ |#1| $)) (SIGNATURE * ($ $ |#1|)) (SIGNATURE ** ($ |#1| (|NonNegativeInteger|))) (SIGNATURE |hclf| ($ $ $)) (SIGNATURE |hcrf| ($ $ $)) (SIGNATURE |lquo| ((|Union| $ "failed") $ $)) (SIGNATURE |rquo| ((|Union| $ "failed") $ $)) (SIGNATURE |divide| ((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $)) (SIGNATURE |overlap| ((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $)) (SIGNATURE |size| ((|NonNegativeInteger|) $)) (SIGNATURE |factors| ((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $)) (SIGNATURE |nthExpon| ((|NonNegativeInteger|) $ (|Integer|))) (SIGNATURE |nthFactor| (|#1| $ (|Integer|))) (SIGNATURE |mapExpon| ($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $)) (SIGNATURE |mapGen| ($ (|Mapping| |#1| |#1|) $)) (IF (|has| |#1| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |noBranch|))) (|SetCategory|)) (T |FreeMonoid|)) 
((* (*1 *1 *2 *1) (AND (|isDomain| *1 (|FreeMonoid| *2)) (|ofCategory| *2 (|SetCategory|)))) (* (*1 *1 *1 *2) (AND (|isDomain| *1 (|FreeMonoid| *2)) (|ofCategory| *2 (|SetCategory|)))) (** (*1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|FreeMonoid| *2)) (|ofCategory| *2 (|SetCategory|)))) (|hclf| (*1 *1 *1 *1) (AND (|isDomain| *1 (|FreeMonoid| *2)) (|ofCategory| *2 (|SetCategory|)))) (|hcrf| (*1 *1 *1 *1) (AND (|isDomain| *1 (|FreeMonoid| *2)) (|ofCategory| *2 (|SetCategory|)))) (|lquo| (*1 *1 *1 *1) (|partial| AND (|isDomain| *1 (|FreeMonoid| *2)) (|ofCategory| *2 (|SetCategory|)))) (|rquo| (*1 *1 *1 *1) (|partial| AND (|isDomain| *1 (|FreeMonoid| *2)) (|ofCategory| *2 (|SetCategory|)))) (|divide| (*1 *2 *1 *1) (|partial| AND (|isDomain| *2 (|Record| (|:| |lm| (|FreeMonoid| *3)) (|:| |rm| (|FreeMonoid| *3)))) (|isDomain| *1 (|FreeMonoid| *3)) (|ofCategory| *3 (|SetCategory|)))) (|overlap| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |lm| (|FreeMonoid| *3)) (|:| |mm| (|FreeMonoid| *3)) (|:| |rm| (|FreeMonoid| *3)))) (|isDomain| *1 (|FreeMonoid| *3)) (|ofCategory| *3 (|SetCategory|)))) (|size| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FreeMonoid| *3)) (|ofCategory| *3 (|SetCategory|)))) (|factors| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| (|NonNegativeInteger|))))) (|isDomain| *1 (|FreeMonoid| *3)) (|ofCategory| *3 (|SetCategory|)))) (|nthExpon| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FreeMonoid| *4)) (|ofCategory| *4 (|SetCategory|)))) (|nthFactor| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|FreeMonoid| *2)) (|ofCategory| *2 (|SetCategory|)))) (|mapExpon| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|))) (|isDomain| *1 (|FreeMonoid| *3)) (|ofCategory| *3 (|SetCategory|)))) (|mapGen| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|FreeMonoid| *3))))) 
(|Join| (|Monoid|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE * ($ |#1| $)) (SIGNATURE * ($ $ |#1|)) (SIGNATURE ** ($ |#1| (|NonNegativeInteger|))) (SIGNATURE |hclf| ($ $ $)) (SIGNATURE |hcrf| ($ $ $)) (SIGNATURE |lquo| ((|Union| $ "failed") $ $)) (SIGNATURE |rquo| ((|Union| $ "failed") $ $)) (SIGNATURE |divide| ((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $)) (SIGNATURE |overlap| ((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $)) (SIGNATURE |size| ((|NonNegativeInteger|) $)) (SIGNATURE |factors| ((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $)) (SIGNATURE |nthExpon| ((|NonNegativeInteger|) $ (|Integer|))) (SIGNATURE |nthFactor| (|#1| $ (|Integer|))) (SIGNATURE |mapExpon| ($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $)) (SIGNATURE |mapGen| ($ (|Mapping| |#1| |#1|) $)) (IF (|has| |#1| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |noBranch|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 46)) (|retract| (((|Integer|) $) 45)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|min| (($ $ $) 53)) (|max| (($ $ $) 52)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42) (($ (|Integer|)) 47)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (>= (((|Boolean|) $ $) 50)) (> (((|Boolean|) $ $) 49)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 51)) (< (((|Boolean|) $ $) 48)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|FortranMachineTypeCategory|) (|Category|)) (T |FortranMachineTypeCategory|)) 
NIL 
(|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|IntegralDomain|) . T) ((|LeftModule| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedSet|) . T) ((|RetractableTo| (|Integer|)) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|writable?| (((|Boolean|) $) 20)) (|readable?| (((|Boolean|) $) 19)) (|new| (($ (|String|) (|String|) (|String|)) 21)) (|name| (((|String|) $) 16)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|filename| (($ (|String|) (|String|) (|String|)) 14)) (|extension| (((|String|) $) 17)) (|exists?| (((|Boolean|) $) 18)) (|directory| (((|String|) $) 15)) (|coerce| (((|OutputForm|) $) 12) (($ (|String|)) 13) (((|String|) $) 9)) (= (((|Boolean|) $ $) 7))) 
(((|FileName|) (|FileNameCategory|)) (T |FileName|)) 
NIL 
(|FileNameCategory|) 
((~= (((|Boolean|) $ $) 7)) (|writable?| (((|Boolean|) $) 13)) (|readable?| (((|Boolean|) $) 14)) (|new| (($ (|String|) (|String|) (|String|)) 12)) (|name| (((|String|) $) 17)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|filename| (($ (|String|) (|String|) (|String|)) 19)) (|extension| (((|String|) $) 16)) (|exists?| (((|Boolean|) $) 15)) (|directory| (((|String|) $) 18)) (|coerce| (((|OutputForm|) $) 11) (($ (|String|)) 21) (((|String|) $) 20)) (= (((|Boolean|) $ $) 6))) 
(((|FileNameCategory|) (|Category|)) (T |FileNameCategory|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|String|)) (|ofCategory| *1 (|FileNameCategory|)))) (|coerce| (*1 *2 *1) (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|String|)))) (|filename| (*1 *1 *2 *2 *2) (AND (|isDomain| *2 (|String|)) (|ofCategory| *1 (|FileNameCategory|)))) (|directory| (*1 *2 *1) (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|String|)))) (|name| (*1 *2 *1) (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|String|)))) (|extension| (*1 *2 *1) (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|String|)))) (|exists?| (*1 *2 *1) (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|Boolean|)))) (|readable?| (*1 *2 *1) (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|Boolean|)))) (|writable?| (*1 *2 *1) (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|Boolean|)))) (|new| (*1 *1 *2 *2 *2) (AND (|isDomain| *2 (|String|)) (|ofCategory| *1 (|FileNameCategory|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|String|))) (SIGNATURE |coerce| ((|String|) $)) (SIGNATURE |filename| ($ (|String|) (|String|) (|String|))) (SIGNATURE |directory| ((|String|) $)) (SIGNATURE |name| ((|String|) $)) (SIGNATURE |extension| ((|String|) $)) (SIGNATURE |exists?| ((|Boolean|) $)) (SIGNATURE |readable?| ((|Boolean|) $)) (SIGNATURE |writable?| ((|Boolean|) $)) (SIGNATURE |new| ($ (|String|) (|String|) (|String|))))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|shallowExpand| (((|OutputForm|) $) 50)) (|sample| (($) NIL T CONST)) (|rightPower| (($ $ (|PositiveInteger|)) NIL)) (|plenaryPower| (($ $ (|PositiveInteger|)) NIL)) (|leftPower| (($ $ (|PositiveInteger|)) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|generator| (($ (|NonNegativeInteger|)) 26)) (|dimension| (((|NonNegativeInteger|)) 15)) (|deepExpand| (((|OutputForm|) $) 52)) (|commutator| (($ $ $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (|associator| (($ $ $ $) NIL)) (|antiCommutator| (($ $ $) NIL)) (|Zero| (($) 20 T CONST)) (= (((|Boolean|) $ $) 28)) (- (($ $) 34) (($ $ $) 36)) (+ (($ $ $) 37)) (** (($ $ (|PositiveInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 38) (($ $ |#3|) NIL) (($ |#3| $) 33))) 
(((|FreeNilpotentLie| |#1| |#2| |#3|) (|Join| (|NonAssociativeAlgebra| |#3|) (CATEGORY |domain| (SIGNATURE |dimension| ((|NonNegativeInteger|))) (SIGNATURE |deepExpand| ((|OutputForm|) $)) (SIGNATURE |shallowExpand| ((|OutputForm|) $)) (SIGNATURE |generator| ($ (|NonNegativeInteger|))))) (|NonNegativeInteger|) (|NonNegativeInteger|) (|CommutativeRing|)) (T |FreeNilpotentLie|)) 
((|dimension| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FreeNilpotentLie| *3 *4 *5)) (|ofType| *3 *2) (|ofType| *4 *2) (|ofCategory| *5 (|CommutativeRing|)))) (|deepExpand| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|FreeNilpotentLie| *3 *4 *5)) (|ofType| *3 (|NonNegativeInteger|)) (|ofType| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|CommutativeRing|)))) (|shallowExpand| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|FreeNilpotentLie| *3 *4 *5)) (|ofType| *3 (|NonNegativeInteger|)) (|ofType| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|CommutativeRing|)))) (|generator| (*1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FreeNilpotentLie| *3 *4 *5)) (|ofType| *3 *2) (|ofType| *4 *2) (|ofCategory| *5 (|CommutativeRing|))))) 
(|Join| (|NonAssociativeAlgebra| |#3|) (CATEGORY |domain| (SIGNATURE |dimension| ((|NonNegativeInteger|))) (SIGNATURE |deepExpand| ((|OutputForm|) $)) (SIGNATURE |shallowExpand| ((|OutputForm|) $)) (SIGNATURE |generator| ($ (|NonNegativeInteger|))))) 
((|topFortranOutputStack| (((|String|)) 10)) (|showFortranOutputStack| (((|Stack| (|String|))) 28)) (|pushFortranOutputStack| (((|Void|) (|String|)) 25) (((|Void|) (|FileName|)) 24)) (|popFortranOutputStack| (((|Void|)) 26)) (|clearFortranOutputStack| (((|Stack| (|String|))) 27))) 
(((|FortranOutputStackPackage|) (CATEGORY |package| (SIGNATURE |clearFortranOutputStack| ((|Stack| (|String|)))) (SIGNATURE |showFortranOutputStack| ((|Stack| (|String|)))) (SIGNATURE |popFortranOutputStack| ((|Void|))) (SIGNATURE |pushFortranOutputStack| ((|Void|) (|FileName|))) (SIGNATURE |pushFortranOutputStack| ((|Void|) (|String|))) (SIGNATURE |topFortranOutputStack| ((|String|))))) (T |FortranOutputStackPackage|)) 
((|topFortranOutputStack| (*1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|FortranOutputStackPackage|)))) (|pushFortranOutputStack| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|FortranOutputStackPackage|)))) (|pushFortranOutputStack| (*1 *2 *3) (AND (|isDomain| *3 (|FileName|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|FortranOutputStackPackage|)))) (|popFortranOutputStack| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|FortranOutputStackPackage|)))) (|showFortranOutputStack| (*1 *2) (AND (|isDomain| *2 (|Stack| (|String|))) (|isDomain| *1 (|FortranOutputStackPackage|)))) (|clearFortranOutputStack| (*1 *2) (AND (|isDomain| *2 (|Stack| (|String|))) (|isDomain| *1 (|FortranOutputStackPackage|))))) 
(CATEGORY |package| (SIGNATURE |clearFortranOutputStack| ((|Stack| (|String|)))) (SIGNATURE |showFortranOutputStack| ((|Stack| (|String|)))) (SIGNATURE |popFortranOutputStack| ((|Void|))) (SIGNATURE |pushFortranOutputStack| ((|Void|) (|FileName|))) (SIGNATURE |pushFortranOutputStack| ((|Void|) (|String|))) (SIGNATURE |topFortranOutputStack| ((|String|)))) 
((|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) 16))) 
(((|FindOrderFinite| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |order| ((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)))) (|Join| (|Finite|) (|Field|)) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|)) (T |FindOrderFinite|)) 
((|order| (*1 *2 *3) (AND (|isDomain| *3 (|FiniteDivisor| *4 *5 *6 *7)) (|ofCategory| *4 (|Join| (|Finite|) (|Field|))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|ofCategory| *7 (|FunctionFieldCategory| *4 *5 *6)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FindOrderFinite| *4 *5 *6 *7))))) 
(CATEGORY |package| (SIGNATURE |order| ((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)))) 
((|coerce| (((|ScriptFormulaFormat|) |#1|) 11))) 
(((|ScriptFormulaFormat1| |#1|) (CATEGORY |package| (SIGNATURE |coerce| ((|ScriptFormulaFormat|) |#1|))) (|SetCategory|)) (T |ScriptFormulaFormat1|)) 
((|coerce| (*1 *2 *3) (AND (|isDomain| *2 (|ScriptFormulaFormat|)) (|isDomain| *1 (|ScriptFormulaFormat1| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(CATEGORY |package| (SIGNATURE |coerce| ((|ScriptFormulaFormat|) |#1|))) 
((~= (((|Boolean|) $ $) NIL)) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) 37)) (|setFormula!| (((|List| (|String|)) $ (|List| (|String|))) 38)) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) 39)) (|prologue| (((|List| (|String|)) $) 34)) (|new| (($) 23)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|formula| (((|List| (|String|)) $) 35)) (|epilogue| (((|List| (|String|)) $) 36)) (|display| (((|Void|) $ (|Integer|)) 32) (((|Void|) $) 33)) (|convert| (($ (|OutputForm|) (|Integer|)) 29)) (|coerce| (((|OutputForm|) $) 41) (($ (|OutputForm|)) 25)) (= (((|Boolean|) $ $) NIL))) 
(((|ScriptFormulaFormat|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|OutputForm|))) (SIGNATURE |convert| ($ (|OutputForm|) (|Integer|))) (SIGNATURE |display| ((|Void|) $ (|Integer|))) (SIGNATURE |display| ((|Void|) $)) (SIGNATURE |epilogue| ((|List| (|String|)) $)) (SIGNATURE |formula| ((|List| (|String|)) $)) (SIGNATURE |new| ($)) (SIGNATURE |prologue| ((|List| (|String|)) $)) (SIGNATURE |setEpilogue!| ((|List| (|String|)) $ (|List| (|String|)))) (SIGNATURE |setFormula!| ((|List| (|String|)) $ (|List| (|String|)))) (SIGNATURE |setPrologue!| ((|List| (|String|)) $ (|List| (|String|))))))) (T |ScriptFormulaFormat|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|ScriptFormulaFormat|)))) (|convert| (*1 *1 *2 *3) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|ScriptFormulaFormat|)))) (|display| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ScriptFormulaFormat|)))) (|display| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ScriptFormulaFormat|)))) (|epilogue| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|ScriptFormulaFormat|)))) (|formula| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|ScriptFormulaFormat|)))) (|new| (*1 *1) (|isDomain| *1 (|ScriptFormulaFormat|))) (|prologue| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|ScriptFormulaFormat|)))) (|setEpilogue!| (*1 *2 *1 *2) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|ScriptFormulaFormat|)))) (|setFormula!| (*1 *2 *1 *2) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|ScriptFormulaFormat|)))) (|setPrologue!| (*1 *2 *1 *2) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|ScriptFormulaFormat|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|OutputForm|))) (SIGNATURE |convert| ($ (|OutputForm|) (|Integer|))) (SIGNATURE |display| ((|Void|) $ (|Integer|))) (SIGNATURE |display| ((|Void|) $)) (SIGNATURE |epilogue| ((|List| (|String|)) $)) (SIGNATURE |formula| ((|List| (|String|)) $)) (SIGNATURE |new| ($)) (SIGNATURE |prologue| ((|List| (|String|)) $)) (SIGNATURE |setEpilogue!| ((|List| (|String|)) $ (|List| (|String|)))) (SIGNATURE |setFormula!| ((|List| (|String|)) $ (|List| (|String|)))) (SIGNATURE |setPrologue!| ((|List| (|String|)) $ (|List| (|String|)))))) 
((|outputAsFortran| (((|Void|) $) 7)) (|coerce| (((|OutputForm|) $) 8))) 
(((|FortranProgramCategory|) (|Category|)) (T |FortranProgramCategory|)) 
((|outputAsFortran| (*1 *2 *1) (AND (|ofCategory| *1 (|FortranProgramCategory|)) (|isDomain| *2 (|Void|))))) 
(|Join| (|Type|) (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |outputAsFortran| ((|Void|) $)))) 
(((|CoercibleTo| (|OutputForm|)) . T) ((|Type|) . T)) 
((|retractIfCan| (((|Union| $ "failed") (|Expression| (|Float|))) 19) (((|Union| $ "failed") (|Expression| (|Integer|))) 17) (((|Union| $ "failed") (|Polynomial| (|Float|))) 15) (((|Union| $ "failed") (|Polynomial| (|Integer|))) 13) (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) 11) (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) 9)) (|retract| (($ (|Expression| (|Float|))) 20) (($ (|Expression| (|Integer|))) 18) (($ (|Polynomial| (|Float|))) 16) (($ (|Polynomial| (|Integer|))) 14) (($ (|Fraction| (|Polynomial| (|Float|)))) 12) (($ (|Fraction| (|Polynomial| (|Integer|)))) 10)) (|outputAsFortran| (((|Void|) $) 7)) (|coerce| (((|OutputForm|) $) 8) (($ (|List| (|FortranCode|))) 23) (($ (|FortranCode|)) 22) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 21))) 
(((|FortranFunctionCategory|) (|Category|)) (T |FortranFunctionCategory|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|FortranCode|))) (|ofCategory| *1 (|FortranFunctionCategory|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|FortranCode|)) (|ofCategory| *1 (|FortranFunctionCategory|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) (|ofCategory| *1 (|FortranFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Expression| (|Float|))) (|ofCategory| *1 (|FortranFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Expression| (|Float|))) (|ofCategory| *1 (|FortranFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Expression| (|Integer|))) (|ofCategory| *1 (|FortranFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Expression| (|Integer|))) (|ofCategory| *1 (|FortranFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| (|Float|))) (|ofCategory| *1 (|FortranFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Polynomial| (|Float|))) (|ofCategory| *1 (|FortranFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| (|Integer|))) (|ofCategory| *1 (|FortranFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Polynomial| (|Integer|))) (|ofCategory| *1 (|FortranFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Polynomial| (|Float|)))) (|ofCategory| *1 (|FortranFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Fraction| (|Polynomial| (|Float|)))) (|ofCategory| *1 (|FortranFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Polynomial| (|Integer|)))) (|ofCategory| *1 (|FortranFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Fraction| (|Polynomial| (|Integer|)))) (|ofCategory| *1 (|FortranFunctionCategory|))))) 
(|Join| (|FortranProgramCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|List| (|FortranCode|)))) (SIGNATURE |coerce| ($ (|FortranCode|))) (SIGNATURE |coerce| ($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|)))))) (SIGNATURE |retract| ($ (|Expression| (|Float|)))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Expression| (|Float|)))) (SIGNATURE |retract| ($ (|Expression| (|Integer|)))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Expression| (|Integer|)))) (SIGNATURE |retract| ($ (|Polynomial| (|Float|)))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| (|Float|)))) (SIGNATURE |retract| ($ (|Polynomial| (|Integer|)))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| (|Integer|)))) (SIGNATURE |retract| ($ (|Fraction| (|Polynomial| (|Float|))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|))))) (SIGNATURE |retract| ($ (|Fraction| (|Polynomial| (|Integer|))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|))))))) 
(((|CoercibleTo| (|OutputForm|)) . T) ((|FortranProgramCategory|) . T) ((|Type|) . T)) 
((|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) 8)) (|outputAsFortran| (((|Void|) (|FileName|)) 27)) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) 59) (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) 35) (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) 34))) 
(((|FortranPackage|) (CATEGORY |package| (SIGNATURE |linkToFortran| ((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)))) (SIGNATURE |linkToFortran| ((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|))) (SIGNATURE |linkToFortran| ((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|)))) (SIGNATURE |outputAsFortran| ((|Void|) (|FileName|))) (SIGNATURE |setLegalFortranSourceExtensions| ((|List| (|String|)) (|List| (|String|)))))) (T |FortranPackage|)) 
((|setLegalFortranSourceExtensions| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|FortranPackage|)))) (|outputAsFortran| (*1 *2 *3) (AND (|isDomain| *3 (|FileName|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|FortranPackage|)))) (|linkToFortran| (*1 *2 *3 *4 *5 *4) (AND (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *5 (|TheSymbolTable|)) (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|SExpression|)) (|isDomain| *1 (|FortranPackage|)))) (|linkToFortran| (*1 *2 *3 *4 *5 *6 *3) (AND (|isDomain| *5 (|List| (|List| (|Union| (|:| |array| *6) (|:| |scalar| *3))))) (|isDomain| *4 (|List| (|Union| (|:| |array| (|List| *3)) (|:| |scalar| (|Symbol|))))) (|isDomain| *6 (|List| (|Symbol|))) (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|SExpression|)) (|isDomain| *1 (|FortranPackage|)))) (|linkToFortran| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *5 (|List| (|List| (|Union| (|:| |array| *6) (|:| |scalar| *3))))) (|isDomain| *4 (|List| (|Union| (|:| |array| (|List| *3)) (|:| |scalar| (|Symbol|))))) (|isDomain| *6 (|List| (|Symbol|))) (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|SExpression|)) (|isDomain| *1 (|FortranPackage|))))) 
(CATEGORY |package| (SIGNATURE |linkToFortran| ((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)))) (SIGNATURE |linkToFortran| ((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|))) (SIGNATURE |linkToFortran| ((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|)))) (SIGNATURE |outputAsFortran| ((|Void|) (|FileName|))) (SIGNATURE |setLegalFortranSourceExtensions| ((|List| (|String|)) (|List| (|String|))))) 
((|outputAsFortran| (((|Void|) $) 37)) (|coerce| (((|OutputForm|) $) 89) (($ (|FortranCode|)) 92) (($ (|List| (|FortranCode|))) 91) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 88) (($ (|Expression| (|MachineInteger|))) 52) (($ (|Expression| (|MachineFloat|))) 66) (($ (|Expression| (|MachineComplex|))) 78) (($ (|Equation| (|Expression| (|MachineInteger|)))) 62) (($ (|Equation| (|Expression| (|MachineFloat|)))) 74) (($ (|Equation| (|Expression| (|MachineComplex|)))) 86) (($ (|Expression| (|Integer|))) 96) (($ (|Expression| (|Float|))) 108) (($ (|Expression| (|Complex| (|Float|)))) 120) (($ (|Equation| (|Expression| (|Integer|)))) 104) (($ (|Equation| (|Expression| (|Float|)))) 116) (($ (|Equation| (|Expression| (|Complex| (|Float|))))) 128))) 
(((|FortranProgram| |#1| |#2| |#3| |#4|) (|Join| (|FortranProgramCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|FortranCode|))) (SIGNATURE |coerce| ($ (|List| (|FortranCode|)))) (SIGNATURE |coerce| ($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|)))))) (SIGNATURE |coerce| ($ (|Expression| (|MachineInteger|)))) (SIGNATURE |coerce| ($ (|Expression| (|MachineFloat|)))) (SIGNATURE |coerce| ($ (|Expression| (|MachineComplex|)))) (SIGNATURE |coerce| ($ (|Equation| (|Expression| (|MachineInteger|))))) (SIGNATURE |coerce| ($ (|Equation| (|Expression| (|MachineFloat|))))) (SIGNATURE |coerce| ($ (|Equation| (|Expression| (|MachineComplex|))))) (SIGNATURE |coerce| ($ (|Expression| (|Integer|)))) (SIGNATURE |coerce| ($ (|Expression| (|Float|)))) (SIGNATURE |coerce| ($ (|Expression| (|Complex| (|Float|))))) (SIGNATURE |coerce| ($ (|Equation| (|Expression| (|Integer|))))) (SIGNATURE |coerce| ($ (|Equation| (|Expression| (|Float|))))) (SIGNATURE |coerce| ($ (|Equation| (|Expression| (|Complex| (|Float|)))))))) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Symbol|)) (|SymbolTable|)) (T |FortranProgram|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|FortranCode|)) (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)) (|ofType| *3 (|Symbol|)) (|ofType| *4 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|SymbolTable|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|FortranCode|))) (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)) (|ofType| *3 (|Symbol|)) (|ofType| *4 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|SymbolTable|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)) (|ofType| *3 (|Symbol|)) (|ofType| *4 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|SymbolTable|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Expression| (|MachineInteger|))) (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)) (|ofType| *3 (|Symbol|)) (|ofType| *4 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|SymbolTable|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Expression| (|MachineFloat|))) (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)) (|ofType| *3 (|Symbol|)) (|ofType| *4 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|SymbolTable|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Expression| (|MachineComplex|))) (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)) (|ofType| *3 (|Symbol|)) (|ofType| *4 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|SymbolTable|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Equation| (|Expression| (|MachineInteger|)))) (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)) (|ofType| *3 (|Symbol|)) (|ofType| *4 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|SymbolTable|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Equation| (|Expression| (|MachineFloat|)))) (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)) (|ofType| *3 (|Symbol|)) (|ofType| *4 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|SymbolTable|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Equation| (|Expression| (|MachineComplex|)))) (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)) (|ofType| *3 (|Symbol|)) (|ofType| *4 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|SymbolTable|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Expression| (|Integer|))) (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)) (|ofType| *3 (|Symbol|)) (|ofType| *4 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|SymbolTable|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Expression| (|Float|))) (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)) (|ofType| *3 (|Symbol|)) (|ofType| *4 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|SymbolTable|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Expression| (|Complex| (|Float|)))) (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)) (|ofType| *3 (|Symbol|)) (|ofType| *4 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|SymbolTable|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Equation| (|Expression| (|Integer|)))) (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)) (|ofType| *3 (|Symbol|)) (|ofType| *4 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|SymbolTable|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Equation| (|Expression| (|Float|)))) (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)) (|ofType| *3 (|Symbol|)) (|ofType| *4 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|SymbolTable|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Equation| (|Expression| (|Complex| (|Float|))))) (|isDomain| *1 (|FortranProgram| *3 *4 *5 *6)) (|ofType| *3 (|Symbol|)) (|ofType| *4 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|SymbolTable|))))) 
(|Join| (|FortranProgramCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|FortranCode|))) (SIGNATURE |coerce| ($ (|List| (|FortranCode|)))) (SIGNATURE |coerce| ($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|)))))) (SIGNATURE |coerce| ($ (|Expression| (|MachineInteger|)))) (SIGNATURE |coerce| ($ (|Expression| (|MachineFloat|)))) (SIGNATURE |coerce| ($ (|Expression| (|MachineComplex|)))) (SIGNATURE |coerce| ($ (|Equation| (|Expression| (|MachineInteger|))))) (SIGNATURE |coerce| ($ (|Equation| (|Expression| (|MachineFloat|))))) (SIGNATURE |coerce| ($ (|Equation| (|Expression| (|MachineComplex|))))) (SIGNATURE |coerce| ($ (|Expression| (|Integer|)))) (SIGNATURE |coerce| ($ (|Expression| (|Float|)))) (SIGNATURE |coerce| ($ (|Expression| (|Complex| (|Float|))))) (SIGNATURE |coerce| ($ (|Equation| (|Expression| (|Integer|))))) (SIGNATURE |coerce| ($ (|Equation| (|Expression| (|Float|))))) (SIGNATURE |coerce| ($ (|Equation| (|Expression| (|Complex| (|Float|)))))))) 
((~= (((|Boolean|) $ $) NIL)) (|polyPart| ((|#2| $) 36)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|fullPartialFraction| (($ (|Fraction| |#2|)) 84)) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) 37)) (|differentiate| (($ $) 32) (($ $ (|NonNegativeInteger|)) 34)) (|convert| (((|Fraction| |#2|) $) 46)) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) 31)) (|coerce| (((|OutputForm|) $) 120)) (D (($ $) 33) (($ $ (|NonNegativeInteger|)) 35)) (= (((|Boolean|) $ $) NIL)) (+ (($ |#2| $) 39))) 
(((|FullPartialFractionExpansion| |#1| |#2|) (|Join| (|SetCategory|) (|ConvertibleTo| (|Fraction| |#2|)) (CATEGORY |domain| (SIGNATURE + ($ |#2| $)) (SIGNATURE |fullPartialFraction| ($ (|Fraction| |#2|))) (SIGNATURE |polyPart| (|#2| $)) (SIGNATURE |fracPart| ((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $)) (SIGNATURE |construct| ($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))))) (SIGNATURE |differentiate| ($ $)) (SIGNATURE D ($ $)) (SIGNATURE |differentiate| ($ $ (|NonNegativeInteger|))) (SIGNATURE D ($ $ (|NonNegativeInteger|))))) (|Join| (|Field|) (|CharacteristicZero|)) (|UnivariatePolynomialCategory| |#1|)) (T |FullPartialFractionExpansion|)) 
((+ (*1 *1 *2 *1) (AND (|ofCategory| *3 (|Join| (|Field|) (|CharacteristicZero|))) (|isDomain| *1 (|FullPartialFractionExpansion| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|fullPartialFraction| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|Join| (|Field|) (|CharacteristicZero|))) (|isDomain| *1 (|FullPartialFractionExpansion| *3 *4)))) (|polyPart| (*1 *2 *1) (AND (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)) (|isDomain| *1 (|FullPartialFractionExpansion| *3 *2)) (|ofCategory| *3 (|Join| (|Field|) (|CharacteristicZero|))))) (|fracPart| (*1 *2 *1) (AND (|ofCategory| *3 (|Join| (|Field|) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| *4) (|:| |num| *4)))) (|isDomain| *1 (|FullPartialFractionExpansion| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|construct| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| *4) (|:| |num| *4)))) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|Join| (|Field|) (|CharacteristicZero|))) (|isDomain| *1 (|FullPartialFractionExpansion| *3 *4)))) (|differentiate| (*1 *1 *1) (AND (|ofCategory| *2 (|Join| (|Field|) (|CharacteristicZero|))) (|isDomain| *1 (|FullPartialFractionExpansion| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (D (*1 *1 *1) (AND (|ofCategory| *2 (|Join| (|Field|) (|CharacteristicZero|))) (|isDomain| *1 (|FullPartialFractionExpansion| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *3 (|Join| (|Field|) (|CharacteristicZero|))) (|isDomain| *1 (|FullPartialFractionExpansion| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (D (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *3 (|Join| (|Field|) (|CharacteristicZero|))) (|isDomain| *1 (|FullPartialFractionExpansion| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))))) 
(|Join| (|SetCategory|) (|ConvertibleTo| (|Fraction| |#2|)) (CATEGORY |domain| (SIGNATURE + ($ |#2| $)) (SIGNATURE |fullPartialFraction| ($ (|Fraction| |#2|))) (SIGNATURE |polyPart| (|#2| $)) (SIGNATURE |fracPart| ((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $)) (SIGNATURE |construct| ($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))))) (SIGNATURE |differentiate| ($ $)) (SIGNATURE D ($ $)) (SIGNATURE |differentiate| ($ $ (|NonNegativeInteger|))) (SIGNATURE D ($ $ (|NonNegativeInteger|))))) 
((~= (((|Boolean|) $ $) 9 (OR (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Float|)))))) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) 15 (|has| |#1| (|PatternMatchable| (|Float|)))) (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) 14 (|has| |#1| (|PatternMatchable| (|Integer|))))) (|latex| (((|String|) $) 13 (OR (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Float|)))))) (|hash| (((|SingleInteger|) $) 12 (OR (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Float|)))))) (|coerce| (((|OutputForm|) $) 11 (OR (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Float|)))))) (= (((|Boolean|) $ $) 10 (OR (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Float|))))))) 
(((|FullyPatternMatchable| |#1|) (|Category|) (|Type|)) (T |FullyPatternMatchable|)) 
NIL 
(|Join| (|Type|) (CATEGORY |package| (IF (|has| |t#1| (|PatternMatchable| (|Integer|))) (ATTRIBUTE (|PatternMatchable| (|Integer|))) |noBranch|) (IF (|has| |t#1| (|PatternMatchable| (|Float|))) (ATTRIBUTE (|PatternMatchable| (|Float|))) |noBranch|))) 
(((|BasicType|) OR (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Float|)))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Float|)))) ((|PatternMatchable| (|Float|)) |has| |#1| (|PatternMatchable| (|Float|))) ((|PatternMatchable| (|Integer|)) |has| |#1| (|PatternMatchable| (|Integer|))) ((|SetCategory|) OR (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Float|)))) ((|Type|) . T)) 
((|primeFrobenius| (($ $) 10) (($ $ (|NonNegativeInteger|)) 11))) 
(((|FieldOfPrimeCharacteristic&| |#1|) (CATEGORY |domain| (SIGNATURE |primeFrobenius| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |primeFrobenius| (|#1| |#1|))) (|FieldOfPrimeCharacteristic|)) (T |FieldOfPrimeCharacteristic&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |primeFrobenius| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |primeFrobenius| (|#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 73)) (|squareFree| (((|Factored| $) $) 72)) (|sizeLess?| (((|Boolean|) $ $) 58)) (|sample| (($) 16 T CONST)) (|rem| (($ $ $) 54)) (|recip| (((|Union| $ "failed") $) 33)) (|quo| (($ $ $) 55)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 50)) (|primeFrobenius| (($ $) 77) (($ $ (|NonNegativeInteger|)) 76)) (|prime?| (((|Boolean|) $) 71)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 79)) (|one?| (((|Boolean|) $) 30)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 51)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 70)) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|factor| (((|Factored| $) $) 74)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 53) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 52)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 49)) (|euclideanSize| (((|NonNegativeInteger|) $) 57)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 56)) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) 78)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42) (($ (|Fraction| (|Integer|))) 65)) (|charthRoot| (((|Union| $ "failed") $) 80)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 69)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (/ (($ $ $) 64)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 68)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ (|Fraction| (|Integer|))) 67) (($ (|Fraction| (|Integer|)) $) 66))) 
(((|FieldOfPrimeCharacteristic|) (|Category|)) (T |FieldOfPrimeCharacteristic|)) 
((|order| (*1 *2 *1) (AND (|ofCategory| *1 (|FieldOfPrimeCharacteristic|)) (|isDomain| *2 (|OnePointCompletion| (|PositiveInteger|))))) (|discreteLog| (*1 *2 *1 *1) (|partial| AND (|ofCategory| *1 (|FieldOfPrimeCharacteristic|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|primeFrobenius| (*1 *1 *1) (|ofCategory| *1 (|FieldOfPrimeCharacteristic|))) (|primeFrobenius| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|FieldOfPrimeCharacteristic|)) (|isDomain| *2 (|NonNegativeInteger|))))) 
(|Join| (|Field|) (|CharacteristicNonZero|) (CATEGORY |domain| (SIGNATURE |order| ((|OnePointCompletion| (|PositiveInteger|)) $)) (SIGNATURE |discreteLog| ((|Union| (|NonNegativeInteger|) "failed") $ $)) (SIGNATURE |primeFrobenius| ($ $)) (SIGNATURE |primeFrobenius| ($ $ (|NonNegativeInteger|))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| (|Fraction| (|Integer|))) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| (|Fraction| (|Integer|))) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightModule| (|Fraction| (|Integer|))) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|UniqueFactorizationDomain|) . T)) 
((|float| (($ (|Integer|) (|Integer|)) 11) (($ (|Integer|) (|Integer|) (|PositiveInteger|)) NIL)) (|digits| (((|PositiveInteger|)) 16) (((|PositiveInteger|) (|PositiveInteger|)) NIL))) 
(((|FloatingPointSystem&| |#1|) (CATEGORY |domain| (SIGNATURE |digits| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |digits| ((|PositiveInteger|))) (SIGNATURE |float| (|#1| (|Integer|) (|Integer|) (|PositiveInteger|))) (SIGNATURE |float| (|#1| (|Integer|) (|Integer|)))) (|FloatingPointSystem|)) (T |FloatingPointSystem&|)) 
((|digits| (*1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|FloatingPointSystem&| *3)) (|ofCategory| *3 (|FloatingPointSystem|)))) (|digits| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|FloatingPointSystem&| *3)) (|ofCategory| *3 (|FloatingPointSystem|))))) 
(CATEGORY |domain| (SIGNATURE |digits| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |digits| ((|PositiveInteger|))) (SIGNATURE |float| (|#1| (|Integer|) (|Integer|) (|PositiveInteger|))) (SIGNATURE |float| (|#1| (|Integer|) (|Integer|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|wholePart| (((|Integer|) $) 87)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|truncate| (($ $) 85)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 73)) (|squareFree| (((|Factored| $) $) 72)) (|sqrt| (($ $) 95)) (|sizeLess?| (((|Boolean|) $ $) 58)) (|sign| (((|Integer|) $) 112)) (|sample| (($) 16 T CONST)) (|round| (($ $) 84)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 100) (((|Union| (|Fraction| (|Integer|)) "failed") $) 97)) (|retract| (((|Integer|) $) 99) (((|Fraction| (|Integer|)) $) 96)) (|rem| (($ $ $) 54)) (|recip| (((|Union| $ "failed") $) 33)) (|quo| (($ $ $) 55)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 50)) (|prime?| (((|Boolean|) $) 71)) (|precision| (((|PositiveInteger|)) 121) (((|PositiveInteger|) (|PositiveInteger|)) 118 (|has| $ (ATTRIBUTE |arbitraryPrecision|)))) (|positive?| (((|Boolean|) $) 110)) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) 91)) (|order| (((|Integer|) $) 127)) (|one?| (((|Boolean|) $) 30)) (|nthRoot| (($ $ (|Integer|)) 94)) (|norm| (($ $) 90)) (|negative?| (((|Boolean|) $) 111)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 51)) (|min| (($ $ $) 109) (($) 115 (AND (|not| (|has| $ (ATTRIBUTE |arbitraryPrecision|))) (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|)))))) (|max| (($ $ $) 108) (($) 114 (AND (|not| (|has| $ (ATTRIBUTE |arbitraryPrecision|))) (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|)))))) (|mantissa| (((|Integer|) $) 124)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 70)) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) 117 (|has| $ (ATTRIBUTE |arbitraryPrecision|)))) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|fractionPart| (($ $) 86)) (|floor| (($ $) 88)) (|float| (($ (|Integer|) (|Integer|)) 129) (($ (|Integer|) (|Integer|) (|PositiveInteger|)) 128)) (|factor| (((|Factored| $) $) 74)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 53) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 52)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 49)) (|exponent| (((|Integer|) $) 125)) (|euclideanSize| (((|NonNegativeInteger|) $) 57)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 56)) (|digits| (((|PositiveInteger|)) 122) (((|PositiveInteger|) (|PositiveInteger|)) 119 (|has| $ (ATTRIBUTE |arbitraryPrecision|)))) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) 116 (|has| $ (ATTRIBUTE |arbitraryPrecision|)))) (|convert| (((|Float|) $) 103) (((|DoubleFloat|) $) 102) (((|Pattern| (|Float|)) $) 92)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42) (($ (|Fraction| (|Integer|))) 65) (($ (|Integer|)) 101) (($ (|Fraction| (|Integer|))) 98)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|ceiling| (($ $) 89)) (|bits| (((|PositiveInteger|)) 123) (((|PositiveInteger|) (|PositiveInteger|)) 120 (|has| $ (ATTRIBUTE |arbitraryPrecision|)))) (|base| (((|PositiveInteger|)) 126)) (|associates?| (((|Boolean|) $ $) 38)) (|abs| (($ $) 113)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 69)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (>= (((|Boolean|) $ $) 106)) (> (((|Boolean|) $ $) 105)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 107)) (< (((|Boolean|) $ $) 104)) (/ (($ $ $) 64)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 68) (($ $ (|Fraction| (|Integer|))) 93)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ (|Fraction| (|Integer|))) 67) (($ (|Fraction| (|Integer|)) $) 66))) 
(((|FloatingPointSystem|) (|Category|)) (T |FloatingPointSystem|)) 
((|float| (*1 *1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|FloatingPointSystem|)))) (|float| (*1 *1 *2 *2 *3) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *1 (|FloatingPointSystem|)))) (|order| (*1 *2 *1) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|Integer|)))) (|base| (*1 *2) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|PositiveInteger|)))) (|exponent| (*1 *2 *1) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|Integer|)))) (|mantissa| (*1 *2 *1) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|Integer|)))) (|bits| (*1 *2) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|PositiveInteger|)))) (|digits| (*1 *2) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|PositiveInteger|)))) (|precision| (*1 *2) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|PositiveInteger|)))) (|bits| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|has| *1 (ATTRIBUTE |arbitraryPrecision|)) (|ofCategory| *1 (|FloatingPointSystem|)))) (|digits| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|has| *1 (ATTRIBUTE |arbitraryPrecision|)) (|ofCategory| *1 (|FloatingPointSystem|)))) (|precision| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|has| *1 (ATTRIBUTE |arbitraryPrecision|)) (|ofCategory| *1 (|FloatingPointSystem|)))) (|increasePrecision| (*1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|has| *1 (ATTRIBUTE |arbitraryPrecision|)) (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|PositiveInteger|)))) (|decreasePrecision| (*1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|has| *1 (ATTRIBUTE |arbitraryPrecision|)) (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|PositiveInteger|)))) (|min| (*1 *1) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|not| (|has| *1 (ATTRIBUTE |arbitraryPrecision|))) (|not| (|has| *1 (ATTRIBUTE |arbitraryExponent|))))) (|max| (*1 *1) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|not| (|has| *1 (ATTRIBUTE |arbitraryPrecision|))) (|not| (|has| *1 (ATTRIBUTE |arbitraryExponent|)))))) 
(|Join| (|RealNumberSystem|) (CATEGORY |domain| (ATTRIBUTE |approximate|) (SIGNATURE |float| ($ (|Integer|) (|Integer|))) (SIGNATURE |float| ($ (|Integer|) (|Integer|) (|PositiveInteger|))) (SIGNATURE |order| ((|Integer|) $)) (SIGNATURE |base| ((|PositiveInteger|))) (SIGNATURE |exponent| ((|Integer|) $)) (SIGNATURE |mantissa| ((|Integer|) $)) (SIGNATURE |bits| ((|PositiveInteger|))) (SIGNATURE |digits| ((|PositiveInteger|))) (SIGNATURE |precision| ((|PositiveInteger|))) (IF (|has| $ (ATTRIBUTE |arbitraryPrecision|)) (PROGN (SIGNATURE |bits| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |digits| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |precision| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |increasePrecision| ((|PositiveInteger|) (|Integer|))) (SIGNATURE |decreasePrecision| ((|PositiveInteger|) (|Integer|)))) |noBranch|) (IF (|has| $ (ATTRIBUTE |arbitraryExponent|)) |noBranch| (IF (|has| $ (ATTRIBUTE |arbitraryPrecision|)) |noBranch| (PROGN (SIGNATURE |min| ($)) (SIGNATURE |max| ($))))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|DoubleFloat|)) . T) ((|ConvertibleTo| (|Float|)) . T) ((|ConvertibleTo| (|Pattern| (|Float|))) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| (|Fraction| (|Integer|))) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| (|Fraction| (|Integer|))) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|PatternMatchable| (|Float|)) . T) ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T) ((|RealConstant|) . T) ((|RealNumberSystem|) . T) ((|RetractableTo| (|Fraction| (|Integer|))) . T) ((|RetractableTo| (|Integer|)) . T) ((|RightModule| (|Fraction| (|Integer|))) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|UniqueFactorizationDomain|) . T)) 
((|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) 20))) 
(((|FactoredFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)))) (|IntegralDomain|) (|IntegralDomain|)) (T |FactoredFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Factored| *5)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|IntegralDomain|)) (|isDomain| *2 (|Factored| *6)) (|isDomain| *1 (|FactoredFunctions2| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |map| ((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)))) 
((|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) 13))) 
(((|FractionFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)))) (|IntegralDomain|) (|IntegralDomain|)) (T |FractionFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Fraction| *5)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|IntegralDomain|)) (|isDomain| *2 (|Fraction| *6)) (|isDomain| *1 (|FractionFunctions2| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |map| ((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 13)) (|wholePart| ((|#1| $) 21 (|has| |#1| (|EuclideanDomain|)))) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sign| (((|Integer|) $) NIL (|has| |#1| (|OrderedIntegralDomain|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 17) (((|Union| (|Symbol|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Symbol|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) 70 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|))))) (|retract| ((|#1| $) 15) (((|Symbol|) $) NIL (|has| |#1| (|RetractableTo| (|Symbol|)))) (((|Fraction| (|Integer|)) $) 67 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|))))) (|rem| (($ $ $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| |#1|) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) 50)) (|random| (($) NIL (|has| |#1| (|IntegerNumberSystem|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|positive?| (((|Boolean|) $) NIL (|has| |#1| (|OrderedIntegralDomain|)))) (|patternMatch| (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (|has| |#1| (|PatternMatchable| (|Integer|)))) (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (|has| |#1| (|PatternMatchable| (|Float|))))) (|one?| (((|Boolean|) $) 64)) (|numerator| (($ $) NIL)) (|numer| ((|#1| $) 71)) (|nextItem| (((|Union| $ "failed") $) NIL (|has| |#1| (|StepThrough|)))) (|negative?| (((|Boolean|) $) NIL (|has| |#1| (|OrderedIntegralDomain|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|init| (($) NIL (|has| |#1| (|StepThrough|)) CONST)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 97)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|fractionPart| (($ $) NIL (|has| |#1| (|EuclideanDomain|)))) (|floor| ((|#1| $) 28 (|has| |#1| (|IntegerNumberSystem|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 133 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 129 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ |#1| |#1|) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ (|Equation| |#1|)) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ (|List| (|Equation| |#1|))) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ (|List| (|Symbol|)) (|List| |#1|)) NIL (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|))) (($ $ (|Symbol|) |#1|) NIL (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|)))) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|elt| (($ $ |#1|) NIL (|has| |#1| (|Eltable| |#1| |#1|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|differentiate| (($ $) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#1| |#1|)) 63)) (|denominator| (($ $) NIL)) (|denom| ((|#1| $) 73)) (|convert| (((|Pattern| (|Integer|)) $) NIL (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|))))) (((|Pattern| (|Float|)) $) NIL (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|))))) (((|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| (|InputForm|)))) (((|Float|) $) NIL (|has| |#1| (|RealConstant|))) (((|DoubleFloat|) $) NIL (|has| |#1| (|RealConstant|)))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 113 (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ |#1|) 10) (($ (|Symbol|)) NIL (|has| |#1| (|RetractableTo| (|Symbol|))))) (|charthRoot| (((|Union| $ "failed") $) 99 (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) 100)) (|ceiling| ((|#1| $) 26 (|has| |#1| (|IntegerNumberSystem|)))) (|associates?| (((|Boolean|) $ $) NIL)) (|abs| (($ $) NIL (|has| |#1| (|OrderedIntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) 22 T CONST)) (|One| (($) 8 T CONST)) (|OMwrite| (((|String|) $) 43 (AND (|has| |#1| (|IntegerNumberSystem|)) (|has| |#1| (|OpenMath|)))) (((|String|) $ (|Boolean|)) 44 (AND (|has| |#1| (|IntegerNumberSystem|)) (|has| |#1| (|OpenMath|)))) (((|Void|) (|OpenMathDevice|) $) 45 (AND (|has| |#1| (|IntegerNumberSystem|)) (|has| |#1| (|OpenMath|)))) (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) 46 (AND (|has| |#1| (|IntegerNumberSystem|)) (|has| |#1| (|OpenMath|))))) (D (($ $) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#1| |#1|)) NIL)) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) 56)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) 24 (|has| |#1| (|OrderedSet|)))) (/ (($ $ $) 124) (($ |#1| |#1|) 52)) (- (($ $) 25) (($ $ $) 55)) (+ (($ $ $) 53)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) 123)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 60) (($ $ $) 57) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ |#1| $) 61) (($ $ |#1|) 85))) 
(((|Fraction| |#1|) (|Join| (|QuotientFieldCategory| |#1|) (CATEGORY |package| (IF (|has| |#1| (|IntegerNumberSystem|)) (IF (|has| |#1| (|OpenMath|)) (ATTRIBUTE (|OpenMath|)) |noBranch|) |noBranch|) (IF (|has| |#1| (ATTRIBUTE |canonical|)) (IF (|has| |#1| (|GcdDomain|)) (IF (|has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (ATTRIBUTE |canonical|) |noBranch|) |noBranch|) |noBranch|))) (|IntegralDomain|)) (T |Fraction|)) 
NIL 
(|Join| (|QuotientFieldCategory| |#1|) (CATEGORY |package| (IF (|has| |#1| (|IntegerNumberSystem|)) (IF (|has| |#1| (|OpenMath|)) (ATTRIBUTE (|OpenMath|)) |noBranch|) |noBranch|) (IF (|has| |#1| (ATTRIBUTE |canonical|)) (IF (|has| |#1| (|GcdDomain|)) (IF (|has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (ATTRIBUTE |canonical|) |noBranch|) |noBranch|) |noBranch|))) 
((|traceMatrix| (((|Matrix| |#2|) (|Vector| $)) NIL) (((|Matrix| |#2|)) 18)) (|represents| (($ (|Vector| |#2|) (|Vector| $)) NIL) (($ (|Vector| |#2|)) 26)) (|regularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) NIL) (((|Matrix| |#2|) $) 22)) (|minimalPolynomial| ((|#3| $) 59)) (|discriminant| ((|#2| (|Vector| $)) NIL) ((|#2|) 20)) (|coordinates| (((|Vector| |#2|) $ (|Vector| $)) NIL) (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) NIL) (((|Vector| |#2|) $) NIL) (((|Matrix| |#2|) (|Vector| $)) 24)) (|convert| (((|Vector| |#2|) $) 11) (($ (|Vector| |#2|)) 13)) (|characteristicPolynomial| ((|#3| $) 51))) 
(((|FramedAlgebra&| |#1| |#2| |#3|) (CATEGORY |domain| (SIGNATURE |regularRepresentation| ((|Matrix| |#2|) |#1|)) (SIGNATURE |discriminant| (|#2|)) (SIGNATURE |traceMatrix| ((|Matrix| |#2|))) (SIGNATURE |convert| (|#1| (|Vector| |#2|))) (SIGNATURE |convert| ((|Vector| |#2|) |#1|)) (SIGNATURE |represents| (|#1| (|Vector| |#2|))) (SIGNATURE |coordinates| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#2|) |#1|)) (SIGNATURE |minimalPolynomial| (|#3| |#1|)) (SIGNATURE |characteristicPolynomial| (|#3| |#1|)) (SIGNATURE |traceMatrix| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |discriminant| (|#2| (|Vector| |#1|))) (SIGNATURE |represents| (|#1| (|Vector| |#2|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Matrix| |#2|) (|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#2|) |#1| (|Vector| |#1|))) (SIGNATURE |regularRepresentation| ((|Matrix| |#2|) |#1| (|Vector| |#1|)))) (|FramedAlgebra| |#2| |#3|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#2|)) (T |FramedAlgebra&|)) 
((|traceMatrix| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|FramedAlgebra&| *3 *4 *5)) (|ofCategory| *3 (|FramedAlgebra| *4 *5)))) (|discriminant| (*1 *2) (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|FramedAlgebra&| *3 *2 *4)) (|ofCategory| *3 (|FramedAlgebra| *2 *4))))) 
(CATEGORY |domain| (SIGNATURE |regularRepresentation| ((|Matrix| |#2|) |#1|)) (SIGNATURE |discriminant| (|#2|)) (SIGNATURE |traceMatrix| ((|Matrix| |#2|))) (SIGNATURE |convert| (|#1| (|Vector| |#2|))) (SIGNATURE |convert| ((|Vector| |#2|) |#1|)) (SIGNATURE |represents| (|#1| (|Vector| |#2|))) (SIGNATURE |coordinates| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#2|) |#1|)) (SIGNATURE |minimalPolynomial| (|#3| |#1|)) (SIGNATURE |characteristicPolynomial| (|#3| |#1|)) (SIGNATURE |traceMatrix| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |discriminant| (|#2| (|Vector| |#1|))) (SIGNATURE |represents| (|#1| (|Vector| |#2|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Matrix| |#2|) (|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#2|) |#1| (|Vector| |#1|))) (SIGNATURE |regularRepresentation| ((|Matrix| |#2|) |#1| (|Vector| |#1|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) 44) (((|Matrix| |#1|)) 55)) (|trace| ((|#1| $) 50)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|represents| (($ (|Vector| |#1|) (|Vector| $)) 46) (($ (|Vector| |#1|)) 58)) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 51) (((|Matrix| |#1|) $) 53)) (|recip| (((|Union| $ "failed") $) 33)) (|rank| (((|PositiveInteger|)) 52)) (|one?| (((|Boolean|) $) 30)) (|norm| ((|#1| $) 49)) (|minimalPolynomial| ((|#2| $) 42 (|has| |#1| (|Field|)))) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|discriminant| ((|#1| (|Vector| $)) 45) ((|#1|) 54)) (|coordinates| (((|Vector| |#1|) $ (|Vector| $)) 48) (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) 47) (((|Vector| |#1|) $) 60) (((|Matrix| |#1|) (|Vector| $)) 59)) (|convert| (((|Vector| |#1|) $) 57) (($ (|Vector| |#1|)) 56)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ |#1|) 36)) (|charthRoot| (((|Union| $ "failed") $) 41 (|has| |#1| (|CharacteristicNonZero|)))) (|characteristicPolynomial| ((|#2| $) 43)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|basis| (((|Vector| $)) 61)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 38) (($ |#1| $) 37))) 
(((|FramedAlgebra| |#1| |#2|) (|Category|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |t#1|)) (T |FramedAlgebra|)) 
((|basis| (*1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FramedAlgebra| *3 *4)))) (|coordinates| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Vector| *3)))) (|coordinates| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FramedAlgebra| *4 *5)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Matrix| *4)))) (|represents| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|convert| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Vector| *3)))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|traceMatrix| (*1 *2) (AND (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Matrix| *3)))) (|discriminant| (*1 *2) (AND (|ofCategory| *1 (|FramedAlgebra| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|regularRepresentation| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Matrix| *3))))) 
(|Join| (|FiniteRankAlgebra| |t#1| |t#2|) (CATEGORY |domain| (SIGNATURE |basis| ((|Vector| $))) (SIGNATURE |coordinates| ((|Vector| |t#1|) $)) (SIGNATURE |coordinates| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |represents| ($ (|Vector| |t#1|))) (SIGNATURE |convert| ((|Vector| |t#1|) $)) (SIGNATURE |convert| ($ (|Vector| |t#1|))) (SIGNATURE |traceMatrix| ((|Matrix| |t#1|))) (SIGNATURE |discriminant| (|t#1|)) (SIGNATURE |regularRepresentation| ((|Matrix| |t#1|) $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|FiniteRankAlgebra| |#1| |#2|) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|retractIfCan| (((|Union| |#2| "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) 27) (((|Union| (|Integer|) "failed") $) 19)) (|retract| ((|#2| $) NIL) (((|Fraction| (|Integer|)) $) 24) (((|Integer|) $) 14)) (|coerce| (($ |#2|) NIL) (($ (|Fraction| (|Integer|))) 22) (($ (|Integer|)) 11))) 
(((|FullyRetractableTo&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |retract| (|#2| |#1|))) (|FullyRetractableTo| |#2|) (|Type|)) (T |FullyRetractableTo&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |retract| (|#2| |#1|))) 
((|retractIfCan| (((|Union| |#1| "failed") $) 7) (((|Union| (|Fraction| (|Integer|)) "failed") $) 15 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Integer|) "failed") $) 12 (|has| |#1| (|RetractableTo| (|Integer|))))) (|retract| ((|#1| $) 8) (((|Fraction| (|Integer|)) $) 14 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Integer|) $) 11 (|has| |#1| (|RetractableTo| (|Integer|))))) (|coerce| (($ |#1|) 6) (($ (|Fraction| (|Integer|))) 16 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (($ (|Integer|)) 13 (|has| |#1| (|RetractableTo| (|Integer|)))))) 
(((|FullyRetractableTo| |#1|) (|Category|) (|Type|)) (T |FullyRetractableTo|)) 
NIL 
(|Join| (|RetractableTo| |t#1|) (CATEGORY |package| (IF (|has| |t#1| (|RetractableTo| (|Integer|))) (ATTRIBUTE (|RetractableTo| (|Integer|))) |noBranch|) (IF (|has| |t#1| (|RetractableTo| (|Fraction| (|Integer|)))) (ATTRIBUTE (|RetractableTo| (|Fraction| (|Integer|)))) |noBranch|))) 
(((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T)) 
((|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) 33))) 
(((|FractionalIdealFunctions2| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (CATEGORY |package| (SIGNATURE |map| ((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)))) (|EuclideanDomain|) (|QuotientFieldCategory| |#1|) (|UnivariatePolynomialCategory| |#2|) (|Join| (|FramedAlgebra| |#2| |#3|) (|RetractableTo| |#2|)) (|EuclideanDomain|) (|QuotientFieldCategory| |#5|) (|UnivariatePolynomialCategory| |#6|) (|Join| (|FramedAlgebra| |#6| |#7|) (|RetractableTo| |#6|))) (T |FractionalIdealFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *9 *5)) (|isDomain| *4 (|FractionalIdeal| *5 *6 *7 *8)) (|ofCategory| *5 (|EuclideanDomain|)) (|ofCategory| *6 (|QuotientFieldCategory| *5)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|ofCategory| *8 (|Join| (|FramedAlgebra| *6 *7) (|RetractableTo| *6))) (|ofCategory| *9 (|EuclideanDomain|)) (|ofCategory| *10 (|QuotientFieldCategory| *9)) (|ofCategory| *11 (|UnivariatePolynomialCategory| *10)) (|isDomain| *2 (|FractionalIdeal| *9 *10 *11 *12)) (|isDomain| *1 (|FractionalIdealFunctions2| *5 *6 *7 *8 *9 *10 *11 *12)) (|ofCategory| *12 (|Join| (|FramedAlgebra| *10 *11) (|RetractableTo| *10)))))) 
(CATEGORY |package| (SIGNATURE |map| ((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)))) 
((~= (((|Boolean|) $ $) NIL)) (|sample| (($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL)) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) 55)) (|one?| (((|Boolean|) $) NIL)) (|numer| (((|Vector| |#4|) $) 17)) (|norm| ((|#2| $) 53)) (|minimize| (($ $) 136)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 98)) (|ideal| (($ (|Vector| |#4|)) 97)) (|hash| (((|SingleInteger|) $) NIL)) (|denom| ((|#1| $) 18)) (|conjugate| (($ $ $) NIL)) (|commutator| (($ $ $) NIL)) (|coerce| (((|OutputForm|) $) 131)) (|basis| (((|Vector| |#4|) $) 126)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|One| (($) 11 T CONST)) (= (((|Boolean|) $ $) 39)) (/ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) 119)) (* (($ $ $) 118))) 
(((|FractionalIdeal| |#1| |#2| |#3| |#4|) (|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |ideal| ($ (|Vector| |#4|))) (SIGNATURE |basis| ((|Vector| |#4|) $)) (SIGNATURE |norm| (|#2| $)) (SIGNATURE |numer| ((|Vector| |#4|) $)) (SIGNATURE |denom| (|#1| $)) (SIGNATURE |minimize| ($ $)) (SIGNATURE |randomLC| (|#4| (|NonNegativeInteger|) (|Vector| |#4|))))) (|EuclideanDomain|) (|QuotientFieldCategory| |#1|) (|UnivariatePolynomialCategory| |#2|) (|Join| (|FramedAlgebra| |#2| |#3|) (|RetractableTo| |#2|))) (T |FractionalIdeal|)) 
((|ideal| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *6)) (|ofCategory| *6 (|Join| (|FramedAlgebra| *4 *5) (|RetractableTo| *4))) (|ofCategory| *4 (|QuotientFieldCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *3 (|EuclideanDomain|)) (|isDomain| *1 (|FractionalIdeal| *3 *4 *5 *6)))) (|basis| (*1 *2 *1) (AND (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *4 (|QuotientFieldCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Vector| *6)) (|isDomain| *1 (|FractionalIdeal| *3 *4 *5 *6)) (|ofCategory| *6 (|Join| (|FramedAlgebra| *4 *5) (|RetractableTo| *4))))) (|norm| (*1 *2 *1) (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|QuotientFieldCategory| *3)) (|isDomain| *1 (|FractionalIdeal| *3 *2 *4 *5)) (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *5 (|Join| (|FramedAlgebra| *2 *4) (|RetractableTo| *2))))) (|numer| (*1 *2 *1) (AND (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *4 (|QuotientFieldCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Vector| *6)) (|isDomain| *1 (|FractionalIdeal| *3 *4 *5 *6)) (|ofCategory| *6 (|Join| (|FramedAlgebra| *4 *5) (|RetractableTo| *4))))) (|denom| (*1 *2 *1) (AND (|ofCategory| *3 (|QuotientFieldCategory| *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *2 (|EuclideanDomain|)) (|isDomain| *1 (|FractionalIdeal| *2 *3 *4 *5)) (|ofCategory| *5 (|Join| (|FramedAlgebra| *3 *4) (|RetractableTo| *3))))) (|minimize| (*1 *1 *1) (AND (|ofCategory| *2 (|EuclideanDomain|)) (|ofCategory| *3 (|QuotientFieldCategory| *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *1 (|FractionalIdeal| *2 *3 *4 *5)) (|ofCategory| *5 (|Join| (|FramedAlgebra| *3 *4) (|RetractableTo| *3))))) (|randomLC| (*1 *2 *3 *4) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|Vector| *2)) (|ofCategory| *5 (|EuclideanDomain|)) (|ofCategory| *6 (|QuotientFieldCategory| *5)) (|ofCategory| *2 (|Join| (|FramedAlgebra| *6 *7) (|RetractableTo| *6))) (|isDomain| *1 (|FractionalIdeal| *5 *6 *7 *2)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))))) 
(|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |ideal| ($ (|Vector| |#4|))) (SIGNATURE |basis| ((|Vector| |#4|) $)) (SIGNATURE |norm| (|#2| $)) (SIGNATURE |numer| ((|Vector| |#4|) $)) (SIGNATURE |denom| (|#1| $)) (SIGNATURE |minimize| ($ $)) (SIGNATURE |randomLC| (|#4| (|NonNegativeInteger|) (|Vector| |#4|))))) 
((~= (((|Boolean|) $ $) NIL)) (|sample| (($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|norm| ((|#2| $) 60)) (|module| (($ (|Vector| |#4|)) 25) (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) 75 (|has| |#4| (|RetractableTo| |#2|)))) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 34)) (|basis| (((|Vector| |#4|) $) 26)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|One| (($) 23 T CONST)) (= (((|Boolean|) $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ $ $) 72))) 
(((|FramedModule| |#1| |#2| |#3| |#4| |#5|) (|Join| (|Monoid|) (CATEGORY |domain| (SIGNATURE |basis| ((|Vector| |#4|) $)) (SIGNATURE |norm| (|#2| $)) (SIGNATURE |module| ($ (|Vector| |#4|))) (IF (|has| |#4| (|RetractableTo| |#2|)) (SIGNATURE |module| ($ (|FractionalIdeal| |#1| |#2| |#3| |#4|))) |noBranch|))) (|EuclideanDomain|) (|QuotientFieldCategory| |#1|) (|UnivariatePolynomialCategory| |#2|) (|FramedAlgebra| |#2| |#3|) (|Vector| |#4|)) (T |FramedModule|)) 
((|basis| (*1 *2 *1) (AND (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *4 (|QuotientFieldCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Vector| *6)) (|isDomain| *1 (|FramedModule| *3 *4 *5 *6 *7)) (|ofCategory| *6 (|FramedAlgebra| *4 *5)) (|ofType| *7 *2))) (|norm| (*1 *2 *1) (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|QuotientFieldCategory| *3)) (|isDomain| *1 (|FramedModule| *3 *2 *4 *5 *6)) (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *5 (|FramedAlgebra| *2 *4)) (|ofType| *6 (|Vector| *5)))) (|module| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *6)) (|ofCategory| *6 (|FramedAlgebra| *4 *5)) (|ofCategory| *4 (|QuotientFieldCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *3 (|EuclideanDomain|)) (|isDomain| *1 (|FramedModule| *3 *4 *5 *6 *7)) (|ofType| *7 *2))) (|module| (*1 *1 *2) (AND (|isDomain| *2 (|FractionalIdeal| *3 *4 *5 *6)) (|ofCategory| *6 (|RetractableTo| *4)) (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *4 (|QuotientFieldCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *6 (|FramedAlgebra| *4 *5)) (|ofType| *7 (|Vector| *6)) (|isDomain| *1 (|FramedModule| *3 *4 *5 *6 *7))))) 
(|Join| (|Monoid|) (CATEGORY |domain| (SIGNATURE |basis| ((|Vector| |#4|) $)) (SIGNATURE |norm| (|#2| $)) (SIGNATURE |module| ($ (|Vector| |#4|))) (IF (|has| |#4| (|RetractableTo| |#2|)) (SIGNATURE |module| ($ (|FractionalIdeal| |#1| |#2| |#3| |#4|))) |noBranch|))) 
((|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) 26))) 
(((|FramedNonAssociativeAlgebraFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#3| (|Mapping| |#4| |#2|) |#1|))) (|FramedNonAssociativeAlgebra| |#2|) (|CommutativeRing|) (|FramedNonAssociativeAlgebra| |#4|) (|CommutativeRing|)) (T |FramedNonAssociativeAlgebraFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|CommutativeRing|)) (|ofCategory| *6 (|CommutativeRing|)) (|ofCategory| *2 (|FramedNonAssociativeAlgebra| *6)) (|isDomain| *1 (|FramedNonAssociativeAlgebraFunctions2| *4 *5 *2 *6)) (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *5))))) 
(CATEGORY |package| (SIGNATURE |map| (|#3| (|Mapping| |#4| |#2|) |#1|))) 
((|unit| (((|Union| $ "failed")) 85)) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) NIL) (((|Vector| (|Matrix| |#2|))) 90)) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) 84)) (|rightUnit| (((|Union| $ "failed")) 83)) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) NIL) (((|Matrix| |#2|)) 101)) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) NIL) (((|Matrix| |#2|) $) 109)) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) 54)) (|rightDiscriminant| ((|#2| (|Vector| $)) NIL) ((|#2|) 105)) (|represents| (($ (|Vector| |#2|) (|Vector| $)) NIL) (($ (|Vector| |#2|)) 112)) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) 82)) (|leftUnit| (((|Union| $ "failed")) 74)) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) NIL) (((|Matrix| |#2|)) 99)) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) NIL) (((|Matrix| |#2|) $) 107)) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) 53)) (|leftDiscriminant| ((|#2| (|Vector| $)) NIL) ((|#2|) 103)) (|coordinates| (((|Vector| |#2|) $ (|Vector| $)) NIL) (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) NIL) (((|Vector| |#2|) $) NIL) (((|Matrix| |#2|) (|Vector| $)) 111)) (|convert| (((|Vector| |#2|) $) 95) (($ (|Vector| |#2|)) 97)) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) NIL) (((|List| (|Polynomial| |#2|))) 93)) (|apply| (($ (|Matrix| |#2|) $) 89))) 
(((|FramedNonAssociativeAlgebra&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |apply| (|#1| (|Matrix| |#2|) |#1|)) (SIGNATURE |rightRankPolynomial| ((|SparseUnivariatePolynomial| (|Polynomial| |#2|)))) (SIGNATURE |leftRankPolynomial| ((|SparseUnivariatePolynomial| (|Polynomial| |#2|)))) (SIGNATURE |rightRegularRepresentation| ((|Matrix| |#2|) |#1|)) (SIGNATURE |leftRegularRepresentation| ((|Matrix| |#2|) |#1|)) (SIGNATURE |rightTraceMatrix| ((|Matrix| |#2|))) (SIGNATURE |leftTraceMatrix| ((|Matrix| |#2|))) (SIGNATURE |rightDiscriminant| (|#2|)) (SIGNATURE |leftDiscriminant| (|#2|)) (SIGNATURE |convert| (|#1| (|Vector| |#2|))) (SIGNATURE |convert| ((|Vector| |#2|) |#1|)) (SIGNATURE |represents| (|#1| (|Vector| |#2|))) (SIGNATURE |conditionsForIdempotents| ((|List| (|Polynomial| |#2|)))) (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| |#2|)))) (SIGNATURE |coordinates| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#2|) |#1|)) (SIGNATURE |unit| ((|Union| |#1| "failed"))) (SIGNATURE |rightUnit| ((|Union| |#1| "failed"))) (SIGNATURE |leftUnit| ((|Union| |#1| "failed"))) (SIGNATURE |rightUnits| ((|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed"))) (SIGNATURE |leftUnits| ((|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed"))) (SIGNATURE |rightTraceMatrix| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |leftTraceMatrix| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |rightDiscriminant| (|#2| (|Vector| |#1|))) (SIGNATURE |leftDiscriminant| (|#2| (|Vector| |#1|))) (SIGNATURE |represents| (|#1| (|Vector| |#2|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Matrix| |#2|) (|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#2|) |#1| (|Vector| |#1|))) (SIGNATURE |rightRegularRepresentation| ((|Matrix| |#2|) |#1| (|Vector| |#1|))) (SIGNATURE |leftRegularRepresentation| ((|Matrix| |#2|) |#1| (|Vector| |#1|))) (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| |#2|)) (|Vector| |#1|))) (SIGNATURE |conditionsForIdempotents| ((|List| (|Polynomial| |#2|)) (|Vector| |#1|)))) (|FramedNonAssociativeAlgebra| |#2|) (|CommutativeRing|)) (T |FramedNonAssociativeAlgebra&|)) 
((|structuralConstants| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Vector| (|Matrix| *4))) (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4)))) (|conditionsForIdempotents| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|List| (|Polynomial| *4))) (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4)))) (|leftDiscriminant| (*1 *2) (AND (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *2)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *2)))) (|rightDiscriminant| (*1 *2) (AND (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *2)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *2)))) (|leftTraceMatrix| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4)))) (|rightTraceMatrix| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4)))) (|leftRankPolynomial| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|SparseUnivariatePolynomial| (|Polynomial| *4))) (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4)))) (|rightRankPolynomial| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|SparseUnivariatePolynomial| (|Polynomial| *4))) (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *4)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4))))) 
(CATEGORY |domain| (SIGNATURE |apply| (|#1| (|Matrix| |#2|) |#1|)) (SIGNATURE |rightRankPolynomial| ((|SparseUnivariatePolynomial| (|Polynomial| |#2|)))) (SIGNATURE |leftRankPolynomial| ((|SparseUnivariatePolynomial| (|Polynomial| |#2|)))) (SIGNATURE |rightRegularRepresentation| ((|Matrix| |#2|) |#1|)) (SIGNATURE |leftRegularRepresentation| ((|Matrix| |#2|) |#1|)) (SIGNATURE |rightTraceMatrix| ((|Matrix| |#2|))) (SIGNATURE |leftTraceMatrix| ((|Matrix| |#2|))) (SIGNATURE |rightDiscriminant| (|#2|)) (SIGNATURE |leftDiscriminant| (|#2|)) (SIGNATURE |convert| (|#1| (|Vector| |#2|))) (SIGNATURE |convert| ((|Vector| |#2|) |#1|)) (SIGNATURE |represents| (|#1| (|Vector| |#2|))) (SIGNATURE |conditionsForIdempotents| ((|List| (|Polynomial| |#2|)))) (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| |#2|)))) (SIGNATURE |coordinates| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#2|) |#1|)) (SIGNATURE |unit| ((|Union| |#1| "failed"))) (SIGNATURE |rightUnit| ((|Union| |#1| "failed"))) (SIGNATURE |leftUnit| ((|Union| |#1| "failed"))) (SIGNATURE |rightUnits| ((|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed"))) (SIGNATURE |leftUnits| ((|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed"))) (SIGNATURE |rightTraceMatrix| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |leftTraceMatrix| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |rightDiscriminant| (|#2| (|Vector| |#1|))) (SIGNATURE |leftDiscriminant| (|#2| (|Vector| |#1|))) (SIGNATURE |represents| (|#1| (|Vector| |#2|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Matrix| |#2|) (|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#2|) |#1| (|Vector| |#1|))) (SIGNATURE |rightRegularRepresentation| ((|Matrix| |#2|) |#1| (|Vector| |#1|))) (SIGNATURE |leftRegularRepresentation| ((|Matrix| |#2|) |#1| (|Vector| |#1|))) (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| |#2|)) (|Vector| |#1|))) (SIGNATURE |conditionsForIdempotents| ((|List| (|Polynomial| |#2|)) (|Vector| |#1|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unit| (((|Union| $ "failed")) 35 (|has| |#1| (|IntegralDomain|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) 76) (((|Vector| (|Matrix| |#1|))) 93)) (|someBasis| (((|Vector| $)) 79)) (|sample| (($) 16 T CONST)) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) 38 (|has| |#1| (|IntegralDomain|)))) (|rightUnit| (((|Union| $ "failed")) 36 (|has| |#1| (|IntegralDomain|)))) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) 63) (((|Matrix| |#1|)) 85)) (|rightTrace| ((|#1| $) 72)) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 74) (((|Matrix| |#1|) $) 83)) (|rightRecip| (((|Union| $ "failed") $) 43 (|has| |#1| (|IntegralDomain|)))) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) 81 (|has| |#1| (|Field|)))) (|rightPower| (($ $ (|PositiveInteger|)) 27)) (|rightNorm| ((|#1| $) 70)) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 40 (|has| |#1| (|IntegralDomain|)))) (|rightDiscriminant| ((|#1| (|Vector| $)) 65) ((|#1|) 87)) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 61)) (|rightAlternative?| (((|Boolean|)) 55)) (|represents| (($ (|Vector| |#1|) (|Vector| $)) 67) (($ (|Vector| |#1|)) 91)) (|recip| (((|Union| $ "failed") $) 45 (|has| |#1| (|IntegralDomain|)))) (|rank| (((|PositiveInteger|)) 78)) (|powerAssociative?| (((|Boolean|)) 52)) (|plenaryPower| (($ $ (|PositiveInteger|)) 32)) (|noncommutativeJordanAlgebra?| (((|Boolean|)) 48)) (|lieAlgebra?| (((|Boolean|)) 46)) (|lieAdmissible?| (((|Boolean|)) 50)) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) 39 (|has| |#1| (|IntegralDomain|)))) (|leftUnit| (((|Union| $ "failed")) 37 (|has| |#1| (|IntegralDomain|)))) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) 64) (((|Matrix| |#1|)) 86)) (|leftTrace| ((|#1| $) 73)) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 75) (((|Matrix| |#1|) $) 84)) (|leftRecip| (((|Union| $ "failed") $) 44 (|has| |#1| (|IntegralDomain|)))) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) 82 (|has| |#1| (|Field|)))) (|leftPower| (($ $ (|PositiveInteger|)) 28)) (|leftNorm| ((|#1| $) 71)) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 41 (|has| |#1| (|IntegralDomain|)))) (|leftDiscriminant| ((|#1| (|Vector| $)) 66) ((|#1|) 88)) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 62)) (|leftAlternative?| (((|Boolean|)) 56)) (|latex| (((|String|) $) 9)) (|jordanAlgebra?| (((|Boolean|)) 47)) (|jordanAdmissible?| (((|Boolean|)) 49)) (|jacobiIdentity?| (((|Boolean|)) 51)) (|hash| (((|SingleInteger|) $) 10)) (|flexible?| (((|Boolean|)) 54)) (|elt| ((|#1| $ (|Integer|)) 94)) (|coordinates| (((|Vector| |#1|) $ (|Vector| $)) 69) (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) 68) (((|Vector| |#1|) $) 96) (((|Matrix| |#1|) (|Vector| $)) 95)) (|convert| (((|Vector| |#1|) $) 90) (($ (|Vector| |#1|)) 89)) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) 77) (((|List| (|Polynomial| |#1|))) 92)) (|commutator| (($ $ $) 24)) (|commutative?| (((|Boolean|)) 60)) (|coerce| (((|OutputForm|) $) 11)) (|basis| (((|Vector| $)) 97)) (|associatorDependence| (((|List| (|Vector| |#1|))) 42 (|has| |#1| (|IntegralDomain|)))) (|associator| (($ $ $ $) 25)) (|associative?| (((|Boolean|)) 58)) (|apply| (($ (|Matrix| |#1|) $) 80)) (|antiCommutator| (($ $ $) 23)) (|antiCommutative?| (((|Boolean|)) 59)) (|antiAssociative?| (((|Boolean|)) 57)) (|alternative?| (((|Boolean|)) 53)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 29)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 26) (($ $ |#1|) 34) (($ |#1| $) 33))) 
(((|FramedNonAssociativeAlgebra| |#1|) (|Category|) (|CommutativeRing|)) (T |FramedNonAssociativeAlgebra|)) 
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(|Join| (|FiniteRankNonAssociativeAlgebra| |t#1|) (CATEGORY |domain| (SIGNATURE |basis| ((|Vector| $))) (SIGNATURE |coordinates| ((|Vector| |t#1|) $)) (SIGNATURE |coordinates| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |elt| (|t#1| $ (|Integer|))) (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| |t#1|)))) (SIGNATURE |conditionsForIdempotents| ((|List| (|Polynomial| |t#1|)))) (SIGNATURE |represents| ($ (|Vector| |t#1|))) (SIGNATURE |convert| ((|Vector| |t#1|) $)) (SIGNATURE |convert| ($ (|Vector| |t#1|))) (SIGNATURE |leftDiscriminant| (|t#1|)) (SIGNATURE |rightDiscriminant| (|t#1|)) (SIGNATURE |leftTraceMatrix| ((|Matrix| |t#1|))) (SIGNATURE |rightTraceMatrix| ((|Matrix| |t#1|))) (SIGNATURE |leftRegularRepresentation| ((|Matrix| |t#1|) $)) (SIGNATURE |rightRegularRepresentation| ((|Matrix| |t#1|) $)) (IF (|has| |t#1| (|Field|)) (PROGN (SIGNATURE |leftRankPolynomial| ((|SparseUnivariatePolynomial| (|Polynomial| |t#1|)))) (SIGNATURE |rightRankPolynomial| ((|SparseUnivariatePolynomial| (|Polynomial| |t#1|))))) |noBranch|) (SIGNATURE |apply| ($ (|Matrix| |t#1|) $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|FiniteRankNonAssociativeAlgebra| |#1|) . T) ((|LeftModule| |#1|) . T) ((|Module| |#1|) . T) ((|Monad|) . T) ((|NonAssociativeAlgebra| |#1|) . T) ((|NonAssociativeRng|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 40)) (|unitNormalize| (($ $) 55)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 142)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) 34)) (|unit| ((|#1| $) 12)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL (|has| |#1| (|UniqueFactorizationDomain|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#1| (|UniqueFactorizationDomain|)))) (|sqfrFactor| (($ |#1| (|Integer|)) 30)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) 112)) (|retract| (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) 53)) (|recip| (((|Union| $ 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$)) NIL (|has| |#1| (|GcdDomain|))) (($ $ $) NIL (|has| |#1| (|GcdDomain|)))) (|latex| (((|String|) $) NIL)) (|irreducibleFactor| (($ |#1| (|Integer|)) 31)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|GcdDomain|)))) (|gcd| (($ (|List| $)) NIL (|has| |#1| (|GcdDomain|))) (($ $ $) 143 (|has| |#1| (|GcdDomain|)))) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) 28)) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) 52)) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) 11)) (|factor| (((|Factored| $) $) NIL (|has| |#1| (|UniqueFactorizationDomain|)))) (|exquo| (((|Union| $ "failed") $ $) 134)) (|exponent| (((|Integer|) $) 128)) (|expand| ((|#1| $) 54)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ |#1| |#1|) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ (|Equation| |#1|)) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ (|List| (|Equation| |#1|))) 76 (|has| |#1| (|Evalable| |#1|))) (($ $ (|List| (|Symbol|)) (|List| |#1|)) 81 (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|))) (($ $ (|Symbol|) |#1|) NIL (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|))) (($ $ (|Symbol|) $) NIL (|has| |#1| (|InnerEvalable| (|Symbol|) $))) (($ $ (|List| (|Symbol|)) (|List| $)) 82 (|has| |#1| (|InnerEvalable| (|Symbol|) $))) (($ $ (|List| (|Equation| $))) 78 (|has| |#1| (|Evalable| $))) (($ $ (|Equation| $)) NIL (|has| |#1| (|Evalable| $))) (($ $ $ $) NIL (|has| |#1| (|Evalable| $))) (($ $ (|List| $) (|List| $)) NIL (|has| |#1| (|Evalable| $)))) (|elt| (($ $ |#1|) 68 (|has| |#1| (|Eltable| |#1| |#1|))) (($ $ $) 69 (|has| |#1| (|Eltable| $ $)))) (|differentiate| (($ $) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#1| |#1|)) 138)) (|convert| (((|InputForm|) $) 26 (|has| |#1| (|ConvertibleTo| (|InputForm|)))) (((|Float|) $) 88 (|has| |#1| (|RealConstant|))) (((|DoubleFloat|) $) 91 (|has| |#1| (|RealConstant|)))) (|coerce| (((|OutputForm|) $) 110) (($ (|Integer|)) 44) (($ $) NIL) (($ |#1|) 43) (($ (|Fraction| (|Integer|))) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))))) (|characteristic| (((|NonNegativeInteger|)) 46)) (|associates?| (((|Boolean|) $ $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 38 T CONST)) (|One| (($) 37 T CONST)) (D (($ $) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#1| |#1|)) NIL)) (= (((|Boolean|) $ $) 92)) (- (($ $) 124) (($ $ $) NIL)) (+ (($ $ $) 136)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 98)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 48) (($ $ $) 47) (($ |#1| $) 49) (($ $ |#1|) NIL))) 
(((|Factored| |#1|) (|Join| (|IntegralDomain|) (|DifferentialExtension| |#1|) (|Algebra| |#1|) (|FullyEvalableOver| |#1|) (|FullyRetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |expand| (|#1| $)) (SIGNATURE |exponent| ((|Integer|) $)) (SIGNATURE |makeFR| ($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))))) (SIGNATURE |factorList| ((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $)) (SIGNATURE |nilFactor| ($ |#1| (|Integer|))) (SIGNATURE |factors| ((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $)) (SIGNATURE |irreducibleFactor| ($ |#1| (|Integer|))) (SIGNATURE |nthExponent| ((|Integer|) $ (|Integer|))) (SIGNATURE |nthFactor| (|#1| $ (|Integer|))) (SIGNATURE |nthFlag| ((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|))) (SIGNATURE |numberOfFactors| ((|NonNegativeInteger|) $)) (SIGNATURE |primeFactor| ($ |#1| (|Integer|))) (SIGNATURE |sqfrFactor| ($ |#1| (|Integer|))) (SIGNATURE |flagFactor| ($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime"))) (SIGNATURE |unit| (|#1| $)) (SIGNATURE |unitNormalize| ($ $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (IF (|has| |#1| (|GcdDomain|)) (ATTRIBUTE (|GcdDomain|)) |noBranch|) (IF (|has| |#1| (|RealConstant|)) (ATTRIBUTE (|RealConstant|)) |noBranch|) (IF (|has| |#1| (|UniqueFactorizationDomain|)) (ATTRIBUTE (|UniqueFactorizationDomain|)) |noBranch|) (IF (|has| |#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |noBranch|) (IF (|has| |#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") $))) |noBranch|) (IF (|has| |#1| (|Eltable| $ $)) (ATTRIBUTE (|Eltable| $ $)) |noBranch|) (IF (|has| |#1| (|Evalable| $)) (ATTRIBUTE (|Evalable| $)) |noBranch|) (IF (|has| |#1| (|InnerEvalable| (|Symbol|) $)) (ATTRIBUTE (|InnerEvalable| (|Symbol|) $)) |noBranch|))) (|IntegralDomain|)) (T |Factored|)) 
((|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|Factored| *3)))) (|expand| (*1 *2 *1) (AND (|isDomain| *1 (|Factored| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|exponent| (*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Factored| *3)) (|ofCategory| *3 (|IntegralDomain|)))) (|makeFR| (*1 *1 *2 *3) (AND (|isDomain| *3 (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| *2) (|:| |xpnt| (|Integer|))))) (|ofCategory| *2 (|IntegralDomain|)) (|isDomain| *1 (|Factored| *2)))) (|factorList| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| *3) (|:| |xpnt| (|Integer|))))) (|isDomain| *1 (|Factored| *3)) (|ofCategory| *3 (|IntegralDomain|)))) (|nilFactor| (*1 *1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|Factored| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|factors| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |factor| *3) (|:| |exponent| (|Integer|))))) (|isDomain| *1 (|Factored| *3)) (|ofCategory| *3 (|IntegralDomain|)))) (|irreducibleFactor| (*1 *1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|Factored| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|nthExponent| (*1 *2 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Factored| *3)) (|ofCategory| *3 (|IntegralDomain|)))) (|nthFactor| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|Factored| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|nthFlag| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Union| "nil" "sqfr" "irred" "prime")) (|isDomain| *1 (|Factored| *4)) (|ofCategory| *4 (|IntegralDomain|)))) (|numberOfFactors| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Factored| *3)) (|ofCategory| *3 (|IntegralDomain|)))) (|primeFactor| (*1 *1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|Factored| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|sqfrFactor| (*1 *1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|Factored| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|flagFactor| (*1 *1 *2 *3 *4) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *4 (|Union| "nil" "sqfr" "irred" "prime")) (|isDomain| *1 (|Factored| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|unit| (*1 *2 *1) (AND (|isDomain| *1 (|Factored| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|unitNormalize| (*1 *1 *1) (AND (|isDomain| *1 (|Factored| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|rational?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Factored| *3)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|ofCategory| *3 (|IntegralDomain|)))) (|rational| (*1 *2 *1) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|Factored| *3)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|ofCategory| *3 (|IntegralDomain|)))) (|rationalIfCan| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|Factored| *3)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|ofCategory| *3 (|IntegralDomain|))))) 
(|Join| (|IntegralDomain|) (|DifferentialExtension| |#1|) (|Algebra| |#1|) (|FullyEvalableOver| |#1|) (|FullyRetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |expand| (|#1| $)) (SIGNATURE |exponent| ((|Integer|) $)) (SIGNATURE |makeFR| ($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))))) (SIGNATURE |factorList| ((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $)) (SIGNATURE |nilFactor| ($ |#1| (|Integer|))) (SIGNATURE |factors| ((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $)) (SIGNATURE |irreducibleFactor| ($ |#1| (|Integer|))) (SIGNATURE |nthExponent| ((|Integer|) $ (|Integer|))) (SIGNATURE |nthFactor| (|#1| $ (|Integer|))) (SIGNATURE |nthFlag| ((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|))) (SIGNATURE |numberOfFactors| ((|NonNegativeInteger|) $)) (SIGNATURE |primeFactor| ($ |#1| (|Integer|))) (SIGNATURE |sqfrFactor| ($ |#1| (|Integer|))) (SIGNATURE |flagFactor| ($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime"))) (SIGNATURE |unit| (|#1| $)) (SIGNATURE |unitNormalize| ($ $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (IF (|has| |#1| (|GcdDomain|)) (ATTRIBUTE (|GcdDomain|)) |noBranch|) (IF (|has| |#1| (|RealConstant|)) (ATTRIBUTE (|RealConstant|)) |noBranch|) (IF (|has| |#1| (|UniqueFactorizationDomain|)) (ATTRIBUTE (|UniqueFactorizationDomain|)) |noBranch|) (IF (|has| |#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |noBranch|) (IF (|has| |#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") $))) |noBranch|) (IF (|has| |#1| (|Eltable| $ $)) (ATTRIBUTE (|Eltable| $ $)) |noBranch|) (IF (|has| |#1| (|Evalable| $)) (ATTRIBUTE (|Evalable| $)) |noBranch|) (IF (|has| |#1| (|InnerEvalable| (|Symbol|) $)) (ATTRIBUTE (|InnerEvalable| (|Symbol|) $)) |noBranch|))) 
((|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) 20)) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) 15))) 
(((|FactoredFunctionUtilities| |#1|) (CATEGORY |package| (SIGNATURE |refine| ((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|))) (SIGNATURE |mergeFactors| ((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)))) (|IntegralDomain|)) (T |FactoredFunctionUtilities|)) 
((|mergeFactors| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Factored| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|FactoredFunctionUtilities| *3)))) (|refine| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Mapping| (|Factored| *4) *4)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Factored| *4)) (|isDomain| *1 (|FactoredFunctionUtilities| *4))))) 
(CATEGORY |package| (SIGNATURE |refine| ((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|))) (SIGNATURE |mergeFactors| ((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)))) 
((|localAbs| ((|#2| |#2|) 160)) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|)) 55))) 
(((|FunctionSpaceToExponentialExpansion| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |exprToXXP| ((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|))) (SIGNATURE |localAbs| (|#2| |#2|))) (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|))) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|)) (|Symbol|) |#2|) (T |FunctionSpaceToExponentialExpansion|)) 
((|localAbs| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|FunctionSpaceToExponentialExpansion| *3 *2 *4 *5)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *3))) (|ofType| *4 (|Symbol|)) (|ofType| *5 *2))) (|exprToXXP| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Union| (|:| |%expansion| (|ExponentialExpansion| *5 *3 *6 *7)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|)))))) (|isDomain| *1 (|FunctionSpaceToExponentialExpansion| *5 *3 *6 *7)) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *5))) (|ofType| *6 (|Symbol|)) (|ofType| *7 *3)))) 
(CATEGORY |package| (SIGNATURE |exprToXXP| ((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|))) (SIGNATURE |localAbs| (|#2| |#2|))) 
((|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) 11))) 
(((|FunctionSpaceFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#3| |#1|) |#2|))) (|Join| (|Ring|) (|OrderedSet|)) (|FunctionSpace| |#1|) (|Join| (|Ring|) (|OrderedSet|)) (|FunctionSpace| |#3|)) (T |FunctionSpaceFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|Join| (|Ring|) (|OrderedSet|))) (|ofCategory| *6 (|Join| (|Ring|) (|OrderedSet|))) (|ofCategory| *2 (|FunctionSpace| *6)) (|isDomain| *1 (|FunctionSpaceFunctions2| *5 *4 *6 *2)) (|ofCategory| *4 (|FunctionSpace| *5))))) 
(CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#3| |#1|) |#2|))) 
((|localAbs| ((|#2| |#2|) 87)) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) 46)) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) 152))) 
(((|FunctionSpaceToUnivariatePowerSeries| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |exprToUPS| ((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|))) (SIGNATURE |exprToGenUPS| ((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|))) (SIGNATURE |localAbs| (|#2| |#2|))) (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|))) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#3|)))) (|OrderedRing|) (|Join| (|UnivariatePowerSeriesCategory| |#2| |#3|) (|Field|) (|TranscendentalFunctionCategory|) (CATEGORY |domain| (SIGNATURE |differentiate| ($ $)) (SIGNATURE |integrate| ($ $)))) (|PartialTranscendentalFunctions| |#4|) (|Symbol|)) (T |FunctionSpaceToUnivariatePowerSeries|)) 
((|localAbs| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *3) (CATEGORY |domain| (SIGNATURE |coerce| ($ *4))))) (|ofCategory| *4 (|OrderedRing|)) (|ofCategory| *5 (|Join| (|UnivariatePowerSeriesCategory| *2 *4) (|Field|) (|TranscendentalFunctionCategory|) (CATEGORY |domain| (SIGNATURE |differentiate| ($ $)) (SIGNATURE |integrate| ($ $))))) (|isDomain| *1 (|FunctionSpaceToUnivariatePowerSeries| *3 *2 *4 *5 *6 *7)) (|ofCategory| *6 (|PartialTranscendentalFunctions| *5)) (|ofType| *7 (|Symbol|)))) (|exprToGenUPS| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *6 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *6) (CATEGORY |domain| (SIGNATURE |coerce| ($ *7))))) (|ofCategory| *7 (|OrderedRing|)) (|ofCategory| *8 (|Join| (|UnivariatePowerSeriesCategory| *3 *7) (|Field|) (|TranscendentalFunctionCategory|) (CATEGORY |domain| (SIGNATURE |differentiate| ($ $)) (SIGNATURE |integrate| ($ $))))) (|isDomain| *2 (|Union| (|:| |%series| *8) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|)))))) (|isDomain| *1 (|FunctionSpaceToUnivariatePowerSeries| *6 *3 *7 *8 *9 *10)) (|isDomain| *5 (|String|)) (|ofCategory| *9 (|PartialTranscendentalFunctions| *8)) (|ofType| *10 (|Symbol|)))) (|exprToUPS| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *6 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *6) (CATEGORY |domain| (SIGNATURE |coerce| ($ *7))))) (|ofCategory| *7 (|OrderedRing|)) (|ofCategory| *8 (|Join| (|UnivariatePowerSeriesCategory| *3 *7) (|Field|) (|TranscendentalFunctionCategory|) (CATEGORY |domain| (SIGNATURE |differentiate| ($ $)) (SIGNATURE |integrate| ($ $))))) (|isDomain| *2 (|Union| (|:| |%series| *8) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|)))))) (|isDomain| *1 (|FunctionSpaceToUnivariatePowerSeries| *6 *3 *7 *8 *9 *10)) (|isDomain| *5 (|String|)) (|ofCategory| *9 (|PartialTranscendentalFunctions| *8)) (|ofType| *10 (|Symbol|))))) 
(CATEGORY |package| (SIGNATURE |exprToUPS| ((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|))) (SIGNATURE |exprToGenUPS| ((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|))) (SIGNATURE |localAbs| (|#2| |#2|))) 
((|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) 22)) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) 20)) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) 17))) 
(((|FiniteSetAggregateFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#3| |#1|) |#2|)) (SIGNATURE |reduce| (|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|)) (SIGNATURE |scan| (|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|))) (|SetCategory|) (|FiniteSetAggregate| |#1|) (|SetCategory|) (|FiniteSetAggregate| |#3|)) (T |FiniteSetAggregateFunctions2|)) 
((|scan| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *5 *6 *5)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *2 (|FiniteSetAggregate| *5)) (|isDomain| *1 (|FiniteSetAggregateFunctions2| *6 *4 *5 *2)) (|ofCategory| *4 (|FiniteSetAggregate| *6)))) (|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)) (|isDomain| *1 (|FiniteSetAggregateFunctions2| *5 *4 *2 *6)) (|ofCategory| *4 (|FiniteSetAggregate| *5)) (|ofCategory| *6 (|FiniteSetAggregate| *2)))) (|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *2 (|FiniteSetAggregate| *6)) (|isDomain| *1 (|FiniteSetAggregateFunctions2| *5 *4 *6 *2)) (|ofCategory| *4 (|FiniteSetAggregate| *5))))) 
(CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#3| |#1|) |#2|)) (SIGNATURE |reduce| (|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|)) (SIGNATURE |scan| (|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|))) 
((|universe| (($) 44)) (|union| (($ |#2| $) NIL) (($ $ |#2|) NIL) (($ $ $) 40)) (|symmetricDifference| (($ $ $) 39)) (|subset?| (((|Boolean|) $ $) 28)) (|size| (((|NonNegativeInteger|)) 47)) (|set| (($ (|List| |#2|)) 20) (($) NIL)) (|random| (($) 53)) (|min| ((|#2| $) 61)) (|max| ((|#2| $) 59)) (|lookup| (((|PositiveInteger|) $) 55)) (|intersect| (($ $ $) 35)) (|index| (($ (|PositiveInteger|)) 50)) (|difference| (($ $ |#2|) NIL) (($ $ $) 38)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) NIL) (((|NonNegativeInteger|) |#2| $) 26)) (|construct| (($ (|List| |#2|)) 24)) (|complement| (($ $) 46)) (|coerce| (((|OutputForm|) $) 33)) (|cardinality| (((|NonNegativeInteger|) $) 21)) (|brace| (($ (|List| |#2|)) 19) (($) NIL)) (= (((|Boolean|) $ $) 16)) (< (((|Boolean|) $ $) 13))) 
(((|FiniteSetAggregate&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |size| ((|NonNegativeInteger|))) (SIGNATURE |index| (|#1| (|PositiveInteger|))) (SIGNATURE |lookup| ((|PositiveInteger|) |#1|)) (SIGNATURE |random| (|#1|)) (SIGNATURE |min| (|#2| |#1|)) (SIGNATURE |max| (|#2| |#1|)) (SIGNATURE |universe| (|#1|)) (SIGNATURE |complement| (|#1| |#1|)) (SIGNATURE |cardinality| ((|NonNegativeInteger|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE |brace| (|#1|)) (SIGNATURE |brace| (|#1| (|List| |#2|))) (SIGNATURE |set| (|#1|)) (SIGNATURE |set| (|#1| (|List| |#2|))) (SIGNATURE |intersect| (|#1| |#1| |#1|)) (SIGNATURE |difference| (|#1| |#1| |#1|)) (SIGNATURE |difference| (|#1| |#1| |#2|)) (SIGNATURE |symmetricDifference| (|#1| |#1| |#1|)) (SIGNATURE |subset?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |union| (|#1| |#1| |#1|)) (SIGNATURE |union| (|#1| |#1| |#2|)) (SIGNATURE |union| (|#1| |#2| |#1|)) (SIGNATURE |construct| (|#1| (|List| |#2|))) (SIGNATURE |count| ((|NonNegativeInteger|) |#2| |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) |#1|))) (|FiniteSetAggregate| |#2|) (|SetCategory|)) (T |FiniteSetAggregate&|)) 
((|size| (*1 *2) (AND (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FiniteSetAggregate&| *3 *4)) (|ofCategory| *3 (|FiniteSetAggregate| *4))))) 
(CATEGORY |domain| (SIGNATURE |size| ((|NonNegativeInteger|))) (SIGNATURE |index| (|#1| (|PositiveInteger|))) (SIGNATURE |lookup| ((|PositiveInteger|) |#1|)) (SIGNATURE |random| (|#1|)) (SIGNATURE |min| (|#2| |#1|)) (SIGNATURE |max| (|#2| |#1|)) (SIGNATURE |universe| (|#1|)) (SIGNATURE |complement| (|#1| |#1|)) (SIGNATURE |cardinality| ((|NonNegativeInteger|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE |brace| (|#1|)) (SIGNATURE |brace| (|#1| (|List| |#2|))) (SIGNATURE |set| (|#1|)) (SIGNATURE |set| (|#1| (|List| |#2|))) (SIGNATURE |intersect| (|#1| |#1| |#1|)) (SIGNATURE |difference| (|#1| |#1| |#1|)) (SIGNATURE |difference| (|#1| |#1| |#2|)) (SIGNATURE |symmetricDifference| (|#1| |#1| |#1|)) (SIGNATURE |subset?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |union| (|#1| |#1| |#1|)) (SIGNATURE |union| (|#1| |#1| |#2|)) (SIGNATURE |union| (|#1| |#2| |#1|)) (SIGNATURE |construct| (|#1| (|List| |#2|))) (SIGNATURE |count| ((|NonNegativeInteger|) |#2| |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) |#1|))) 
((~= (((|Boolean|) $ $) 18)) (|universe| (($) 64 (|has| |#1| (|Finite|)))) (|union| (($ |#1| $) 79) (($ $ |#1|) 78) (($ $ $) 77)) (|symmetricDifference| (($ $ $) 75)) (|subset?| (((|Boolean|) $ $) 76)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|size| (((|NonNegativeInteger|)) 57 (|has| |#1| (|Finite|)))) (|set| (($ (|List| |#1|)) 71) (($) 70)) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) 42 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 52 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) 7 T CONST)) (|removeDuplicates| (($ $) 55 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove!| (($ |#1| $) 44 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) |#1|) $) 43 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remove| (($ |#1| $) 54 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#1|) $) 51 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 53 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 50 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 49 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|random| (($) 60 (|has| |#1| (|Finite|)))) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|min| ((|#1| $) 62 (|has| |#1| (|OrderedSet|)))) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|max| ((|#1| $) 63 (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|lookup| (((|PositiveInteger|) $) 59 (|has| |#1| (|Finite|)))) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22)) (|intersect| (($ $ $) 72)) (|inspect| ((|#1| $) 36)) (|insert!| (($ |#1| $) 37)) (|index| (($ (|PositiveInteger|)) 58 (|has| |#1| (|Finite|)))) (|hash| (((|SingleInteger|) $) 21)) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) 48)) (|extract!| ((|#1| $) 38)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|enumerate| (((|List| $)) 61 (|has| |#1| (|Finite|)))) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|difference| (($ $ |#1|) 74) (($ $ $) 73)) (|dictionary| (($) 46) (($ (|List| |#1|)) 45)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|convert| (((|InputForm|) $) 56 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 47)) (|complement| (($ $) 65 (|has| |#1| (|Finite|)))) (|coerce| (((|OutputForm|) $) 20)) (|cardinality| (((|NonNegativeInteger|) $) 66)) (|brace| (($ (|List| |#1|)) 69) (($) 68)) (|bag| (($ (|List| |#1|)) 39)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19)) (< (((|Boolean|) $ $) 67)) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|FiniteSetAggregate| |#1|) (|Category|) (|SetCategory|)) (T |FiniteSetAggregate|)) 
((|cardinality| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteSetAggregate| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|complement| (*1 *1 *1) (AND (|ofCategory| *1 (|FiniteSetAggregate| *2)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|Finite|)))) (|universe| (*1 *1) (AND (|ofCategory| *1 (|FiniteSetAggregate| *2)) (|ofCategory| *2 (|Finite|)) (|ofCategory| *2 (|SetCategory|)))) (|max| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteSetAggregate| *2)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|OrderedSet|)))) (|min| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteSetAggregate| *2)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|OrderedSet|))))) 
(|Join| (|Dictionary| |t#1|) (|SetAggregate| |t#1|) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (SIGNATURE |cardinality| ((|NonNegativeInteger|) $)) (IF (|has| |t#1| (|Finite|)) (PROGN (ATTRIBUTE (|Finite|)) (SIGNATURE |complement| ($ $)) (SIGNATURE |universe| ($))) |noBranch|) (IF (|has| |t#1| (|OrderedSet|)) (PROGN (SIGNATURE |max| (|t#1| $)) (SIGNATURE |min| (|t#1| $))) |noBranch|))) 
(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Dictionary| |#1|) . T) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Finite|) |has| |#1| (|Finite|)) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetAggregate| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) 35)) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) 19)) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) 24))) 
(((|FunctionSpaceComplexIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |internalIntegrate| ((|IntegrationResult| |#2|) |#2| (|Symbol|))) (SIGNATURE |internalIntegrate0| ((|IntegrationResult| |#2|) |#2| (|Symbol|))) (SIGNATURE |complexIntegrate| (|#2| |#2| (|Symbol|)))) (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|))) (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| |#1|))) (T |FunctionSpaceComplexIntegration|)) 
((|complexIntegrate| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|FunctionSpaceComplexIntegration| *4 *2)) (|ofCategory| *2 (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *4))))) (|internalIntegrate0| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|IntegrationResult| *3)) (|isDomain| *1 (|FunctionSpaceComplexIntegration| *5 *3)) (|ofCategory| *3 (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *5))))) (|internalIntegrate| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|IntegrationResult| *3)) (|isDomain| *1 (|FunctionSpaceComplexIntegration| *5 *3)) (|ofCategory| *3 (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *5)))))) 
(CATEGORY |package| (SIGNATURE |internalIntegrate| ((|IntegrationResult| |#2|) |#2| (|Symbol|))) (SIGNATURE |internalIntegrate0| ((|IntegrationResult| |#2|) |#2| (|Symbol|))) (SIGNATURE |complexIntegrate| (|#2| |#2| (|Symbol|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|makeSin| (($ |#2| |#1|) 35)) (|makeCos| (($ |#2| |#1|) 33)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ |#1|) NIL) (($ (|FourierComponent| |#2|)) 25)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 10 T CONST)) (|One| (($) 16 T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) 34)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 36) (($ $ |#1|) NIL) (($ |#1| $) NIL))) 
(((|FourierSeries| |#1| |#2|) (|Join| (|Algebra| |#1|) (CATEGORY |domain| (IF (|has| |#2| (ATTRIBUTE |canonical|)) (IF (|has| |#1| (ATTRIBUTE |canonical|)) (ATTRIBUTE |canonical|) |noBranch|) |noBranch|) (SIGNATURE |coerce| ($ |#1|)) (SIGNATURE |coerce| ($ (|FourierComponent| |#2|))) (SIGNATURE |makeSin| ($ |#2| |#1|)) (SIGNATURE |makeCos| ($ |#2| |#1|)))) (|Join| (|CommutativeRing|) (|Algebra| (|Fraction| (|Integer|)))) (|Join| (|OrderedSet|) (|AbelianGroup|))) (T |FourierSeries|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *1 (|FourierSeries| *2 *3)) (|ofCategory| *2 (|Join| (|CommutativeRing|) (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Join| (|OrderedSet|) (|AbelianGroup|))))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|FourierComponent| *4)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|AbelianGroup|))) (|isDomain| *1 (|FourierSeries| *3 *4)) (|ofCategory| *3 (|Join| (|CommutativeRing|) (|Algebra| (|Fraction| (|Integer|))))))) (|makeSin| (*1 *1 *2 *3) (AND (|isDomain| *1 (|FourierSeries| *3 *2)) (|ofCategory| *3 (|Join| (|CommutativeRing|) (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *2 (|Join| (|OrderedSet|) (|AbelianGroup|))))) (|makeCos| (*1 *1 *2 *3) (AND (|isDomain| *1 (|FourierSeries| *3 *2)) (|ofCategory| *3 (|Join| (|CommutativeRing|) (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *2 (|Join| (|OrderedSet|) (|AbelianGroup|)))))) 
(|Join| (|Algebra| |#1|) (CATEGORY |domain| (IF (|has| |#2| (ATTRIBUTE |canonical|)) (IF (|has| |#1| (ATTRIBUTE |canonical|)) (ATTRIBUTE |canonical|) |noBranch|) |noBranch|) (SIGNATURE |coerce| ($ |#1|)) (SIGNATURE |coerce| ($ (|FourierComponent| |#2|))) (SIGNATURE |makeSin| ($ |#2| |#1|)) (SIGNATURE |makeCos| ($ |#2| |#1|)))) 
((|logGamma| (((|Complex| (|Float|)) (|Complex| (|Float|))) 64) (((|Float|) (|Float|)) 65)) (|Gamma| (((|Complex| (|Float|)) (|Complex| (|Float|))) 52) (((|Float|) (|Float|)) 61))) 
(((|FloatSpecialFunctions|) (CATEGORY |package| (SIGNATURE |logGamma| ((|Float|) (|Float|))) (SIGNATURE |logGamma| ((|Complex| (|Float|)) (|Complex| (|Float|)))) (SIGNATURE |Gamma| ((|Float|) (|Float|))) (SIGNATURE |Gamma| ((|Complex| (|Float|)) (|Complex| (|Float|)))))) (T |FloatSpecialFunctions|)) 
((|Gamma| (*1 *2 *2) (AND (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|FloatSpecialFunctions|)))) (|Gamma| (*1 *2 *2) (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|FloatSpecialFunctions|)))) (|logGamma| (*1 *2 *2) (AND (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|FloatSpecialFunctions|)))) (|logGamma| (*1 *2 *2) (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|FloatSpecialFunctions|))))) 
(CATEGORY |package| (SIGNATURE |logGamma| ((|Float|) (|Float|))) (SIGNATURE |logGamma| ((|Complex| (|Float|)) (|Complex| (|Float|)))) (SIGNATURE |Gamma| ((|Float|) (|Float|))) (SIGNATURE |Gamma| ((|Complex| (|Float|)) (|Complex| (|Float|))))) 
((|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) 104))) 
(((|FunctionSpaceIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |integrate| ((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)))) (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|))) (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| |#1|))) (T |FunctionSpaceIntegration|)) 
((|integrate| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Union| *3 (|List| *3))) (|isDomain| *1 (|FunctionSpaceIntegration| *5 *3)) (|ofCategory| *3 (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *5)))))) 
(CATEGORY |package| (SIGNATURE |integrate| ((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)))) 
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(|Ring|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *1 (|FunctionSpace| *3)))) (|numer| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|SparseMultivariatePolynomial| *3 (|Kernel| *1))) (|ofCategory| *1 (|FunctionSpace| *3)))) (|numerator| (*1 *1 *1) (AND (|ofCategory| *1 (|FunctionSpace| *2)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *2 (|Ring|)))) (|isExpt| (*1 *2 *1 *3) (|partial| AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |var| (|Kernel| *1)) (|:| |exponent| (|Integer|)))) (|ofCategory| *1 (|FunctionSpace| *4)))) (|isExpt| (*1 *2 *1 *3) (|partial| AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |var| (|Kernel| *1)) (|:| |exponent| (|Integer|)))) (|ofCategory| *1 (|FunctionSpace| *4)))) (|isPower| (*1 *2 *1) (|partial| AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |val| *1) (|:| |exponent| (|Integer|)))) (|ofCategory| *1 (|FunctionSpace| *3)))) (|eval| (*1 *1 *1 *2 *3 *4) (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *3 (|List| (|NonNegativeInteger|))) (|isDomain| *4 (|List| (|Mapping| *1 *1))) (|ofCategory| *1 (|FunctionSpace| *5)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *5 (|Ring|)))) (|eval| (*1 *1 *1 *2 *3 *4) (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *3 (|List| (|NonNegativeInteger|))) (|isDomain| *4 (|List| (|Mapping| *1 (|List| *1)))) (|ofCategory| *1 (|FunctionSpace| *5)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *5 (|Ring|)))) (|eval| (*1 *1 *1 *2 *3 *4) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|Mapping| *1 (|List| *1))) (|ofCategory| *1 (|FunctionSpace| *5)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *5 (|Ring|)))) (|eval| (*1 *1 *1 *2 *3 *4) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|Mapping| *1 *1)) (|ofCategory| *1 (|FunctionSpace| *5)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *5 (|Ring|)))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|Factored| *1)) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|OrderedSet|)))) (|denom| (*1 *2 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|SparseMultivariatePolynomial| *3 (|Kernel| *1))) (|ofCategory| *1 (|FunctionSpace| *3)))) (|denominator| (*1 *1 *1) (AND (|ofCategory| *1 (|FunctionSpace| *2)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (/ (*1 *1 *2 *2) (AND (|isDomain| *2 (|SparseMultivariatePolynomial| *3 (|Kernel| *1))) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *1 (|FunctionSpace| *3)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *1 (|FunctionSpace| *3)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| (|Fraction| *3))) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *1 (|FunctionSpace| *3)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Polynomial| (|Fraction| *3)))) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *1 (|FunctionSpace| *3)))) (|univariate| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Kernel| *1)) (|ofCategory| *1 (|FunctionSpace| *4)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Fraction| (|SparseUnivariatePolynomial| *1))))) (** (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *3 (|SemiGroup|))))) 
(|Join| (|ExpressionSpace|) (|RetractableTo| (|Symbol|)) (|Patternable| |t#1|) (|FullyPatternMatchable| |t#1|) (|FullyRetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE |ground?| ((|Boolean|) $)) (SIGNATURE |ground| (|t#1| $)) (SIGNATURE |variables| ((|List| (|Symbol|)) $)) (SIGNATURE |applyQuote| ($ (|Symbol|) $)) (SIGNATURE |applyQuote| ($ (|Symbol|) $ $)) (SIGNATURE |applyQuote| ($ (|Symbol|) $ $ $)) (SIGNATURE |applyQuote| ($ (|Symbol|) $ $ $ $)) (SIGNATURE |applyQuote| ($ (|Symbol|) (|List| $))) (IF (|has| |t#1| (|ConvertibleTo| (|InputForm|))) (PROGN (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) (SIGNATURE |eval| ($ $ (|Symbol|))) (SIGNATURE |eval| ($ $ (|List| (|Symbol|)))) (SIGNATURE |eval| ($ $)) (SIGNATURE |eval| ($ $ (|BasicOperator|) $ (|Symbol|))) (SIGNATURE |eval| ($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)))) |noBranch|) (IF (|has| |t#1| (|SemiGroup|)) (PROGN (ATTRIBUTE (|Monoid|)) (SIGNATURE ** ($ $ (|NonNegativeInteger|))) (SIGNATURE |isTimes| ((|Union| (|List| $) "failed") $)) (SIGNATURE |isExpt| ((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $))) |noBranch|) (IF (|has| |t#1| (|Group|)) (ATTRIBUTE (|Group|)) |noBranch|) (IF (|has| |t#1| (|AbelianSemiGroup|)) (PROGN (ATTRIBUTE (|AbelianMonoid|)) (SIGNATURE |isPlus| ((|Union| (|List| $) "failed") $)) (SIGNATURE |isMult| ((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $))) |noBranch|) (IF (|has| |t#1| (|AbelianGroup|)) (ATTRIBUTE (|AbelianGroup|)) |noBranch|) (IF (|has| |t#1| (|Ring|)) (PROGN (ATTRIBUTE (|Ring|)) (ATTRIBUTE (|RetractableTo| (|Polynomial| |t#1|))) (ATTRIBUTE (|PartialDifferentialRing| (|Symbol|))) (ATTRIBUTE (|FullyLinearlyExplicitRingOver| |t#1|)) (SIGNATURE |coerce| ($ (|SparseMultivariatePolynomial| |t#1| (|Kernel| $)))) (SIGNATURE |numer| ((|SparseMultivariatePolynomial| |t#1| (|Kernel| $)) $)) (SIGNATURE |numerator| ($ $)) (SIGNATURE |isExpt| ((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|))) (SIGNATURE |isExpt| ((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|))) (SIGNATURE |isPower| ((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $)) (SIGNATURE |eval| ($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $)))) (SIGNATURE |eval| ($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $))))) (SIGNATURE |eval| ($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $)))) (SIGNATURE |eval| ($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)))) |noBranch|) (IF (|has| |t#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |noBranch|) (IF (|has| |t#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |noBranch|) (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |t#1|)) |noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (ATTRIBUTE (|Field|)) (ATTRIBUTE (|RetractableTo| (|Fraction| (|Polynomial| |t#1|)))) (SIGNATURE |convert| ($ (|Factored| $))) (SIGNATURE |denom| ((|SparseMultivariatePolynomial| |t#1| (|Kernel| $)) $)) (SIGNATURE |denominator| ($ $)) (SIGNATURE / ($ (|SparseMultivariatePolynomial| |t#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |t#1| (|Kernel| $)))) (SIGNATURE |coerce| ($ (|Fraction| |t#1|))) (SIGNATURE |coerce| ($ (|Polynomial| (|Fraction| |t#1|)))) (SIGNATURE |coerce| ($ (|Fraction| (|Polynomial| (|Fraction| |t#1|))))) (SIGNATURE |univariate| ((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $))) (IF (|has| |t#1| (|RetractableTo| (|Integer|))) (ATTRIBUTE (|RetractableTo| (|Fraction| (|Integer|)))) |noBranch|)) |noBranch|))) 
(((|AbelianGroup|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|AbelianGroup|))) ((|AbelianMonoid|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|AbelianSemiGroup|)) (|has| |#1| (|AbelianGroup|))) ((|AbelianSemiGroup|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|AbelianSemiGroup|)) (|has| |#1| (|AbelianGroup|))) ((|Algebra| (|Fraction| (|Integer|))) |has| |#1| (|IntegralDomain|)) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) |has| |#1| (|IntegralDomain|)) ((|BiModule| |#1| |#1|) |has| |#1| (|CommutativeRing|)) ((|BiModule| $ $) |has| |#1| (|IntegralDomain|)) ((|CancellationAbelianMonoid|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|AbelianGroup|))) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) |has| |#1| (|IntegralDomain|)) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|ConvertibleTo| (|Pattern| (|Float|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) ((|ConvertibleTo| (|Pattern| (|Integer|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) ((|DivisionRing|) |has| |#1| (|IntegralDomain|)) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|EuclideanDomain|) |has| |#1| (|IntegralDomain|)) ((|Evalable| $) . T) ((|ExpressionSpace|) . T) ((|Field|) |has| |#1| (|IntegralDomain|)) ((|FullyLinearlyExplicitRingOver| |#1|) |has| |#1| (|Ring|)) ((|FullyPatternMatchable| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|GcdDomain|) |has| |#1| (|IntegralDomain|)) ((|Group|) |has| |#1| (|Group|)) ((|InnerEvalable| (|Kernel| $) $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftModule| (|Fraction| (|Integer|))) |has| |#1| (|IntegralDomain|)) ((|LeftModule| |#1|) |has| |#1| (|CommutativeRing|)) ((|LeftModule| $) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|))) ((|LeftOreRing|) |has| |#1| (|IntegralDomain|)) ((|LinearlyExplicitRingOver| (|Integer|)) AND (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|))) ((|LinearlyExplicitRingOver| |#1|) |has| |#1| (|Ring|)) ((|Module| (|Fraction| (|Integer|))) |has| |#1| (|IntegralDomain|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) OR (|has| |#1| (|SemiGroup|)) (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Group|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|))) ((|OrderedSet|) . T) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|Ring|)) ((|PatternMatchable| (|Float|)) |has| |#1| (|PatternMatchable| (|Float|))) ((|PatternMatchable| (|Integer|)) |has| |#1| (|PatternMatchable| (|Integer|))) ((|Patternable| |#1|) . T) ((|PrincipalIdealDomain|) |has| |#1| (|IntegralDomain|)) ((|RetractableTo| (|Fraction| (|Integer|))) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (AND (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|RetractableTo| (|Integer|))))) ((|RetractableTo| (|Fraction| (|Polynomial| |#1|))) |has| |#1| (|IntegralDomain|)) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| (|Kernel| $)) . T) ((|RetractableTo| (|Polynomial| |#1|)) |has| |#1| (|Ring|)) ((|RetractableTo| (|Symbol|)) . T) ((|RetractableTo| |#1|) . T) ((|RightModule| (|Fraction| (|Integer|))) |has| |#1| (|IntegralDomain|)) ((|RightModule| |#1|) |has| |#1| (|CommutativeRing|)) ((|RightModule| $) |has| |#1| (|IntegralDomain|)) ((|Ring|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|))) ((|Rng|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|))) ((|SemiGroup|) OR (|has| |#1| (|SemiGroup|)) (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Group|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|))) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|IntegralDomain|))) 
((|polygamma| ((|#2| |#2| |#2|) 33)) (|operator| (((|BasicOperator|) (|BasicOperator|)) 44)) (|iipolygamma| ((|#2| (|List| |#2|)) 79)) (|iidigamma| ((|#2| |#2|) 77)) (|iiabs| ((|#2| |#2|) 68)) (|iiGamma| ((|#2| |#2|) 71)) (|iiBeta| ((|#2| (|List| |#2|)) 75)) (|iiBesselY| ((|#2| (|List| |#2|)) 83)) (|iiBesselK| ((|#2| (|List| |#2|)) 87)) (|iiBesselJ| ((|#2| (|List| |#2|)) 81)) (|iiBesselI| ((|#2| (|List| |#2|)) 85)) (|iiAiryBi| ((|#2| |#2|) 91)) (|iiAiryAi| ((|#2| |#2|) 89)) (|digamma| ((|#2| |#2|) 32)) (|besselY| ((|#2| |#2| |#2|) 35)) (|besselK| ((|#2| |#2| |#2|) 37)) (|besselJ| ((|#2| |#2| |#2|) 34)) (|besselI| ((|#2| |#2| |#2|) 36)) (|belong?| (((|Boolean|) (|BasicOperator|)) 42)) (|airyBi| ((|#2| |#2|) 39)) (|airyAi| ((|#2| |#2|) 38)) (|abs| ((|#2| |#2|) 27)) (|Gamma| ((|#2| |#2| |#2|) 30) ((|#2| |#2|) 28)) (|Beta| ((|#2| |#2| |#2|) 31))) 
(((|FunctionalSpecialFunction| |#1| |#2|) (CATEGORY |package| (SIGNATURE |belong?| ((|Boolean|) (|BasicOperator|))) (SIGNATURE |operator| ((|BasicOperator|) (|BasicOperator|))) (SIGNATURE |abs| (|#2| |#2|)) (SIGNATURE |Gamma| (|#2| |#2|)) (SIGNATURE |Gamma| (|#2| |#2| |#2|)) (SIGNATURE |Beta| (|#2| |#2| |#2|)) (SIGNATURE |digamma| (|#2| |#2|)) (SIGNATURE |polygamma| (|#2| |#2| |#2|)) (SIGNATURE |besselJ| (|#2| |#2| |#2|)) (SIGNATURE |besselY| (|#2| |#2| |#2|)) (SIGNATURE |besselI| (|#2| |#2| |#2|)) (SIGNATURE |besselK| (|#2| |#2| |#2|)) (SIGNATURE |airyAi| (|#2| |#2|)) (SIGNATURE |airyBi| (|#2| |#2|)) (SIGNATURE |iiGamma| (|#2| |#2|)) (SIGNATURE |iiabs| (|#2| |#2|)) (SIGNATURE |iiBeta| (|#2| (|List| |#2|))) (SIGNATURE |iidigamma| (|#2| |#2|)) (SIGNATURE |iipolygamma| (|#2| (|List| |#2|))) (SIGNATURE |iiBesselJ| (|#2| (|List| |#2|))) (SIGNATURE |iiBesselY| (|#2| (|List| |#2|))) (SIGNATURE |iiBesselI| (|#2| (|List| |#2|))) (SIGNATURE |iiBesselK| (|#2| (|List| |#2|))) (SIGNATURE |iiAiryAi| (|#2| |#2|)) (SIGNATURE |iiAiryBi| (|#2| |#2|))) (|Join| (|OrderedSet|) (|IntegralDomain|)) (|FunctionSpace| |#1|)) (T |FunctionalSpecialFunction|)) 
((|iiAiryBi| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|iiAiryAi| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|iiBesselK| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4)) (|isDomain| *1 (|FunctionalSpecialFunction| *4 *2)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|iiBesselI| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4)) (|isDomain| *1 (|FunctionalSpecialFunction| *4 *2)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|iiBesselY| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4)) (|isDomain| *1 (|FunctionalSpecialFunction| *4 *2)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|iiBesselJ| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4)) (|isDomain| *1 (|FunctionalSpecialFunction| *4 *2)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|iipolygamma| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4)) (|isDomain| *1 (|FunctionalSpecialFunction| *4 *2)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|iidigamma| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|iiBeta| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4)) (|isDomain| *1 (|FunctionalSpecialFunction| *4 *2)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|iiabs| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|iiGamma| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|airyBi| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|airyAi| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|besselK| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|besselI| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|besselY| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|besselJ| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|polygamma| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|digamma| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|Beta| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|Gamma| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|Gamma| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|abs| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|operator| (*1 *2 *2) (AND (|isDomain| *2 (|BasicOperator|)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *4)) (|ofCategory| *4 (|FunctionSpace| *3)))) (|belong?| (*1 *2 *3) (AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FunctionalSpecialFunction| *4 *5)) (|ofCategory| *5 (|FunctionSpace| *4))))) 
(CATEGORY |package| (SIGNATURE |belong?| ((|Boolean|) (|BasicOperator|))) (SIGNATURE |operator| ((|BasicOperator|) (|BasicOperator|))) (SIGNATURE |abs| (|#2| |#2|)) (SIGNATURE |Gamma| (|#2| |#2|)) (SIGNATURE |Gamma| (|#2| |#2| |#2|)) (SIGNATURE |Beta| (|#2| |#2| |#2|)) (SIGNATURE |digamma| (|#2| |#2|)) (SIGNATURE |polygamma| (|#2| |#2| |#2|)) (SIGNATURE |besselJ| (|#2| |#2| |#2|)) (SIGNATURE |besselY| (|#2| |#2| |#2|)) (SIGNATURE |besselI| (|#2| |#2| |#2|)) (SIGNATURE |besselK| (|#2| |#2| |#2|)) (SIGNATURE |airyAi| (|#2| |#2|)) (SIGNATURE |airyBi| (|#2| |#2|)) (SIGNATURE |iiGamma| (|#2| |#2|)) (SIGNATURE |iiabs| (|#2| |#2|)) (SIGNATURE |iiBeta| (|#2| (|List| |#2|))) (SIGNATURE |iidigamma| (|#2| |#2|)) (SIGNATURE |iipolygamma| (|#2| (|List| |#2|))) (SIGNATURE |iiBesselJ| (|#2| (|List| |#2|))) (SIGNATURE |iiBesselY| (|#2| (|List| |#2|))) (SIGNATURE |iiBesselI| (|#2| (|List| |#2|))) (SIGNATURE |iiBesselK| (|#2| (|List| |#2|))) (SIGNATURE |iiAiryAi| (|#2| |#2|)) (SIGNATURE |iiAiryBi| (|#2| |#2|))) 
((|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) 93 (|has| |#2| (|AlgebraicallyClosedField|))) (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) 58))) 
(((|FunctionSpacePrimitiveElement| |#1| |#2|) (CATEGORY |package| (SIGNATURE |primitiveElement| ((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|))) (IF (|has| |#2| (|AlgebraicallyClosedField|)) (SIGNATURE |primitiveElement| ((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|)) |noBranch|)) (|Join| (|IntegralDomain|) (|OrderedSet|) (|CharacteristicZero|)) (|FunctionSpace| |#1|)) (T |FunctionSpacePrimitiveElement|)) 
((|primitiveElement| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|CharacteristicZero|))) (|isDomain| *2 (|Record| (|:| |primelt| *3) (|:| |pol1| (|SparseUnivariatePolynomial| *3)) (|:| |pol2| (|SparseUnivariatePolynomial| *3)) (|:| |prim| (|SparseUnivariatePolynomial| *3)))) (|isDomain| *1 (|FunctionSpacePrimitiveElement| *4 *3)) (|ofCategory| *3 (|AlgebraicallyClosedField|)) (|ofCategory| *3 (|FunctionSpace| *4)))) (|primitiveElement| (*1 *2 *3) (AND (|isDomain| *3 (|List| *5)) (|ofCategory| *5 (|FunctionSpace| *4)) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|CharacteristicZero|))) (|isDomain| *2 (|Record| (|:| |primelt| *5) (|:| |poly| (|List| (|SparseUnivariatePolynomial| *5))) (|:| |prim| (|SparseUnivariatePolynomial| *5)))) (|isDomain| *1 (|FunctionSpacePrimitiveElement| *4 *5))))) 
(CATEGORY |package| (SIGNATURE |primitiveElement| ((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|))) (IF (|has| |#2| (|AlgebraicallyClosedField|)) (SIGNATURE |primitiveElement| ((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|)) |noBranch|)) 
((|newReduc| (((|Void|)) 18)) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) 40) (((|Fraction| (|Integer|)) |#2|) 23))) 
(((|FunctionSpaceReduce| |#1| |#2|) (CATEGORY |package| (SIGNATURE |bringDown| ((|Fraction| (|Integer|)) |#2|)) (SIGNATURE |bringDown| ((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|))) (SIGNATURE |newReduc| ((|Void|)))) (|Join| (|OrderedSet|) (|IntegralDomain|) (|RetractableTo| (|Integer|))) (|FunctionSpace| |#1|)) (T |FunctionSpaceReduce|)) 
((|newReduc| (*1 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|FunctionSpaceReduce| *3 *4)) (|ofCategory| *4 (|FunctionSpace| *3)))) (|bringDown| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Kernel| *3)) (|ofCategory| *3 (|FunctionSpace| *5)) (|ofCategory| *5 (|Join| (|OrderedSet|) (|IntegralDomain|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|FunctionSpaceReduce| *5 *3)))) (|bringDown| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|FunctionSpaceReduce| *4 *3)) (|ofCategory| *3 (|FunctionSpace| *4))))) 
(CATEGORY |package| (SIGNATURE |bringDown| ((|Fraction| (|Integer|)) |#2|)) (SIGNATURE |bringDown| ((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|))) (SIGNATURE |newReduc| ((|Void|)))) 
((|real?| (((|Boolean|) $) 28)) (|logical?| (((|Boolean|) $) 30)) (|integer?| (((|Boolean|) $) 31)) (|doubleComplex?| (((|Boolean|) $) 34)) (|double?| (((|Boolean|) $) 29)) (|complex?| (((|Boolean|) $) 33)) (|coerce| (((|OutputForm|) $) 18) (($ (|String|)) 27) (($ (|Symbol|)) 23) (((|Symbol|) $) 22) (((|SExpression|) $) 21)) (|character?| (((|Boolean|) $) 32)) (= (((|Boolean|) $ $) 15))) 
(((|FortranScalarType|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|String|))) (SIGNATURE |coerce| ($ (|Symbol|))) (SIGNATURE |coerce| ((|Symbol|) $)) (SIGNATURE |coerce| ((|SExpression|) $)) (SIGNATURE |real?| ((|Boolean|) $)) (SIGNATURE |double?| ((|Boolean|) $)) (SIGNATURE |integer?| ((|Boolean|) $)) (SIGNATURE |complex?| ((|Boolean|) $)) (SIGNATURE |doubleComplex?| ((|Boolean|) $)) (SIGNATURE |character?| ((|Boolean|) $)) (SIGNATURE |logical?| ((|Boolean|) $)) (SIGNATURE = ((|Boolean|) $ $))))) (T |FortranScalarType|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|FortranScalarType|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|FortranScalarType|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|FortranScalarType|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|SExpression|)) (|isDomain| *1 (|FortranScalarType|)))) (|real?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranScalarType|)))) (|double?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranScalarType|)))) (|integer?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranScalarType|)))) (|complex?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranScalarType|)))) (|doubleComplex?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranScalarType|)))) (|character?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranScalarType|)))) (|logical?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranScalarType|)))) (= (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranScalarType|))))) 
(|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|String|))) (SIGNATURE |coerce| ($ (|Symbol|))) (SIGNATURE |coerce| ((|Symbol|) $)) (SIGNATURE |coerce| ((|SExpression|) $)) (SIGNATURE |real?| ((|Boolean|) $)) (SIGNATURE |double?| ((|Boolean|) $)) (SIGNATURE |integer?| ((|Boolean|) $)) (SIGNATURE |complex?| ((|Boolean|) $)) (SIGNATURE |doubleComplex?| ((|Boolean|) $)) (SIGNATURE |character?| ((|Boolean|) $)) (SIGNATURE |logical?| ((|Boolean|) $)) (SIGNATURE = ((|Boolean|) $ $)))) 
((|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) 68)) (|ffactor| (((|Factored| |#3|) |#3|) 33)) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) 27 (|has| |#2| (|RetractableTo| (|AlgebraicNumber|))))) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) 35))) 
(((|FunctionSpaceUnivariatePolynomialFactor| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |ffactor| ((|Factored| |#3|) |#3|)) (SIGNATURE |qfactor| ((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|)) (SIGNATURE |UP2ifCan| ((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|)) (IF (|has| |#2| (|RetractableTo| (|AlgebraicNumber|))) (SIGNATURE |anfactor| ((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|)) |noBranch|)) (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|))) (|FunctionSpace| |#1|) (|UnivariatePolynomialCategory| |#2|)) (T |FunctionSpaceUnivariatePolynomialFactor|)) 
((|anfactor| (*1 *2 *3) (|partial| AND (|ofCategory| *5 (|RetractableTo| (|AlgebraicNumber|))) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|ofCategory| *5 (|FunctionSpace| *4)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|)))) (|isDomain| *1 (|FunctionSpaceUnivariatePolynomialFactor| *4 *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|UP2ifCan| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|ofCategory| *5 (|FunctionSpace| *4)) (|isDomain| *2 (|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|)))) (|isDomain| *1 (|FunctionSpaceUnivariatePolynomialFactor| *4 *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|qfactor| (*1 *2 *3) (|partial| AND (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|ofCategory| *5 (|FunctionSpace| *4)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|))))) (|isDomain| *1 (|FunctionSpaceUnivariatePolynomialFactor| *4 *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|ffactor| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|ofCategory| *5 (|FunctionSpace| *4)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|FunctionSpaceUnivariatePolynomialFactor| *4 *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |ffactor| ((|Factored| |#3|) |#3|)) (SIGNATURE |qfactor| ((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|)) (SIGNATURE |UP2ifCan| ((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|)) (IF (|has| |#2| (|RetractableTo| (|AlgebraicNumber|))) (SIGNATURE |anfactor| ((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|)) |noBranch|)) 
((~= (((|Boolean|) $ $) NIL)) (|write!| (((|String|) $ (|String|)) NIL)) (|reopen!| (($ $ (|String|)) NIL)) (|read!| (((|String|) $) NIL)) (|processTemplate| (((|FileName|) (|FileName|) (|FileName|)) 17) (((|FileName|) (|FileName|)) 15)) (|open| (($ (|FileName|)) NIL) (($ (|FileName|) (|String|)) NIL)) (|name| (((|FileName|) $) NIL)) (|latex| (((|String|) $) NIL)) (|iomode| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|fortranLiteralLine| (((|Void|) (|String|)) 9)) (|fortranLiteral| (((|Void|) (|String|)) 10)) (|fortranCarriageReturn| (((|Void|)) 11)) (|flush| (((|Void|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (|close!| (($ $) 34)) (= (((|Boolean|) $ $) NIL))) 
(((|FortranTemplate|) (|Join| (|FileCategory| (|FileName|) (|String|)) (CATEGORY |package| (SIGNATURE |processTemplate| ((|FileName|) (|FileName|) (|FileName|))) (SIGNATURE |processTemplate| ((|FileName|) (|FileName|))) (SIGNATURE |fortranLiteralLine| ((|Void|) (|String|))) (SIGNATURE |fortranLiteral| ((|Void|) (|String|))) (SIGNATURE |fortranCarriageReturn| ((|Void|)))))) (T |FortranTemplate|)) 
((|processTemplate| (*1 *2 *2 *2) (AND (|isDomain| *2 (|FileName|)) (|isDomain| *1 (|FortranTemplate|)))) (|processTemplate| (*1 *2 *2) (AND (|isDomain| *2 (|FileName|)) (|isDomain| *1 (|FortranTemplate|)))) (|fortranLiteralLine| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|FortranTemplate|)))) (|fortranLiteral| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|FortranTemplate|)))) (|fortranCarriageReturn| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|FortranTemplate|))))) 
(|Join| (|FileCategory| (|FileName|) (|String|)) (CATEGORY |package| (SIGNATURE |processTemplate| ((|FileName|) (|FileName|) (|FileName|))) (SIGNATURE |processTemplate| ((|FileName|) (|FileName|))) (SIGNATURE |fortranLiteralLine| ((|Void|) (|String|))) (SIGNATURE |fortranLiteral| ((|Void|) (|String|))) (SIGNATURE |fortranCarriageReturn| ((|Void|))))) 
((~= (((|Boolean|) $ $) NIL)) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) 10)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|fortranReal| (($) 31)) (|fortranLogical| (($) 37)) (|fortranInteger| (($) 33)) (|fortranDoubleComplex| (($) 35)) (|fortranDouble| (($) 32)) (|fortranComplex| (($) 34)) (|fortranCharacter| (($) 36)) (|external?| (((|Boolean|) $) 8)) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) 16)) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Symbol|)) (|Boolean|)) 25) (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) 26)) (|coerce| (((|OutputForm|) $) 21) (($ (|FortranScalarType|)) 28)) (= (((|Boolean|) $ $) NIL))) 
(((|FortranType|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE |coerce| ($ (|FortranScalarType|))) (SIGNATURE |scalarTypeOf| ((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $)) (SIGNATURE |dimensionsOf| ((|List| (|Polynomial| (|Integer|))) $)) (SIGNATURE |external?| ((|Boolean|) $)) (SIGNATURE |construct| ($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Symbol|)) (|Boolean|))) (SIGNATURE |construct| ($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|))) (SIGNATURE |fortranReal| ($)) (SIGNATURE |fortranDouble| ($)) (SIGNATURE |fortranInteger| ($)) (SIGNATURE |fortranLogical| ($)) (SIGNATURE |fortranComplex| ($)) (SIGNATURE |fortranDoubleComplex| ($)) (SIGNATURE |fortranCharacter| ($))))) (T |FortranType|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|FortranType|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|FortranScalarType|)) (|isDomain| *1 (|FortranType|)))) (|scalarTypeOf| (*1 *2 *1) (AND (|isDomain| *2 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|isDomain| *1 (|FortranType|)))) (|dimensionsOf| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Polynomial| (|Integer|)))) (|isDomain| *1 (|FortranType|)))) (|external?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranType|)))) (|construct| (*1 *1 *2 *3 *4) (AND (|isDomain| *2 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|isDomain| *3 (|List| (|Symbol|))) (|isDomain| *4 (|Boolean|)) (|isDomain| *1 (|FortranType|)))) (|construct| (*1 *1 *2 *3 *4) (AND (|isDomain| *2 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|isDomain| *3 (|List| (|Polynomial| (|Integer|)))) (|isDomain| *4 (|Boolean|)) (|isDomain| *1 (|FortranType|)))) (|fortranReal| (*1 *1) (|isDomain| *1 (|FortranType|))) (|fortranDouble| (*1 *1) (|isDomain| *1 (|FortranType|))) (|fortranInteger| (*1 *1) (|isDomain| *1 (|FortranType|))) (|fortranLogical| (*1 *1) (|isDomain| *1 (|FortranType|))) (|fortranComplex| (*1 *1) (|isDomain| *1 (|FortranType|))) (|fortranDoubleComplex| (*1 *1) (|isDomain| *1 (|FortranType|))) (|fortranCharacter| (*1 *1) (|isDomain| *1 (|FortranType|)))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE |coerce| ($ (|FortranScalarType|))) (SIGNATURE |scalarTypeOf| ((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $)) (SIGNATURE |dimensionsOf| ((|List| (|Polynomial| (|Integer|))) $)) (SIGNATURE |external?| ((|Boolean|) $)) (SIGNATURE |construct| ($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Symbol|)) (|Boolean|))) (SIGNATURE |construct| ($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|))) (SIGNATURE |fortranReal| ($)) (SIGNATURE |fortranDouble| ($)) (SIGNATURE |fortranInteger| ($)) (SIGNATURE |fortranLogical| ($)) (SIGNATURE |fortranComplex| ($)) (SIGNATURE |fortranDoubleComplex| ($)) (SIGNATURE |fortranCharacter| ($)))) 
((~= (((|Boolean|) $ $) NIL)) (|name| (((|Symbol|) $) 8)) (|latex| (((|String|) $) 16)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 11)) (= (((|Boolean|) $ $) 13))) 
(((|FunctionCalled| |#1|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |name| ((|Symbol|) $)))) (|Symbol|)) (T |FunctionCalled|)) 
((|name| (*1 *2 *1) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|FunctionCalled| *3)) (|ofType| *3 *2)))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |name| ((|Symbol|) $)))) 
((|outputAsFortran| (((|Void|) $) 7)) (|coerce| (((|OutputForm|) $) 8) (($ (|Vector| (|MachineFloat|))) 12) (($ (|List| (|FortranCode|))) 11) (($ (|FortranCode|)) 10) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 9))) 
(((|FortranVectorCategory|) (|Category|)) (T |FortranVectorCategory|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|MachineFloat|))) (|ofCategory| *1 (|FortranVectorCategory|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|FortranCode|))) (|ofCategory| *1 (|FortranVectorCategory|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|FortranCode|)) (|ofCategory| *1 (|FortranVectorCategory|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) (|ofCategory| *1 (|FortranVectorCategory|))))) 
(|Join| (|FortranProgramCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| (|MachineFloat|)))) (SIGNATURE |coerce| ($ (|List| (|FortranCode|)))) (SIGNATURE |coerce| ($ (|FortranCode|))) (SIGNATURE |coerce| ($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|)))))))) 
(((|CoercibleTo| (|OutputForm|)) . T) ((|FortranProgramCategory|) . T) ((|Type|) . T)) 
((|retractIfCan| (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) 19) (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) 17) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) 15) (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) 13) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 11) (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 9)) (|retract| (($ (|Vector| (|Expression| (|Float|)))) 20) (($ (|Vector| (|Expression| (|Integer|)))) 18) (($ (|Vector| (|Polynomial| (|Float|)))) 16) (($ (|Vector| (|Polynomial| (|Integer|)))) 14) (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) 12) (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) 10)) (|outputAsFortran| (((|Void|) $) 7)) (|coerce| (((|OutputForm|) $) 8) (($ (|List| (|FortranCode|))) 23) (($ (|FortranCode|)) 22) (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) 21))) 
(((|FortranVectorFunctionCategory|) (|Category|)) (T |FortranVectorFunctionCategory|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|FortranCode|))) (|ofCategory| *1 (|FortranVectorFunctionCategory|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|FortranCode|)) (|ofCategory| *1 (|FortranVectorFunctionCategory|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) (|ofCategory| *1 (|FortranVectorFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|Expression| (|Float|)))) (|ofCategory| *1 (|FortranVectorFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Vector| (|Expression| (|Float|)))) (|ofCategory| *1 (|FortranVectorFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|Expression| (|Integer|)))) (|ofCategory| *1 (|FortranVectorFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Vector| (|Expression| (|Integer|)))) (|ofCategory| *1 (|FortranVectorFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|Polynomial| (|Float|)))) (|ofCategory| *1 (|FortranVectorFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Vector| (|Polynomial| (|Float|)))) (|ofCategory| *1 (|FortranVectorFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|Polynomial| (|Integer|)))) (|ofCategory| *1 (|FortranVectorFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Vector| (|Polynomial| (|Integer|)))) (|ofCategory| *1 (|FortranVectorFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|Fraction| (|Polynomial| (|Float|))))) (|ofCategory| *1 (|FortranVectorFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Vector| (|Fraction| (|Polynomial| (|Float|))))) (|ofCategory| *1 (|FortranVectorFunctionCategory|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) (|ofCategory| *1 (|FortranVectorFunctionCategory|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) (|ofCategory| *1 (|FortranVectorFunctionCategory|))))) 
(|Join| (|FortranProgramCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|List| (|FortranCode|)))) (SIGNATURE |coerce| ($ (|FortranCode|))) (SIGNATURE |coerce| ($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|)))))) (SIGNATURE |retract| ($ (|Vector| (|Expression| (|Float|))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Vector| (|Expression| (|Float|))))) (SIGNATURE |retract| ($ (|Vector| (|Expression| (|Integer|))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Vector| (|Expression| (|Integer|))))) (SIGNATURE |retract| ($ (|Vector| (|Polynomial| (|Float|))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|))))) (SIGNATURE |retract| ($ (|Vector| (|Polynomial| (|Integer|))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|))))) (SIGNATURE |retract| ($ (|Vector| (|Fraction| (|Polynomial| (|Float|)))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|)))))) (SIGNATURE |retract| ($ (|Vector| (|Fraction| (|Polynomial| (|Integer|)))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|)))))))) 
(((|CoercibleTo| (|OutputForm|)) . T) ((|FortranProgramCategory|) . T) ((|Type|) . T)) 
((|useSingleFactorBound?| (((|Boolean|)) 17)) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) 18)) (|useEisensteinCriterion?| (((|Boolean|)) 13)) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) 14)) (|tryFunctionalDecomposition?| (((|Boolean|)) 15)) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) 16)) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) 21) (((|PositiveInteger|)) 20)) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) 41)) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) 23) (((|PositiveInteger|)) 22)) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) 61)) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) 125)) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) 151)) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) 164) (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) 161) (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) 163) (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) 162) (((|Factored| |#1|) |#1|) 160)) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) 166) (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) 167) (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) 169) (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) 168) (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) 170)) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) 159) (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) 155) (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) 157) (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) 156) (((|Factored| |#1|) |#1|) 154)) (|eisensteinIrreducible?| (((|Boolean|) |#1|) 36)) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) 66)) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) 153))) 
(((|GaloisGroupFactorizer| |#1|) (CATEGORY |package| (SIGNATURE |makeFR| ((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))))) (SIGNATURE |degreePartition| ((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))))) (SIGNATURE |musserTrials| ((|PositiveInteger|))) (SIGNATURE |musserTrials| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |stopMusserTrials| ((|PositiveInteger|))) (SIGNATURE |stopMusserTrials| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |numberOfFactors| ((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))))) (SIGNATURE |modularFactor| ((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|)) (SIGNATURE |useSingleFactorBound?| ((|Boolean|))) (SIGNATURE |useSingleFactorBound| ((|Boolean|) (|Boolean|))) (SIGNATURE |useEisensteinCriterion?| ((|Boolean|))) (SIGNATURE |useEisensteinCriterion| ((|Boolean|) (|Boolean|))) (SIGNATURE |eisensteinIrreducible?| ((|Boolean|) |#1|)) (SIGNATURE |tryFunctionalDecomposition?| ((|Boolean|))) (SIGNATURE |tryFunctionalDecomposition| ((|Boolean|) (|Boolean|))) (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) (SIGNATURE |factor| ((|Factored| |#1|) |#1| (|NonNegativeInteger|))) (SIGNATURE |factor| ((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)))) (SIGNATURE |factor| ((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|))) (SIGNATURE |factor| ((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |factorSquareFree| ((|Factored| |#1|) |#1|)) (SIGNATURE |factorSquareFree| ((|Factored| |#1|) |#1| (|NonNegativeInteger|))) (SIGNATURE |factorSquareFree| ((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)))) (SIGNATURE |factorSquareFree| ((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|))) (SIGNATURE |factorSquareFree| ((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |factorOfDegree| ((|Union| |#1| "failed") (|PositiveInteger|) |#1|)) (SIGNATURE |factorOfDegree| ((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|))) (SIGNATURE |factorOfDegree| ((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)))) (SIGNATURE |factorOfDegree| ((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|))) (SIGNATURE |factorOfDegree| ((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|))) (SIGNATURE |henselFact| ((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|))) (SIGNATURE |btwFact| ((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)))) (|UnivariatePolynomialCategory| (|Integer|))) (T |GaloisGroupFactorizer|)) 
((|btwFact| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *4 (|Boolean|)) (|isDomain| *5 (|Set| (|NonNegativeInteger|))) (|isDomain| *6 (|NonNegativeInteger|)) (|isDomain| *2 (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| *3) (|:| |pow| (|Integer|))))))) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|henselFact| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Boolean|)) (|isDomain| *2 (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| *3) (|:| |pow| (|Integer|))))))) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|factorOfDegree| (*1 *2 *3 *2 *4 *5 *6) (|partial| AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|List| (|NonNegativeInteger|))) (|isDomain| *5 (|NonNegativeInteger|)) (|isDomain| *6 (|Boolean|)) (|isDomain| *1 (|GaloisGroupFactorizer| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Integer|))))) (|factorOfDegree| (*1 *2 *3 *2 *4 *5) (|partial| AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|List| (|NonNegativeInteger|))) (|isDomain| *5 (|NonNegativeInteger|)) (|isDomain| *1 (|GaloisGroupFactorizer| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Integer|))))) (|factorOfDegree| (*1 *2 *3 *2 *4) (|partial| AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|List| (|NonNegativeInteger|))) (|isDomain| *1 (|GaloisGroupFactorizer| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Integer|))))) (|factorOfDegree| (*1 *2 *3 *2 *4) (|partial| AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *1 (|GaloisGroupFactorizer| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Integer|))))) (|factorOfDegree| (*1 *2 *3 *2) (|partial| AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *1 (|GaloisGroupFactorizer| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Integer|))))) (|factorSquareFree| (*1 *2 *3 *4 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|factorSquareFree| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|List| (|NonNegativeInteger|))) (|isDomain| *5 (|NonNegativeInteger|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|factorSquareFree| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| (|NonNegativeInteger|))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|factorSquareFree| (*1 *2 *3 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|factorSquareFree| (*1 *2 *3) (AND (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|factor| (*1 *2 *3 *4 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|factor| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|List| (|NonNegativeInteger|))) (|isDomain| *5 (|NonNegativeInteger|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|factor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| (|NonNegativeInteger|))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|factor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|factor| (*1 *2 *3) (AND (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|tryFunctionalDecomposition| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|tryFunctionalDecomposition?| (*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|eisensteinIrreducible?| (*1 *2 *3) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|useEisensteinCriterion| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|useEisensteinCriterion?| (*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|useSingleFactorBound| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|useSingleFactorBound?| (*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|modularFactor| (*1 *2 *3) (AND (|isDomain| *2 (|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| *3)))) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|numberOfFactors| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Record| (|:| |factor| *4) (|:| |degree| (|Integer|))))) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Integer|))) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|GaloisGroupFactorizer| *4)))) (|stopMusserTrials| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|stopMusserTrials| (*1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|musserTrials| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|musserTrials| (*1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|degreePartition| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Record| (|:| |factor| *4) (|:| |degree| (|Integer|))))) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Integer|))) (|isDomain| *2 (|Multiset| (|NonNegativeInteger|))) (|isDomain| *1 (|GaloisGroupFactorizer| *4)))) (|makeFR| (*1 *2 *3) (AND (|isDomain| *3 (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| *4) (|:| |pow| (|Integer|))))))) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Integer|))) (|isDomain| *2 (|Factored| *4)) (|isDomain| *1 (|GaloisGroupFactorizer| *4))))) 
(CATEGORY |package| (SIGNATURE |makeFR| ((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))))) (SIGNATURE |degreePartition| ((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))))) (SIGNATURE |musserTrials| ((|PositiveInteger|))) (SIGNATURE |musserTrials| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |stopMusserTrials| ((|PositiveInteger|))) (SIGNATURE |stopMusserTrials| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |numberOfFactors| ((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))))) (SIGNATURE |modularFactor| ((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|)) (SIGNATURE |useSingleFactorBound?| ((|Boolean|))) (SIGNATURE |useSingleFactorBound| ((|Boolean|) (|Boolean|))) (SIGNATURE |useEisensteinCriterion?| ((|Boolean|))) (SIGNATURE |useEisensteinCriterion| ((|Boolean|) (|Boolean|))) (SIGNATURE |eisensteinIrreducible?| ((|Boolean|) |#1|)) (SIGNATURE |tryFunctionalDecomposition?| ((|Boolean|))) (SIGNATURE |tryFunctionalDecomposition| ((|Boolean|) (|Boolean|))) (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) (SIGNATURE |factor| ((|Factored| |#1|) |#1| (|NonNegativeInteger|))) (SIGNATURE |factor| ((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)))) (SIGNATURE |factor| ((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|))) (SIGNATURE |factor| ((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |factorSquareFree| ((|Factored| |#1|) |#1|)) (SIGNATURE |factorSquareFree| ((|Factored| |#1|) |#1| (|NonNegativeInteger|))) (SIGNATURE |factorSquareFree| ((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)))) (SIGNATURE |factorSquareFree| ((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|))) (SIGNATURE |factorSquareFree| ((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |factorOfDegree| ((|Union| |#1| "failed") (|PositiveInteger|) |#1|)) (SIGNATURE |factorOfDegree| ((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|))) (SIGNATURE |factorOfDegree| ((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)))) (SIGNATURE |factorOfDegree| ((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|))) (SIGNATURE |factorOfDegree| ((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|))) (SIGNATURE |henselFact| ((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|))) (SIGNATURE |btwFact| ((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)))) 
((|singleFactorBound| (((|Integer|) |#2|) 48) (((|Integer|) |#2| (|NonNegativeInteger|)) 47)) (|rootBound| (((|Integer|) |#2|) 55)) (|quadraticNorm| ((|#3| |#2|) 25)) (|norm| ((|#3| |#2| (|PositiveInteger|)) 14)) (|length| ((|#3| |#2|) 15)) (|infinityNorm| ((|#3| |#2|) 9)) (|height| ((|#3| |#2|) 10)) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) 62) ((|#3| |#2|) 30)) (|beauzamyBound| (((|Integer|) |#2|) 57))) 
(((|GaloisGroupFactorizationUtilities| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |beauzamyBound| ((|Integer|) |#2|)) (SIGNATURE |bombieriNorm| (|#3| |#2|)) (SIGNATURE |bombieriNorm| (|#3| |#2| (|PositiveInteger|))) (SIGNATURE |rootBound| ((|Integer|) |#2|)) (SIGNATURE |singleFactorBound| ((|Integer|) |#2| (|NonNegativeInteger|))) (SIGNATURE |singleFactorBound| ((|Integer|) |#2|)) (SIGNATURE |norm| (|#3| |#2| (|PositiveInteger|))) (SIGNATURE |quadraticNorm| (|#3| |#2|)) (SIGNATURE |infinityNorm| (|#3| |#2|)) (SIGNATURE |height| (|#3| |#2|)) (SIGNATURE |length| (|#3| |#2|))) (|Ring|) (|UnivariatePolynomialCategory| |#1|) (|Join| (|FloatingPointSystem|) (|RetractableTo| |#1|) (|Field|) (|TranscendentalFunctionCategory|) (|ElementaryFunctionCategory|))) (T |GaloisGroupFactorizationUtilities|)) 
((|length| (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|RetractableTo| *4) (|Field|) (|TranscendentalFunctionCategory|) (|ElementaryFunctionCategory|))) (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *2)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|height| (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|RetractableTo| *4) (|Field|) (|TranscendentalFunctionCategory|) (|ElementaryFunctionCategory|))) (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *2)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|infinityNorm| (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|RetractableTo| *4) (|Field|) (|TranscendentalFunctionCategory|) (|ElementaryFunctionCategory|))) (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *2)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|quadraticNorm| (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|RetractableTo| *4) (|Field|) (|TranscendentalFunctionCategory|) (|ElementaryFunctionCategory|))) (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *2)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|norm| (*1 *2 *3 *4) (AND (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|RetractableTo| *5) (|Field|) (|TranscendentalFunctionCategory|) (|ElementaryFunctionCategory|))) (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *5 *3 *2)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|singleFactorBound| (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *5)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|Join| (|FloatingPointSystem|) (|RetractableTo| *4) (|Field|) (|TranscendentalFunctionCategory|) (|ElementaryFunctionCategory|))))) (|singleFactorBound| (*1 *2 *3 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *5 *3 *6)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *6 (|Join| (|FloatingPointSystem|) (|RetractableTo| *5) (|Field|) (|TranscendentalFunctionCategory|) (|ElementaryFunctionCategory|))))) (|rootBound| (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *5)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|Join| (|FloatingPointSystem|) (|RetractableTo| *4) (|Field|) (|TranscendentalFunctionCategory|) (|ElementaryFunctionCategory|))))) (|bombieriNorm| (*1 *2 *3 *4) (AND (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|RetractableTo| *5) (|Field|) (|TranscendentalFunctionCategory|) (|ElementaryFunctionCategory|))) (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *5 *3 *2)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|bombieriNorm| (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|RetractableTo| *4) (|Field|) (|TranscendentalFunctionCategory|) (|ElementaryFunctionCategory|))) (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *2)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|beauzamyBound| (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *5)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|Join| (|FloatingPointSystem|) (|RetractableTo| *4) (|Field|) (|TranscendentalFunctionCategory|) (|ElementaryFunctionCategory|)))))) 
(CATEGORY |package| (SIGNATURE |beauzamyBound| ((|Integer|) |#2|)) (SIGNATURE |bombieriNorm| (|#3| |#2|)) (SIGNATURE |bombieriNorm| (|#3| |#2| (|PositiveInteger|))) (SIGNATURE |rootBound| ((|Integer|) |#2|)) (SIGNATURE |singleFactorBound| ((|Integer|) |#2| (|NonNegativeInteger|))) (SIGNATURE |singleFactorBound| ((|Integer|) |#2|)) (SIGNATURE |norm| (|#3| |#2| (|PositiveInteger|))) (SIGNATURE |quadraticNorm| (|#3| |#2|)) (SIGNATURE |infinityNorm| (|#3| |#2|)) (SIGNATURE |height| (|#3| |#2|)) (SIGNATURE |length| (|#3| |#2|))) 
((|unvectorise| ((|#2| (|Vector| |#1|)) 36)) (|shiftRoots| ((|#2| |#2| |#1|) 49)) (|scaleRoots| ((|#2| |#2| |#1|) 41)) (|reverse| ((|#2| |#2|) 38)) (|monic?| (((|Boolean|) |#2|) 30)) (|factorsOfDegree| (((|List| |#2|) (|PositiveInteger|) (|Factored| |#2|)) 16)) (|factorOfDegree| ((|#2| (|PositiveInteger|) (|Factored| |#2|)) 21)) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|Factored| |#2|)) 25))) 
(((|GaloisGroupPolynomialUtilities| |#1| |#2|) (CATEGORY |package| (SIGNATURE |monic?| ((|Boolean|) |#2|)) (SIGNATURE |unvectorise| (|#2| (|Vector| |#1|))) (SIGNATURE |reverse| (|#2| |#2|)) (SIGNATURE |scaleRoots| (|#2| |#2| |#1|)) (SIGNATURE |shiftRoots| (|#2| |#2| |#1|)) (SIGNATURE |degreePartition| ((|Multiset| (|NonNegativeInteger|)) (|Factored| |#2|))) (SIGNATURE |factorOfDegree| (|#2| (|PositiveInteger|) (|Factored| |#2|))) (SIGNATURE |factorsOfDegree| ((|List| |#2|) (|PositiveInteger|) (|Factored| |#2|)))) (|Ring|) (|UnivariatePolynomialCategory| |#1|)) (T |GaloisGroupPolynomialUtilities|)) 
((|factorsOfDegree| (*1 *2 *3 *4) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|Factored| *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|List| *6)) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *5 *6)))) (|factorOfDegree| (*1 *2 *3 *4) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|Factored| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *5)) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *5 *2)) (|ofCategory| *5 (|Ring|)))) (|degreePartition| (*1 *2 *3) (AND (|isDomain| *3 (|Factored| *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Multiset| (|NonNegativeInteger|))) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *4 *5)))) (|shiftRoots| (*1 *2 *2 *3) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|scaleRoots| (*1 *2 *2 *3) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|reverse| (*1 *2 *2) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|unvectorise| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *4)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *4 *2)))) (|monic?| (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |monic?| ((|Boolean|) |#2|)) (SIGNATURE |unvectorise| (|#2| (|Vector| |#1|))) (SIGNATURE |reverse| (|#2| |#2|)) (SIGNATURE |scaleRoots| (|#2| |#2| |#1|)) (SIGNATURE |shiftRoots| (|#2| |#2| |#1|)) (SIGNATURE |degreePartition| ((|Multiset| (|NonNegativeInteger|)) (|Factored| |#2|))) (SIGNATURE |factorOfDegree| (|#2| (|PositiveInteger|) (|Factored| |#2|))) (SIGNATURE |factorsOfDegree| ((|List| |#2|) (|PositiveInteger|) (|Factored| |#2|)))) 
((|sizePascalTriangle| (((|NonNegativeInteger|)) 41)) (|safetyMargin| (((|NonNegativeInteger|)) 23 (|has| |#1| (|FloatingPointSystem|))) (((|NonNegativeInteger|) (|NonNegativeInteger|)) 22 (|has| |#1| (|FloatingPointSystem|)))) (|safeFloor| (((|Integer|) |#1|) 18 (|has| |#1| (|FloatingPointSystem|)))) (|safeCeiling| (((|Integer|) |#1|) 20 (|has| |#1| (|FloatingPointSystem|)))) (|rangePascalTriangle| (((|NonNegativeInteger|)) 40) (((|NonNegativeInteger|) (|NonNegativeInteger|)) 39)) (|pascalTriangle| ((|#1| (|NonNegativeInteger|) (|Integer|)) 29)) (|fillPascalTriangle| (((|Void|)) 43))) 
(((|GaloisGroupUtilities| |#1|) (CATEGORY |package| (SIGNATURE |pascalTriangle| (|#1| (|NonNegativeInteger|) (|Integer|))) (SIGNATURE |rangePascalTriangle| ((|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |rangePascalTriangle| ((|NonNegativeInteger|))) (SIGNATURE |sizePascalTriangle| ((|NonNegativeInteger|))) (SIGNATURE |fillPascalTriangle| ((|Void|))) (IF (|has| |#1| (|FloatingPointSystem|)) (PROGN (SIGNATURE |safeCeiling| ((|Integer|) |#1|)) (SIGNATURE |safeFloor| ((|Integer|) |#1|)) (SIGNATURE |safetyMargin| ((|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |safetyMargin| ((|NonNegativeInteger|)))) |noBranch|)) (|Ring|)) (T |GaloisGroupUtilities|)) 
((|safetyMargin| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|GaloisGroupUtilities| *3)) (|ofCategory| *3 (|FloatingPointSystem|)) (|ofCategory| *3 (|Ring|)))) (|safetyMargin| (*1 *2 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|GaloisGroupUtilities| *3)) (|ofCategory| *3 (|FloatingPointSystem|)) (|ofCategory| *3 (|Ring|)))) (|safeFloor| (*1 *2 *3) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GaloisGroupUtilities| *3)) (|ofCategory| *3 (|FloatingPointSystem|)) (|ofCategory| *3 (|Ring|)))) (|safeCeiling| (*1 *2 *3) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GaloisGroupUtilities| *3)) (|ofCategory| *3 (|FloatingPointSystem|)) (|ofCategory| *3 (|Ring|)))) (|fillPascalTriangle| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GaloisGroupUtilities| *3)) (|ofCategory| *3 (|Ring|)))) (|sizePascalTriangle| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|GaloisGroupUtilities| *3)) (|ofCategory| *3 (|Ring|)))) (|rangePascalTriangle| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|GaloisGroupUtilities| *3)) (|ofCategory| *3 (|Ring|)))) (|rangePascalTriangle| (*1 *2 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|GaloisGroupUtilities| *3)) (|ofCategory| *3 (|Ring|)))) (|pascalTriangle| (*1 *2 *3 *4) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|Integer|)) (|isDomain| *1 (|GaloisGroupUtilities| *2)) (|ofCategory| *2 (|Ring|))))) 
(CATEGORY |package| (SIGNATURE |pascalTriangle| (|#1| (|NonNegativeInteger|) (|Integer|))) (SIGNATURE |rangePascalTriangle| ((|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |rangePascalTriangle| ((|NonNegativeInteger|))) (SIGNATURE |sizePascalTriangle| ((|NonNegativeInteger|))) (SIGNATURE |fillPascalTriangle| ((|Void|))) (IF (|has| |#1| (|FloatingPointSystem|)) (PROGN (SIGNATURE |safeCeiling| ((|Integer|) |#1|)) (SIGNATURE |safeFloor| ((|Integer|) |#1|)) (SIGNATURE |safetyMargin| ((|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |safetyMargin| ((|NonNegativeInteger|)))) |noBranch|)) 
((|sumSquares| (((|List| (|Integer|)) (|Integer|)) 57)) (|prime?| (((|Boolean|) (|Complex| (|Integer|))) 61)) (|factor| (((|Factored| (|Complex| (|Integer|))) (|Complex| (|Integer|))) 56))) 
(((|GaussianFactorizationPackage|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| (|Complex| (|Integer|))) (|Complex| (|Integer|)))) (SIGNATURE |sumSquares| ((|List| (|Integer|)) (|Integer|))) (SIGNATURE |prime?| ((|Boolean|) (|Complex| (|Integer|)))))) (T |GaussianFactorizationPackage|)) 
((|prime?| (*1 *2 *3) (AND (|isDomain| *3 (|Complex| (|Integer|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaussianFactorizationPackage|)))) (|sumSquares| (*1 *2 *3) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|GaussianFactorizationPackage|)) (|isDomain| *3 (|Integer|)))) (|factor| (*1 *2 *3) (AND (|isDomain| *2 (|Factored| (|Complex| (|Integer|)))) (|isDomain| *1 (|GaussianFactorizationPackage|)) (|isDomain| *3 (|Complex| (|Integer|)))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| (|Complex| (|Integer|))) (|Complex| (|Integer|)))) (SIGNATURE |sumSquares| ((|List| (|Integer|)) (|Integer|))) (SIGNATURE |prime?| ((|Boolean|) (|Complex| (|Integer|))))) 
((|euclideanNormalForm| ((|#4| |#4| (|List| |#4|)) 57)) (|euclideanGroebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) 17) (((|List| |#4|) (|List| |#4|) (|String|)) 16) (((|List| |#4|) (|List| |#4|)) 11))) 
(((|EuclideanGroebnerBasisPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |euclideanNormalForm| (|#4| |#4| (|List| |#4|))) (SIGNATURE |euclideanGroebner| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |euclideanGroebner| ((|List| |#4|) (|List| |#4|) (|String|))) (SIGNATURE |euclideanGroebner| ((|List| |#4|) (|List| |#4|) (|String|) (|String|)))) (|EuclideanDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |EuclideanGroebnerBasisPackage|)) 
((|euclideanGroebner| (*1 *2 *2 *3 *3) (AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|String|)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|EuclideanDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *1 (|EuclideanGroebnerBasisPackage| *4 *5 *6 *7)))) (|euclideanGroebner| (*1 *2 *2 *3) (AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|String|)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|EuclideanDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *1 (|EuclideanGroebnerBasisPackage| *4 *5 *6 *7)))) (|euclideanGroebner| (*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|EuclideanGroebnerBasisPackage| *3 *4 *5 *6)))) (|euclideanNormalForm| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|EuclideanDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *1 (|EuclideanGroebnerBasisPackage| *4 *5 *6 *2))))) 
(CATEGORY |package| (SIGNATURE |euclideanNormalForm| (|#4| |#4| (|List| |#4|))) (SIGNATURE |euclideanGroebner| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |euclideanGroebner| ((|List| |#4|) (|List| |#4|) (|String|))) (SIGNATURE |euclideanGroebner| ((|List| |#4|) (|List| |#4|) (|String|) (|String|)))) 
((|groebnerFactorize| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) 70) (((|List| (|List| |#4|)) (|List| |#4|)) 69) (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|) (|Boolean|)) 63) (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|)) 64)) (|factorGroebnerBasis| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) 40) (((|List| (|List| |#4|)) (|List| |#4|)) 60))) 
(((|GroebnerFactorizationPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factorGroebnerBasis| ((|List| (|List| |#4|)) (|List| |#4|))) (SIGNATURE |factorGroebnerBasis| ((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|))) (SIGNATURE |groebnerFactorize| ((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|))) (SIGNATURE |groebnerFactorize| ((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|) (|Boolean|))) (SIGNATURE |groebnerFactorize| ((|List| (|List| |#4|)) (|List| |#4|))) (SIGNATURE |groebnerFactorize| ((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|)) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |GroebnerFactorizationPackage|)) 
((|groebnerFactorize| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|PolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|List| *8))) (|isDomain| *1 (|GroebnerFactorizationPackage| *5 *6 *7 *8)) (|isDomain| *3 (|List| *8)))) (|groebnerFactorize| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| (|List| *7))) (|isDomain| *1 (|GroebnerFactorizationPackage| *4 *5 *6 *7)) (|isDomain| *3 (|List| *7)))) (|groebnerFactorize| (*1 *2 *3 *3 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|PolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|List| *8))) (|isDomain| *1 (|GroebnerFactorizationPackage| *5 *6 *7 *8)) (|isDomain| *3 (|List| *8)))) (|groebnerFactorize| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| (|List| *7))) (|isDomain| *1 (|GroebnerFactorizationPackage| *4 *5 *6 *7)) (|isDomain| *3 (|List| *7)))) (|factorGroebnerBasis| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|PolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|List| *8))) (|isDomain| *1 (|GroebnerFactorizationPackage| *5 *6 *7 *8)) (|isDomain| *3 (|List| *8)))) (|factorGroebnerBasis| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| (|List| *7))) (|isDomain| *1 (|GroebnerFactorizationPackage| *4 *5 *6 *7)) (|isDomain| *3 (|List| *7))))) 
(CATEGORY |package| (SIGNATURE |factorGroebnerBasis| ((|List| (|List| |#4|)) (|List| |#4|))) (SIGNATURE |factorGroebnerBasis| ((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|))) (SIGNATURE |groebnerFactorize| ((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|))) (SIGNATURE |groebnerFactorize| ((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|) (|Boolean|))) (SIGNATURE |groebnerFactorize| ((|List| (|List| |#4|)) (|List| |#4|))) (SIGNATURE |groebnerFactorize| ((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)))) 
((|virtualDegree| (((|NonNegativeInteger|) |#4|) 12)) (|updatF| (((|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))) |#4| (|NonNegativeInteger|) (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)))) 31)) (|updatD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) 37)) (|sPol| ((|#4| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) 38)) (|redPol| ((|#4| |#4| (|List| |#4|)) 39)) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (|List| |#4|)) 68)) (|prinshINFO| (((|Void|) |#4|) 41)) (|prinpolINFO| (((|Void|) (|List| |#4|)) 50)) (|prindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|)) 47)) (|prinb| (((|Void|) (|Integer|)) 75)) (|minGbasis| (((|List| |#4|) (|List| |#4|)) 73)) (|makeCrit| (((|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)) |#4| (|NonNegativeInteger|)) 25)) (|lepol| (((|Integer|) |#4|) 74)) (|hMonic| ((|#4| |#4|) 29)) (|gbasis| (((|List| |#4|) (|List| |#4|) (|Integer|) (|Integer|)) 54)) (|fprindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|) (|Integer|)) 85)) (|critpOrder| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) 16)) (|critT| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) 57)) (|critMonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) 56)) (|critMTonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) 35)) (|critM| (((|Boolean|) |#2| |#2|) 55)) (|critBonD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) 36)) (|critB| (((|Boolean|) |#2| |#2| |#2| |#2|) 58)) (|credPol| ((|#4| |#4| (|List| |#4|)) 69))) 
(((|GroebnerInternalPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |credPol| (|#4| |#4| (|List| |#4|))) (SIGNATURE |redPol| (|#4| |#4| (|List| |#4|))) (SIGNATURE |gbasis| ((|List| |#4|) (|List| |#4|) (|Integer|) (|Integer|))) (SIGNATURE |critT| ((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) (SIGNATURE |critM| ((|Boolean|) |#2| |#2|)) (SIGNATURE |critB| ((|Boolean|) |#2| |#2| |#2| |#2|)) (SIGNATURE |critBonD| ((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))))) (SIGNATURE |critMTonD1| ((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))))) (SIGNATURE |critMonD1| ((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))))) (SIGNATURE |redPo| ((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (|List| |#4|))) (SIGNATURE |hMonic| (|#4| |#4|)) (SIGNATURE |updatF| ((|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))) |#4| (|NonNegativeInteger|) (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))))) (SIGNATURE |sPol| (|#4| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) (SIGNATURE |updatD| ((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))))) (SIGNATURE |minGbasis| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |lepol| ((|Integer|) |#4|)) (SIGNATURE |prinshINFO| ((|Void|) |#4|)) (SIGNATURE |prindINFO| ((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |fprindINFO| ((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |prinpolINFO| ((|Void|) (|List| |#4|))) (SIGNATURE |prinb| ((|Void|) (|Integer|))) (SIGNATURE |critpOrder| ((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) (SIGNATURE |makeCrit| ((|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)) |#4| (|NonNegativeInteger|))) (SIGNATURE |virtualDegree| ((|NonNegativeInteger|) |#4|))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |GroebnerInternalPackage|)) 
((|virtualDegree| (*1 *2 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *4 *5 *6)))) (|makeCrit| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| *4))) (|isDomain| *5 (|NonNegativeInteger|)) (|ofCategory| *4 (|PolynomialCategory| *6 *7 *8)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |lcmfij| *7) (|:| |totdeg| *5) (|:| |poli| *4) (|:| |polj| *4))) (|isDomain| *1 (|GroebnerInternalPackage| *6 *7 *8 *4)))) (|critpOrder| (*1 *2 *3 *3) (AND (|isDomain| *3 (|Record| (|:| |lcmfij| *5) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| *7) (|:| |polj| *7))) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *7)))) (|prinb| (*1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *7)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)))) (|prinpolINFO| (*1 *2 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *7)))) (|fprindINFO| (*1 *2 *3 *4 *4 *2 *2 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *3 (|Record| (|:| |lcmfij| *6) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| *4) (|:| |polj| *4))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|PolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *1 (|GroebnerInternalPackage| *5 *6 *7 *4)))) (|prindINFO| (*1 *2 *3 *4 *4 *2 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *3 (|Record| (|:| |lcmfij| *6) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| *4) (|:| |polj| *4))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|PolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *1 (|GroebnerInternalPackage| *5 *6 *7 *4)))) (|prinshINFO| (*1 *2 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *4 *5 *6)))) (|lepol| (*1 *2 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *4 *5 *6)))) (|minGbasis| (*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|GroebnerInternalPackage| *3 *4 *5 *6)))) (|updatD| (*1 *2 *2 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |lcmfij| *4) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| *6) (|:| |polj| *6)))) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|GroebnerInternalPackage| *3 *4 *5 *6)))) (|sPol| (*1 *2 *3) (AND (|isDomain| *3 (|Record| (|:| |lcmfij| *5) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| *2) (|:| |polj| *2))) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|PolynomialCategory| *4 *5 *6)) (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *2)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *6 (|OrderedSet|)))) (|updatF| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| *3)))) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *3 (|PolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *1 (|GroebnerInternalPackage| *5 *6 *7 *3)))) (|hMonic| (*1 *2 *2) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|GroebnerInternalPackage| *3 *4 *5 *2)) (|ofCategory| *2 (|PolynomialCategory| *3 *4 *5)))) (|redPo| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *3)) (|ofCategory| *3 (|PolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |poly| *3) (|:| |mult| *5))) (|isDomain| *1 (|GroebnerInternalPackage| *5 *6 *7 *3)))) (|critMonD1| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |lcmfij| *3) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| *6) (|:| |polj| *6)))) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|PolynomialCategory| *4 *3 *5)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|GroebnerInternalPackage| *4 *3 *5 *6)))) (|critMTonD1| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |lcmfij| *4) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| *6) (|:| |polj| *6)))) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|GroebnerInternalPackage| *3 *4 *5 *6)))) (|critBonD| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |lcmfij| *5) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| *3) (|:| |polj| *3)))) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *3)))) (|critB| (*1 *2 *3 *3 *3 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GroebnerInternalPackage| *4 *3 *5 *6)) (|ofCategory| *6 (|PolynomialCategory| *4 *3 *5)))) (|critM| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GroebnerInternalPackage| *4 *3 *5 *6)) (|ofCategory| *6 (|PolynomialCategory| *4 *3 *5)))) (|critT| (*1 *2 *3) (AND (|isDomain| *3 (|Record| (|:| |lcmfij| *5) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| *7) (|:| |polj| *7))) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *7)))) (|gbasis| (*1 *2 *2 *3 *3) (AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|Integer|)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *7)))) (|redPol| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *2)))) (|credPol| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *2))))) 
(CATEGORY |package| (SIGNATURE |credPol| (|#4| |#4| (|List| |#4|))) (SIGNATURE |redPol| (|#4| |#4| (|List| |#4|))) (SIGNATURE |gbasis| ((|List| |#4|) (|List| |#4|) (|Integer|) (|Integer|))) (SIGNATURE |critT| ((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) (SIGNATURE |critM| ((|Boolean|) |#2| |#2|)) (SIGNATURE |critB| ((|Boolean|) |#2| |#2| |#2| |#2|)) (SIGNATURE |critBonD| ((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))))) (SIGNATURE |critMTonD1| ((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))))) (SIGNATURE |critMonD1| ((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))))) (SIGNATURE |redPo| ((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (|List| |#4|))) (SIGNATURE |hMonic| (|#4| |#4|)) (SIGNATURE |updatF| ((|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))) |#4| (|NonNegativeInteger|) (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))))) (SIGNATURE |sPol| (|#4| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) (SIGNATURE |updatD| ((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))))) (SIGNATURE |minGbasis| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |lepol| ((|Integer|) |#4|)) (SIGNATURE |prinshINFO| ((|Void|) |#4|)) (SIGNATURE |prindINFO| ((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |fprindINFO| ((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |prinpolINFO| ((|Void|) (|List| |#4|))) (SIGNATURE |prinb| ((|Void|) (|Integer|))) (SIGNATURE |critpOrder| ((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) (SIGNATURE |makeCrit| ((|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)) |#4| (|NonNegativeInteger|))) (SIGNATURE |virtualDegree| ((|NonNegativeInteger|) |#4|))) 
((|normalForm| ((|#4| |#4| (|List| |#4|)) 22 (|has| |#1| (|Field|)))) (|groebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) 41) (((|List| |#4|) (|List| |#4|) (|String|)) 40) (((|List| |#4|) (|List| |#4|)) 35))) 
(((|GroebnerPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |groebner| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |groebner| ((|List| |#4|) (|List| |#4|) (|String|))) (SIGNATURE |groebner| ((|List| |#4|) (|List| |#4|) (|String|) (|String|))) (IF (|has| |#1| (|Field|)) (SIGNATURE |normalForm| (|#4| |#4| (|List| |#4|))) |noBranch|)) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |GroebnerPackage|)) 
((|normalForm| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Field|)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *1 (|GroebnerPackage| *4 *5 *6 *2)))) (|groebner| (*1 *2 *2 *3 *3) (AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|String|)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *1 (|GroebnerPackage| *4 *5 *6 *7)))) (|groebner| (*1 *2 *2 *3) (AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|String|)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *1 (|GroebnerPackage| *4 *5 *6 *7)))) (|groebner| (*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|GroebnerPackage| *3 *4 *5 *6))))) 
(CATEGORY |package| (SIGNATURE |groebner| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |groebner| ((|List| |#4|) (|List| |#4|) (|String|))) (SIGNATURE |groebner| ((|List| |#4|) (|List| |#4|) (|String|) (|String|))) (IF (|has| |#1| (|Field|)) (SIGNATURE |normalForm| (|#4| |#4| (|List| |#4|))) |noBranch|)) 
((|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 43)) (|lcm| (($ $ $) 14) (($ (|List| $)) 21)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 41)) (|gcd| (($ $ $) NIL) (($ (|List| $)) 22))) 
(((|GcdDomain&| |#1|) (CATEGORY |domain| (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |lcm| (|#1| (|List| |#1|))) (SIGNATURE |lcm| (|#1| |#1| |#1|)) (SIGNATURE |gcd| (|#1| (|List| |#1|))) (SIGNATURE |gcd| (|#1| |#1| |#1|)) (SIGNATURE |lcmCoef| ((|Record| (|:| |llcmres| |#1|) (|:| |coeff1| |#1|) (|:| |coeff2| |#1|)) |#1| |#1|))) (|GcdDomain|)) (T |GcdDomain&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |lcm| (|#1| (|List| |#1|))) (SIGNATURE |lcm| (|#1| |#1| |#1|)) (SIGNATURE |gcd| (|#1| (|List| |#1|))) (SIGNATURE |gcd| (|#1| |#1| |#1|)) (SIGNATURE |lcmCoef| ((|Record| (|:| |llcmres| |#1|) (|:| |coeff1| |#1|) (|:| |coeff2| |#1|)) |#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|GcdDomain|) (|Category|)) (T |GcdDomain|)) 
((|gcd| (*1 *1 *1 *1) (|ofCategory| *1 (|GcdDomain|))) (|gcd| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|GcdDomain|)))) (|lcm| (*1 *1 *1 *1) (|ofCategory| *1 (|GcdDomain|))) (|lcm| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|GcdDomain|)))) (|gcdPolynomial| (*1 *2 *2 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|GcdDomain|))))) 
(|Join| (|IntegralDomain|) (|LeftOreRing|) (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $)) (SIGNATURE |gcd| ($ (|List| $))) (SIGNATURE |lcm| ($ $ $)) (SIGNATURE |lcm| ($ (|List| $))) (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|IntegralDomain|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unit| (((|Union| $ "failed")) NIL (|has| (|Fraction| (|Polynomial| |#1|)) (|IntegralDomain|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|structuralConstants| (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Vector| $)) NIL) (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|))))) NIL)) (|someBasis| (((|Vector| $)) NIL)) (|sample| (($) NIL T CONST)) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) NIL)) (|rightUnit| (((|Union| $ "failed")) NIL (|has| (|Fraction| (|Polynomial| |#1|)) (|IntegralDomain|)))) (|rightTraceMatrix| (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Vector| $)) NIL) (((|Matrix| (|Fraction| (|Polynomial| |#1|)))) NIL)) (|rightTrace| (((|Fraction| (|Polynomial| |#1|)) $) NIL)) (|rightRegularRepresentation| (((|Matrix| (|Fraction| (|Polynomial| |#1|))) $ (|Vector| $)) NIL) (((|Matrix| (|Fraction| (|Polynomial| |#1|))) $) NIL)) (|rightRecip| (((|Union| $ "failed") $) NIL (|has| (|Fraction| (|Polynomial| |#1|)) (|IntegralDomain|)))) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| (|Fraction| (|Polynomial| |#1|))))) NIL (|has| (|Fraction| (|Polynomial| |#1|)) (|Field|))) (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) 79 (|has| |#1| (|IntegralDomain|)))) (|rightPower| (($ $ (|PositiveInteger|)) NIL)) (|rightNorm| (((|Fraction| (|Polynomial| |#1|)) $) NIL)) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) 77 (|has| (|Fraction| (|Polynomial| |#1|)) (|IntegralDomain|)))) (|rightDiscriminant| (((|Fraction| (|Polynomial| |#1|)) (|Vector| $)) NIL) (((|Fraction| (|Polynomial| |#1|))) NIL)) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) NIL)) (|rightAlternative?| (((|Boolean|)) NIL)) (|represents| (($ (|Vector| (|Fraction| (|Polynomial| |#1|))) (|Vector| $)) 97) (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) NIL)) (|recip| (((|Union| $ "failed") $) NIL (|has| (|Fraction| (|Polynomial| |#1|)) (|IntegralDomain|)))) (|rank| (((|PositiveInteger|)) NIL)) (|powerAssociative?| (((|Boolean|)) NIL)) (|plenaryPower| (($ $ (|PositiveInteger|)) NIL)) (|noncommutativeJordanAlgebra?| (((|Boolean|)) NIL)) (|lieAlgebra?| (((|Boolean|)) NIL)) (|lieAdmissible?| (((|Boolean|)) NIL)) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) NIL)) (|leftUnit| (((|Union| $ "failed")) NIL (|has| (|Fraction| (|Polynomial| |#1|)) (|IntegralDomain|)))) (|leftTraceMatrix| (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Vector| $)) NIL) (((|Matrix| (|Fraction| (|Polynomial| |#1|)))) NIL)) (|leftTrace| (((|Fraction| (|Polynomial| |#1|)) $) NIL)) (|leftRegularRepresentation| (((|Matrix| (|Fraction| (|Polynomial| |#1|))) $ (|Vector| $)) NIL) (((|Matrix| (|Fraction| (|Polynomial| |#1|))) $) NIL)) (|leftRecip| (((|Union| $ "failed") $) NIL (|has| (|Fraction| (|Polynomial| |#1|)) (|IntegralDomain|)))) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| (|Fraction| (|Polynomial| |#1|))))) NIL (|has| (|Fraction| (|Polynomial| |#1|)) (|Field|))) (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) 78 (|has| |#1| (|IntegralDomain|)))) (|leftPower| (($ $ (|PositiveInteger|)) NIL)) (|leftNorm| (((|Fraction| (|Polynomial| |#1|)) $) NIL)) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) 72 (|has| (|Fraction| (|Polynomial| |#1|)) (|IntegralDomain|)))) (|leftDiscriminant| (((|Fraction| (|Polynomial| |#1|)) (|Vector| $)) NIL) (((|Fraction| (|Polynomial| |#1|))) NIL)) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) NIL)) (|leftAlternative?| (((|Boolean|)) NIL)) (|latex| (((|String|) $) NIL)) (|jordanAlgebra?| (((|Boolean|)) NIL)) (|jordanAdmissible?| (((|Boolean|)) NIL)) (|jacobiIdentity?| (((|Boolean|)) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) 66 (|has| |#1| (|IntegralDomain|)))) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) 65 (|has| |#1| (|IntegralDomain|)))) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) 89 (|has| |#1| (|IntegralDomain|)))) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) 83 (|has| |#1| (|IntegralDomain|)))) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) 67 (|has| |#1| (|IntegralDomain|)))) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) 54 (|has| |#1| (|IntegralDomain|)))) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) 53 (|has| |#1| (|IntegralDomain|)))) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) 88 (|has| |#1| (|IntegralDomain|)))) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) 82 (|has| |#1| (|IntegralDomain|)))) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) 64 (|has| |#1| (|IntegralDomain|)))) (|generic| (($) 95) (($ (|Symbol|)) 101) (($ (|Vector| (|Symbol|))) 100) (($ (|Vector| $)) 90) (($ (|Symbol|) (|Vector| $)) 99) (($ (|Vector| (|Symbol|)) (|Vector| $)) 98)) (|flexible?| (((|Boolean|)) NIL)) (|elt| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) NIL)) (|coordinates| (((|Vector| (|Fraction| (|Polynomial| |#1|))) $ (|Vector| $)) 92) (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Vector| $) (|Vector| $)) NIL) (((|Vector| (|Fraction| (|Polynomial| |#1|))) $) 37) (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Vector| $)) NIL)) (|convert| (((|Vector| (|Fraction| (|Polynomial| |#1|))) $) NIL) (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) 34)) (|conditionsForIdempotents| (((|List| (|Polynomial| (|Fraction| (|Polynomial| |#1|)))) (|Vector| $)) NIL) (((|List| (|Polynomial| (|Fraction| (|Polynomial| |#1|))))) NIL) (((|List| (|Polynomial| |#1|)) (|Vector| $)) 93 (|has| |#1| (|IntegralDomain|))) (((|List| (|Polynomial| |#1|))) 94 (|has| |#1| (|IntegralDomain|)))) (|commutator| (($ $ $) NIL)) (|commutative?| (((|Boolean|)) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) NIL)) (|basis| (((|Vector| $)) 56)) (|associatorDependence| (((|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))) NIL (|has| (|Fraction| (|Polynomial| |#1|)) (|IntegralDomain|)))) (|associator| (($ $ $ $) NIL)) (|associative?| (((|Boolean|)) NIL)) (|apply| (($ (|Matrix| (|Fraction| (|Polynomial| |#1|))) $) NIL)) (|antiCommutator| (($ $ $) NIL)) (|antiCommutative?| (((|Boolean|)) NIL)) (|antiAssociative?| (((|Boolean|)) NIL)) (|alternative?| (((|Boolean|)) NIL)) (|Zero| (($) NIL T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) 91)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 52) (($ $ (|Fraction| (|Polynomial| |#1|))) NIL) (($ (|Fraction| (|Polynomial| |#1|)) $) NIL) (($ (|SquareMatrix| |#2| (|Fraction| (|Polynomial| |#1|))) $) NIL))) 
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(|discriminant| (($ $ (|OrderedVariableList| |#1|)) NIL (|has| |#2| (|CommutativeRing|)))) (|differentiate| (($ $ (|OrderedVariableList| |#1|)) 53) (($ $ (|List| (|OrderedVariableList| |#1|))) NIL) (($ $ (|OrderedVariableList| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| (|NonNegativeInteger|))) NIL)) (|degree| ((|#3| $) 66) (((|NonNegativeInteger|) $ (|OrderedVariableList| |#1|)) 37) (((|List| (|NonNegativeInteger|)) $ (|List| (|OrderedVariableList| |#1|))) 56)) (|convert| (((|Pattern| (|Float|)) $) NIL (AND (|has| (|OrderedVariableList| |#1|) (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Float|)))))) (((|Pattern| (|Integer|)) $) NIL (AND (|has| (|OrderedVariableList| |#1|) (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Integer|)))))) (((|InputForm|) $) NIL (AND (|has| (|OrderedVariableList| |#1|) (|ConvertibleTo| (|InputForm|))) (|has| |#2| (|ConvertibleTo| (|InputForm|)))))) (|content| ((|#2| $) 122 (|has| |#2| (|GcdDomain|))) (($ $ (|OrderedVariableList| |#1|)) NIL (|has| |#2| (|GcdDomain|)))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#2| (|PolynomialFactorizationExplicit|))))) (|coerce| (((|OutputForm|) $) 141) (($ (|Integer|)) NIL) (($ |#2|) 84) (($ (|OrderedVariableList| |#1|)) 31) (($ (|Fraction| (|Integer|))) NIL (OR (|has| |#2| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))))) (($ $) NIL (|has| |#2| (|IntegralDomain|)))) (|coefficients| (((|List| |#2|) $) NIL)) (|coefficient| ((|#2| $ |#3|) NIL) (($ $ (|OrderedVariableList| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| (|NonNegativeInteger|))) NIL)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#2| (|PolynomialFactorizationExplicit|))) (|has| |#2| (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|CommutativeRing|)))) (|associates?| (((|Boolean|) $ $) NIL (|has| |#2| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 16 T CONST)) (|One| (($) 25 T CONST)) (D (($ $ (|OrderedVariableList| |#1|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|))) NIL) (($ $ (|OrderedVariableList| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| (|NonNegativeInteger|))) NIL)) (>= (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (/ (($ $ |#2|) 64 (|has| |#2| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) 109)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 107)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 29) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#2| (|Algebra| (|Fraction| (|Integer|))))) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#2| (|Algebra| (|Fraction| (|Integer|))))) (($ |#2| $) 63) (($ $ |#2|) NIL))) 
(((|GeneralDistributedMultivariatePolynomial| |#1| |#2| |#3|) (|Join| (|PolynomialCategory| |#2| |#3| (|OrderedVariableList| |#1|)) (CATEGORY |domain| (SIGNATURE |reorder| ($ $ (|List| (|Integer|)))))) (|List| (|Symbol|)) (|Ring|) (|DirectProductCategory| (|#| |#1|) (|NonNegativeInteger|))) (T |GeneralDistributedMultivariatePolynomial|)) 
((|reorder| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|ofType| *3 (|List| (|Symbol|))) (|isDomain| *1 (|GeneralDistributedMultivariatePolynomial| *3 *4 *5)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| (|#| *3) (|NonNegativeInteger|)))))) 
(|Join| (|PolynomialCategory| |#2| |#3| (|OrderedVariableList| |#1|)) (CATEGORY |domain| (SIGNATURE |reorder| ($ $ (|List| (|Integer|)))))) 
((|gnuDraw| (((|Void|) (|Expression| (|Float|)) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|String|)) 49) (((|Void|) (|Expression| (|Float|)) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|String|) (|List| (|DrawOption|))) 48) (((|Void|) (|Expression| (|Float|)) (|SegmentBinding| (|Float|)) (|String|)) 42) (((|Void|) (|Expression| (|Float|)) (|SegmentBinding| (|Float|)) (|String|) (|List| (|DrawOption|))) 39))) 
(((|GnuDraw|) (CATEGORY |package| (SIGNATURE |gnuDraw| ((|Void|) (|Expression| (|Float|)) (|SegmentBinding| (|Float|)) (|String|) (|List| (|DrawOption|)))) (SIGNATURE |gnuDraw| ((|Void|) (|Expression| (|Float|)) (|SegmentBinding| (|Float|)) (|String|))) (SIGNATURE |gnuDraw| ((|Void|) (|Expression| (|Float|)) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|String|) (|List| (|DrawOption|)))) (SIGNATURE |gnuDraw| ((|Void|) (|Expression| (|Float|)) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|String|))))) (T |GnuDraw|)) 
((|gnuDraw| (*1 *2 *3 *4 *4 *5) (AND (|isDomain| *3 (|Expression| (|Float|))) (|isDomain| *4 (|SegmentBinding| (|Float|))) (|isDomain| *5 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GnuDraw|)))) (|gnuDraw| (*1 *2 *3 *4 *4 *5 *6) (AND (|isDomain| *3 (|Expression| (|Float|))) (|isDomain| *4 (|SegmentBinding| (|Float|))) (|isDomain| *5 (|String|)) (|isDomain| *6 (|List| (|DrawOption|))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GnuDraw|)))) (|gnuDraw| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Expression| (|Float|))) (|isDomain| *4 (|SegmentBinding| (|Float|))) (|isDomain| *5 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GnuDraw|)))) (|gnuDraw| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *3 (|Expression| (|Float|))) (|isDomain| *4 (|SegmentBinding| (|Float|))) (|isDomain| *5 (|String|)) (|isDomain| *6 (|List| (|DrawOption|))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GnuDraw|))))) 
(CATEGORY |package| (SIGNATURE |gnuDraw| ((|Void|) (|Expression| (|Float|)) (|SegmentBinding| (|Float|)) (|String|) (|List| (|DrawOption|)))) (SIGNATURE |gnuDraw| ((|Void|) (|Expression| (|Float|)) (|SegmentBinding| (|Float|)) (|String|))) (SIGNATURE |gnuDraw| ((|Void|) (|Expression| (|Float|)) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|String|) (|List| (|DrawOption|)))) (SIGNATURE |gnuDraw| ((|Void|) (|Expression| (|Float|)) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|String|)))) 
((|testModulus| (((|Boolean|) |#1| (|List| |#2|)) 65)) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) 74)) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) 76)) (|reduction| ((|#2| |#2| |#1|) 28)) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) 20))) 
(((|GenExEuclid| |#1| |#2|) (CATEGORY |package| (SIGNATURE |reduction| (|#2| |#2| |#1|)) (SIGNATURE |compBound| ((|NonNegativeInteger|) |#2| (|List| |#2|))) (SIGNATURE |tablePow| ((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|))) (SIGNATURE |solveid| ((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|)))) (SIGNATURE |testModulus| ((|Boolean|) |#1| (|List| |#2|)))) (|EuclideanDomain|) (|UnivariatePolynomialCategory| |#1|)) (T |GenExEuclid|)) 
((|testModulus| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|EuclideanDomain|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GenExEuclid| *3 *5)))) (|solveid| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *5 (|Vector| (|List| *3))) (|ofCategory| *4 (|EuclideanDomain|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|GenExEuclid| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|tablePow| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|EuclideanDomain|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Vector| (|List| *6))) (|isDomain| *1 (|GenExEuclid| *4 *6)) (|isDomain| *5 (|List| *6)))) (|compBound| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|EuclideanDomain|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|GenExEuclid| *5 *3)))) (|reduction| (*1 *2 *2 *3) (AND (|ofCategory| *3 (|EuclideanDomain|)) (|isDomain| *1 (|GenExEuclid| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(CATEGORY |package| (SIGNATURE |reduction| (|#2| |#2| |#1|)) (SIGNATURE |compBound| ((|NonNegativeInteger|) |#2| (|List| |#2|))) (SIGNATURE |tablePow| ((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|))) (SIGNATURE |solveid| ((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|)))) (SIGNATURE |testModulus| ((|Boolean|) |#1| (|List| |#2|)))) 
((|factor| (((|Factored| |#5|) |#5|) 24))) 
(((|GeneralizedMultivariateFactorize| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#5|) |#5|))) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") (|Symbol|))))) (|OrderedAbelianMonoidSup|) (|IntegralDomain|) (|IntegralDomain|) (|PolynomialCategory| |#4| |#2| |#1|)) (T |GeneralizedMultivariateFactorize|)) 
((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") (|Symbol|)))))) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|IntegralDomain|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|GeneralizedMultivariateFactorize| *4 *5 *6 *7 *3)) (|ofCategory| *6 (|IntegralDomain|)) (|ofCategory| *3 (|PolynomialCategory| *7 *5 *4))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#5|) |#5|))) 
((|randomR| ((|#3|) 36)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) 32))) 
(((|GeneralPolynomialGcdPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |randomR| (|#3|))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialFactorizationExplicit|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |GeneralPolynomialGcdPackage|)) 
((|randomR| (*1 *2) (AND (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|PolynomialFactorizationExplicit|)) (|isDomain| *1 (|GeneralPolynomialGcdPackage| *3 *4 *2 *5)) (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4)))) (|gcdPolynomial| (*1 *2 *2 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *6)) (|ofCategory| *6 (|PolynomialCategory| *5 *3 *4)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|PolynomialFactorizationExplicit|)) (|isDomain| *1 (|GeneralPolynomialGcdPackage| *3 *4 *5 *6))))) 
(CATEGORY |package| (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |randomR| (|#3|))) 
((|factor| (((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) 41))) 
(((|GenUFactorize| |#1|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)))) (|EuclideanDomain|)) (T |GenUFactorize|)) 
((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|EuclideanDomain|)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *4))) (|isDomain| *1 (|GenUFactorize| *4)) (|isDomain| *3 (|SparseUnivariatePolynomial| *4))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)))) 
((|taylor| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) 42) (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) 41) (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) 35) (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) 27)) (|series| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) 80) (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) 79) (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) 78) (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) 77) (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) 72) (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) 71)) (|puiseux| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) 66) (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) 64)) (|laurent| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) 48) (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) 47))) 
(((|GenerateUnivariatePowerSeries| |#1| |#2|) (CATEGORY |package| (SIGNATURE |taylor| ((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|))) (SIGNATURE |taylor| ((|Any|) |#2| (|Symbol|) (|Equation| |#2|))) (SIGNATURE |taylor| ((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|)))) (SIGNATURE |taylor| ((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|)))) (SIGNATURE |laurent| ((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|)))) (SIGNATURE |laurent| ((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|)))) (SIGNATURE |puiseux| ((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|)))) (SIGNATURE |puiseux| ((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|)))) (SIGNATURE |series| ((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|))) (SIGNATURE |series| ((|Any|) |#2| (|Symbol|) (|Equation| |#2|))) (SIGNATURE |series| ((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|)))) (SIGNATURE |series| ((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|)))) (SIGNATURE |series| ((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|)))) (SIGNATURE |series| ((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))))) (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|))) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |GenerateUnivariatePowerSeries|)) 
((|series| (*1 *2 *3 *4 *5 *6 *7) (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|Equation| *3)) (|isDomain| *6 (|UniversalSegment| (|Fraction| (|Integer|)))) (|isDomain| *7 (|Fraction| (|Integer|))) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *8))) (|ofCategory| *8 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|GenerateUnivariatePowerSeries| *8 *3)))) (|series| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *3 (|Mapping| *8 (|Fraction| (|Integer|)))) (|isDomain| *4 (|Equation| *8)) (|isDomain| *5 (|UniversalSegment| (|Fraction| (|Integer|)))) (|isDomain| *6 (|Fraction| (|Integer|))) (|ofCategory| *8 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *7))) (|ofCategory| *7 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|GenerateUnivariatePowerSeries| *7 *8)))) (|series| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|Equation| *3)) (|isDomain| *6 (|UniversalSegment| (|Integer|))) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *7))) (|ofCategory| *7 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|GenerateUnivariatePowerSeries| *7 *3)))) (|series| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *7 (|Integer|))) (|isDomain| *4 (|Equation| *7)) (|isDomain| *5 (|UniversalSegment| (|Integer|))) (|ofCategory| *7 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *6))) (|ofCategory| *6 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|GenerateUnivariatePowerSeries| *6 *7)))) (|series| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|Equation| *3)) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *6))) (|ofCategory| *6 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|GenerateUnivariatePowerSeries| *6 *3)))) (|series| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 (|Integer|))) (|isDomain| *4 (|Equation| *6)) (|ofCategory| *6 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *5))) (|ofCategory| *5 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|GenerateUnivariatePowerSeries| *5 *6)))) (|puiseux| (*1 *2 *3 *4 *5 *6 *7) (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|Equation| *3)) (|isDomain| *6 (|UniversalSegment| (|Fraction| (|Integer|)))) (|isDomain| *7 (|Fraction| (|Integer|))) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *8))) (|ofCategory| *8 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|GenerateUnivariatePowerSeries| *8 *3)))) (|puiseux| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *3 (|Mapping| *8 (|Fraction| (|Integer|)))) (|isDomain| *4 (|Equation| *8)) (|isDomain| *5 (|UniversalSegment| (|Fraction| (|Integer|)))) (|isDomain| *6 (|Fraction| (|Integer|))) (|ofCategory| *8 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *7))) (|ofCategory| *7 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|GenerateUnivariatePowerSeries| *7 *8)))) (|laurent| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|Equation| *3)) (|isDomain| *6 (|UniversalSegment| (|Integer|))) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *7))) (|ofCategory| *7 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|GenerateUnivariatePowerSeries| *7 *3)))) (|laurent| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *7 (|Integer|))) (|isDomain| *4 (|Equation| *7)) (|isDomain| *5 (|UniversalSegment| (|Integer|))) (|ofCategory| *7 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *6))) (|ofCategory| *6 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|GenerateUnivariatePowerSeries| *6 *7)))) (|taylor| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|Equation| *3)) (|isDomain| *6 (|UniversalSegment| (|NonNegativeInteger|))) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *7))) (|ofCategory| *7 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|GenerateUnivariatePowerSeries| *7 *3)))) (|taylor| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *7 (|Integer|))) (|isDomain| *4 (|Equation| *7)) (|isDomain| *5 (|UniversalSegment| (|NonNegativeInteger|))) (|ofCategory| *7 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *6))) (|ofCategory| *6 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|GenerateUnivariatePowerSeries| *6 *7)))) (|taylor| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|Equation| *3)) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *6))) (|ofCategory| *6 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|GenerateUnivariatePowerSeries| *6 *3)))) (|taylor| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 (|Integer|))) (|isDomain| *4 (|Equation| *6)) (|ofCategory| *6 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *5))) (|ofCategory| *5 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|GenerateUnivariatePowerSeries| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |taylor| ((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|))) (SIGNATURE |taylor| ((|Any|) |#2| (|Symbol|) (|Equation| |#2|))) (SIGNATURE |taylor| ((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|)))) (SIGNATURE |taylor| ((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|)))) (SIGNATURE |laurent| ((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|)))) (SIGNATURE |laurent| ((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|)))) (SIGNATURE |puiseux| ((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|)))) (SIGNATURE |puiseux| ((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|)))) (SIGNATURE |series| ((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|))) (SIGNATURE |series| ((|Any|) |#2| (|Symbol|) (|Equation| |#2|))) (SIGNATURE |series| ((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|)))) (SIGNATURE |series| ((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|)))) (SIGNATURE |series| ((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|)))) (SIGNATURE |series| ((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))))) 
((|reduction| ((|#2| |#2| |#1|) 15)) (|completeHensel| (((|List| |#2|) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) 65)) (|HenselLift| (((|Record| (|:| |plist| (|List| |#2|)) (|:| |modulo| |#1|)) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) 58))) 
(((|GeneralHenselPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |HenselLift| ((|Record| (|:| |plist| (|List| |#2|)) (|:| |modulo| |#1|)) |#2| (|List| |#2|) |#1| (|PositiveInteger|))) (SIGNATURE |completeHensel| ((|List| |#2|) |#2| (|List| |#2|) |#1| (|PositiveInteger|))) (SIGNATURE |reduction| (|#2| |#2| |#1|))) (|EuclideanDomain|) (|UnivariatePolynomialCategory| |#1|)) (T |GeneralHenselPackage|)) 
((|reduction| (*1 *2 *2 *3) (AND (|ofCategory| *3 (|EuclideanDomain|)) (|isDomain| *1 (|GeneralHenselPackage| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|completeHensel| (*1 *2 *3 *2 *4 *5) (AND (|isDomain| *2 (|List| *3)) (|isDomain| *5 (|PositiveInteger|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|EuclideanDomain|)) (|isDomain| *1 (|GeneralHenselPackage| *4 *3)))) (|HenselLift| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *6 (|PositiveInteger|)) (|ofCategory| *5 (|EuclideanDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|Record| (|:| |plist| (|List| *3)) (|:| |modulo| *5))) (|isDomain| *1 (|GeneralHenselPackage| *5 *3)) (|isDomain| *4 (|List| *3))))) 
(CATEGORY |package| (SIGNATURE |HenselLift| ((|Record| (|:| |plist| (|List| |#2|)) (|:| |modulo| |#1|)) |#2| (|List| |#2|) |#1| (|PositiveInteger|))) (SIGNATURE |completeHensel| ((|List| |#2|) |#2| (|List| |#2|) |#1| (|PositiveInteger|))) (SIGNATURE |reduction| (|#2| |#2| |#1|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 28)) (|unitVector| (($ |#3|) 25)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|reductum| (($ $) 32)) (|multMonom| (($ |#2| |#4| $) 33)) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) 24)) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) 15)) (|leadingIndex| ((|#3| $) 19)) (|leadingExponent| ((|#4| $) 17)) (|leadingCoefficient| ((|#2| $) 29)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (|build| (($ |#2| |#3| |#4|) 26)) (|Zero| (($) 36 T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) 34)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ |#6| $) 40) (($ $ |#6|) NIL) (($ $ |#2|) NIL) (($ |#2| $) NIL))) 
(((|GeneralModulePolynomial| |#1| |#2| |#3| |#4| |#5| |#6|) (|Join| (|Module| |#6|) (|Module| |#2|) (CATEGORY |domain| (SIGNATURE |leadingCoefficient| (|#2| $)) (SIGNATURE |leadingMonomial| ((|ModuleMonomial| |#3| |#4| |#5|) $)) (SIGNATURE |leadingExponent| (|#4| $)) (SIGNATURE |leadingIndex| (|#3| $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |monomial| ($ |#2| (|ModuleMonomial| |#3| |#4| |#5|))) (SIGNATURE |unitVector| ($ |#3|)) (SIGNATURE |build| ($ |#2| |#3| |#4|)) (SIGNATURE |multMonom| ($ |#2| |#4| $)) (SIGNATURE * ($ |#6| $)))) (|List| (|Symbol|)) (|CommutativeRing|) (|OrderedSet|) (|DirectProductCategory| (|#| |#1|) (|NonNegativeInteger|)) (|Mapping| (|Boolean|) (|Record| (|:| |index| |#3|) (|:| |exponent| |#4|)) (|Record| (|:| |index| |#3|) (|:| |exponent| |#4|))) (|PolynomialCategory| |#2| |#4| (|OrderedVariableList| |#1|))) (T |GeneralModulePolynomial|)) 
((* (*1 *1 *2 *1) (AND (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *6 (|DirectProductCategory| (|#| *3) (|NonNegativeInteger|))) (|ofType| *7 (|Mapping| (|Boolean|) (|Record| (|:| |index| *5) (|:| |exponent| *6)) (|Record| (|:| |index| *5) (|:| |exponent| *6)))) (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *5 *6 *7 *2)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|PolynomialCategory| *4 *6 (|OrderedVariableList| *3))))) (|leadingCoefficient| (*1 *2 *1) (AND (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *5 (|DirectProductCategory| (|#| *3) (|NonNegativeInteger|))) (|ofType| *6 (|Mapping| (|Boolean|) (|Record| (|:| |index| *4) (|:| |exponent| *5)) (|Record| (|:| |index| *4) (|:| |exponent| *5)))) (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|GeneralModulePolynomial| *3 *2 *4 *5 *6 *7)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *7 (|PolynomialCategory| *2 *5 (|OrderedVariableList| *3))))) (|leadingMonomial| (*1 *2 *1) (AND (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *6 (|DirectProductCategory| (|#| *3) (|NonNegativeInteger|))) (|ofType| *7 (|Mapping| (|Boolean|) (|Record| (|:| |index| *5) (|:| |exponent| *6)) (|Record| (|:| |index| *5) (|:| |exponent| *6)))) (|isDomain| *2 (|ModuleMonomial| *5 *6 *7)) (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *5 *6 *7 *8)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *8 (|PolynomialCategory| *4 *6 (|OrderedVariableList| *3))))) (|leadingExponent| (*1 *2 *1) (AND (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|CommutativeRing|)) (|ofType| *6 (|Mapping| (|Boolean|) (|Record| (|:| |index| *5) (|:| |exponent| *2)) (|Record| (|:| |index| *5) (|:| |exponent| *2)))) (|ofCategory| *2 (|DirectProductCategory| (|#| *3) (|NonNegativeInteger|))) (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *5 *2 *6 *7)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *7 (|PolynomialCategory| *4 *2 (|OrderedVariableList| *3))))) (|leadingIndex| (*1 *2 *1) (AND (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|DirectProductCategory| (|#| *3) (|NonNegativeInteger|))) (|ofType| *6 (|Mapping| (|Boolean|) (|Record| (|:| |index| *2) (|:| |exponent| *5)) (|Record| (|:| |index| *2) (|:| |exponent| *5)))) (|ofCategory| *2 (|OrderedSet|)) (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *2 *5 *6 *7)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 (|OrderedVariableList| *3))))) (|reductum| (*1 *1 *1) (AND (|ofType| *2 (|List| (|Symbol|))) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *5 (|DirectProductCategory| (|#| *2) (|NonNegativeInteger|))) (|ofType| *6 (|Mapping| (|Boolean|) (|Record| (|:| |index| *4) (|:| |exponent| *5)) (|Record| (|:| |index| *4) (|:| |exponent| *5)))) (|isDomain| *1 (|GeneralModulePolynomial| *2 *3 *4 *5 *6 *7)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *7 (|PolynomialCategory| *3 *5 (|OrderedVariableList| *2))))) (|monomial| (*1 *1 *2 *3) (AND (|isDomain| *3 (|ModuleMonomial| *5 *6 *7)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofType| *7 (|Mapping| (|Boolean|) (|Record| (|:| |index| *5) (|:| |exponent| *6)) (|Record| (|:| |index| *5) (|:| |exponent| *6)))) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|GeneralModulePolynomial| *4 *2 *5 *6 *7 *8)) (|ofCategory| *8 (|PolynomialCategory| *2 *6 (|OrderedVariableList| *4))))) (|unitVector| (*1 *1 *2) (AND (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|DirectProductCategory| (|#| *3) (|NonNegativeInteger|))) (|ofType| *6 (|Mapping| (|Boolean|) (|Record| (|:| |index| *2) (|:| |exponent| *5)) (|Record| (|:| |index| *2) (|:| |exponent| *5)))) (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *2 *5 *6 *7)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 (|OrderedVariableList| *3))))) (|build| (*1 *1 *2 *3 *4) (AND (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *4 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofType| *6 (|Mapping| (|Boolean|) (|Record| (|:| |index| *3) (|:| |exponent| *4)) (|Record| (|:| |index| *3) (|:| |exponent| *4)))) (|isDomain| *1 (|GeneralModulePolynomial| *5 *2 *3 *4 *6 *7)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *7 (|PolynomialCategory| *2 *4 (|OrderedVariableList| *5))))) (|multMonom| (*1 *1 *2 *3 *1) (AND (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofType| *6 (|Mapping| (|Boolean|) (|Record| (|:| |index| *5) (|:| |exponent| *3)) (|Record| (|:| |index| *5) (|:| |exponent| *3)))) (|isDomain| *1 (|GeneralModulePolynomial| *4 *2 *5 *3 *6 *7)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *7 (|PolynomialCategory| *2 *3 (|OrderedVariableList| *4)))))) 
(|Join| (|Module| |#6|) (|Module| |#2|) (CATEGORY |domain| (SIGNATURE |leadingCoefficient| (|#2| $)) (SIGNATURE |leadingMonomial| ((|ModuleMonomial| |#3| |#4| |#5|) $)) (SIGNATURE |leadingExponent| (|#4| $)) (SIGNATURE |leadingIndex| (|#3| $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |monomial| ($ |#2| (|ModuleMonomial| |#3| |#4| |#5|))) (SIGNATURE |unitVector| ($ |#3|)) (SIGNATURE |build| ($ |#2| |#3| |#4|)) (SIGNATURE |multMonom| ($ |#2| |#4| $)) (SIGNATURE * ($ |#6| $)))) 
((~= (((|Boolean|) $ $) NIL)) (|variableName| (((|Symbol|) (|List| (|GuessOption|))) 48)) (|safety| (((|NonNegativeInteger|) (|List| (|GuessOption|))) 33)) (|one| (((|Boolean|) (|List| (|GuessOption|))) 39)) (|maxSubst| (((|Union| (|PositiveInteger|) "arbitrary") (|List| (|GuessOption|))) 20)) (|maxShift| (((|Union| (|NonNegativeInteger|) "arbitrary") (|List| (|GuessOption|))) 18)) (|maxPower| (((|Union| (|PositiveInteger|) "arbitrary") (|List| (|GuessOption|))) 32)) (|maxMixedDegree| (((|NonNegativeInteger|) (|List| (|GuessOption|))) 25)) (|maxLevel| (((|Union| (|NonNegativeInteger|) "arbitrary") (|List| (|GuessOption|))) 16)) (|maxDerivative| (((|Union| (|NonNegativeInteger|) "arbitrary") (|List| (|GuessOption|))) 17)) (|maxDegree| (((|Union| (|NonNegativeInteger|) "arbitrary") (|List| (|GuessOption|))) 21)) (|latex| (((|String|) $) NIL)) (|indexName| (((|Symbol|) (|List| (|GuessOption|))) 50)) (|homogeneous| (((|Union| (|PositiveInteger|) (|Boolean|)) (|List| (|GuessOption|))) 44)) (|hash| (((|SingleInteger|) $) NIL)) (|functionName| (((|Symbol|) (|List| (|GuessOption|))) 49)) (|displayAsGF| (((|Boolean|) (|List| (|GuessOption|))) 51)) (|debug| (((|Boolean|) (|List| (|GuessOption|))) 40)) (|coerce| (((|OutputForm|) $) NIL)) (|checkOptions| (((|Void|) (|List| (|GuessOption|))) 61)) (|checkExtraValues| (((|Boolean|) (|List| (|GuessOption|))) 38)) (|check| (((|Union| "skip" "MonteCarlo" "deterministic") (|List| (|GuessOption|))) 37)) (|allDegrees| (((|Boolean|) (|List| (|GuessOption|))) 29)) (|Somos| (((|Union| (|PositiveInteger|) (|Boolean|)) (|List| (|GuessOption|))) 45)) (= (((|Boolean|) $ $) NIL))) 
(((|GuessOptionFunctions0|) (|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE |maxDerivative| ((|Union| (|NonNegativeInteger|) "arbitrary") (|List| (|GuessOption|)))) (SIGNATURE |maxShift| ((|Union| (|NonNegativeInteger|) "arbitrary") (|List| (|GuessOption|)))) (SIGNATURE |maxSubst| ((|Union| (|PositiveInteger|) "arbitrary") (|List| (|GuessOption|)))) (SIGNATURE |maxPower| ((|Union| (|PositiveInteger|) "arbitrary") (|List| (|GuessOption|)))) (SIGNATURE |homogeneous| ((|Union| (|PositiveInteger|) (|Boolean|)) (|List| (|GuessOption|)))) (SIGNATURE |Somos| ((|Union| (|PositiveInteger|) (|Boolean|)) (|List| (|GuessOption|)))) (SIGNATURE |maxLevel| ((|Union| (|NonNegativeInteger|) "arbitrary") (|List| (|GuessOption|)))) (SIGNATURE |maxDegree| ((|Union| (|NonNegativeInteger|) "arbitrary") (|List| (|GuessOption|)))) (SIGNATURE |maxMixedDegree| ((|NonNegativeInteger|) (|List| (|GuessOption|)))) (SIGNATURE |allDegrees| ((|Boolean|) (|List| (|GuessOption|)))) (SIGNATURE |safety| ((|NonNegativeInteger|) (|List| (|GuessOption|)))) (SIGNATURE |check| ((|Union| "skip" "MonteCarlo" "deterministic") (|List| (|GuessOption|)))) (SIGNATURE |checkExtraValues| ((|Boolean|) (|List| (|GuessOption|)))) (SIGNATURE |one| ((|Boolean|) (|List| (|GuessOption|)))) (SIGNATURE |functionName| ((|Symbol|) (|List| (|GuessOption|)))) (SIGNATURE |variableName| ((|Symbol|) (|List| (|GuessOption|)))) (SIGNATURE |indexName| ((|Symbol|) (|List| (|GuessOption|)))) (SIGNATURE |displayAsGF| ((|Boolean|) (|List| (|GuessOption|)))) (SIGNATURE |debug| ((|Boolean|) (|List| (|GuessOption|)))) (SIGNATURE |checkOptions| ((|Void|) (|List| (|GuessOption|))))))) (T |GuessOptionFunctions0|)) 
((|maxDerivative| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Union| (|NonNegativeInteger|) "arbitrary")) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|maxShift| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Union| (|NonNegativeInteger|) "arbitrary")) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|maxSubst| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Union| (|PositiveInteger|) "arbitrary")) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|maxPower| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Union| (|PositiveInteger|) "arbitrary")) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|homogeneous| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Union| (|PositiveInteger|) (|Boolean|))) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|Somos| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Union| (|PositiveInteger|) (|Boolean|))) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|maxLevel| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Union| (|NonNegativeInteger|) "arbitrary")) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|maxDegree| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Union| (|NonNegativeInteger|) "arbitrary")) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|maxMixedDegree| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|allDegrees| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|safety| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|check| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Union| "skip" "MonteCarlo" "deterministic")) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|checkExtraValues| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|one| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|functionName| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|variableName| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|indexName| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|displayAsGF| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|debug| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GuessOptionFunctions0|)))) (|checkOptions| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GuessOptionFunctions0|))))) 
(|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE |maxDerivative| ((|Union| (|NonNegativeInteger|) "arbitrary") (|List| (|GuessOption|)))) (SIGNATURE |maxShift| ((|Union| (|NonNegativeInteger|) "arbitrary") (|List| (|GuessOption|)))) (SIGNATURE |maxSubst| ((|Union| (|PositiveInteger|) "arbitrary") (|List| (|GuessOption|)))) (SIGNATURE |maxPower| ((|Union| (|PositiveInteger|) "arbitrary") (|List| (|GuessOption|)))) (SIGNATURE |homogeneous| ((|Union| (|PositiveInteger|) (|Boolean|)) (|List| (|GuessOption|)))) (SIGNATURE |Somos| ((|Union| (|PositiveInteger|) (|Boolean|)) (|List| (|GuessOption|)))) (SIGNATURE |maxLevel| ((|Union| (|NonNegativeInteger|) "arbitrary") (|List| (|GuessOption|)))) (SIGNATURE |maxDegree| ((|Union| (|NonNegativeInteger|) "arbitrary") (|List| (|GuessOption|)))) (SIGNATURE |maxMixedDegree| ((|NonNegativeInteger|) (|List| (|GuessOption|)))) (SIGNATURE |allDegrees| ((|Boolean|) (|List| (|GuessOption|)))) (SIGNATURE |safety| ((|NonNegativeInteger|) (|List| (|GuessOption|)))) (SIGNATURE |check| ((|Union| "skip" "MonteCarlo" "deterministic") (|List| (|GuessOption|)))) (SIGNATURE |checkExtraValues| ((|Boolean|) (|List| (|GuessOption|)))) (SIGNATURE |one| ((|Boolean|) (|List| (|GuessOption|)))) (SIGNATURE |functionName| ((|Symbol|) (|List| (|GuessOption|)))) (SIGNATURE |variableName| ((|Symbol|) (|List| (|GuessOption|)))) (SIGNATURE |indexName| ((|Symbol|) (|List| (|GuessOption|)))) (SIGNATURE |displayAsGF| ((|Boolean|) (|List| (|GuessOption|)))) (SIGNATURE |debug| ((|Boolean|) (|List| (|GuessOption|)))) (SIGNATURE |checkOptions| ((|Void|) (|List| (|GuessOption|)))))) 
((~= (((|Boolean|) $ $) NIL)) (|variableName| (($ (|Symbol|)) 49)) (|safety| (($ (|NonNegativeInteger|)) 28)) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) 61)) (|one| (($ (|Boolean|)) 40)) (|maxSubst| (($ (|Union| (|PositiveInteger|) "arbitrary")) 15)) (|maxShift| (($ (|Union| (|NonNegativeInteger|) "arbitrary")) 13)) (|maxPower| (($ (|Union| (|PositiveInteger|) "arbitrary")) 27)) (|maxMixedDegree| (($ (|NonNegativeInteger|)) 20)) (|maxLevel| (($ (|Union| (|NonNegativeInteger|) "arbitrary")) 11)) (|maxDerivative| (($ (|Union| (|NonNegativeInteger|) "arbitrary")) 12)) (|maxDegree| (($ (|Union| (|NonNegativeInteger|) "arbitrary")) 16)) (|latex| (((|String|) $) NIL)) (|indexName| (($ (|Symbol|)) 50)) (|homogeneous| (($ (|Union| (|PositiveInteger|) (|Boolean|))) 32)) (|hash| (((|SingleInteger|) $) NIL)) (|functionNames| (($ (|List| (|Symbol|))) 48)) (|functionName| (($ (|Symbol|)) 44)) (|displayKind| (($ (|Symbol|)) 51)) (|debug| (($ (|Boolean|)) 34)) (|coerce| (((|OutputForm|) $) 56)) (|checkExtraValues| (($ (|Boolean|)) 39)) (|check| (($ (|Union| "skip" "MonteCarlo" "deterministic")) 38)) (|allDegrees| (($ (|Boolean|)) 24)) (|Somos| (($ (|Union| (|PositiveInteger|) (|Boolean|))) 33)) (= (((|Boolean|) $ $) 58))) 
(((|GuessOption|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |maxDerivative| ($ (|Union| (|NonNegativeInteger|) "arbitrary"))) (SIGNATURE |maxShift| ($ (|Union| (|NonNegativeInteger|) "arbitrary"))) (SIGNATURE |maxSubst| ($ (|Union| (|PositiveInteger|) "arbitrary"))) (SIGNATURE |maxPower| ($ (|Union| (|PositiveInteger|) "arbitrary"))) (SIGNATURE |homogeneous| ($ (|Union| (|PositiveInteger|) (|Boolean|)))) (SIGNATURE |Somos| ($ (|Union| (|PositiveInteger|) (|Boolean|)))) (SIGNATURE |maxLevel| ($ (|Union| (|NonNegativeInteger|) "arbitrary"))) (SIGNATURE |maxDegree| ($ (|Union| (|NonNegativeInteger|) "arbitrary"))) (SIGNATURE |maxMixedDegree| ($ (|NonNegativeInteger|))) (SIGNATURE |allDegrees| ($ (|Boolean|))) (SIGNATURE |safety| ($ (|NonNegativeInteger|))) (SIGNATURE |check| ($ (|Union| "skip" "MonteCarlo" "deterministic"))) (SIGNATURE |checkExtraValues| ($ (|Boolean|))) (SIGNATURE |one| ($ (|Boolean|))) (SIGNATURE |debug| ($ (|Boolean|))) (SIGNATURE |functionName| ($ (|Symbol|))) (SIGNATURE |functionNames| ($ (|List| (|Symbol|)))) (SIGNATURE |variableName| ($ (|Symbol|))) (SIGNATURE |indexName| ($ (|Symbol|))) (SIGNATURE |displayKind| ($ (|Symbol|))) (SIGNATURE |option| ((|Union| (|Any|) "failed") (|List| $) (|Symbol|)))))) (T |GuessOption|)) 
((|maxDerivative| (*1 *1 *2) (AND (|isDomain| *2 (|Union| (|NonNegativeInteger|) "arbitrary")) (|isDomain| *1 (|GuessOption|)))) (|maxShift| (*1 *1 *2) (AND (|isDomain| *2 (|Union| (|NonNegativeInteger|) "arbitrary")) (|isDomain| *1 (|GuessOption|)))) (|maxSubst| (*1 *1 *2) (AND (|isDomain| *2 (|Union| (|PositiveInteger|) "arbitrary")) (|isDomain| *1 (|GuessOption|)))) (|maxPower| (*1 *1 *2) (AND (|isDomain| *2 (|Union| (|PositiveInteger|) "arbitrary")) (|isDomain| *1 (|GuessOption|)))) (|homogeneous| (*1 *1 *2) (AND (|isDomain| *2 (|Union| (|PositiveInteger|) (|Boolean|))) (|isDomain| *1 (|GuessOption|)))) (|Somos| (*1 *1 *2) (AND (|isDomain| *2 (|Union| (|PositiveInteger|) (|Boolean|))) (|isDomain| *1 (|GuessOption|)))) (|maxLevel| (*1 *1 *2) (AND (|isDomain| *2 (|Union| (|NonNegativeInteger|) "arbitrary")) (|isDomain| *1 (|GuessOption|)))) (|maxDegree| (*1 *1 *2) (AND (|isDomain| *2 (|Union| (|NonNegativeInteger|) "arbitrary")) (|isDomain| *1 (|GuessOption|)))) (|maxMixedDegree| (*1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|GuessOption|)))) (|allDegrees| (*1 *1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GuessOption|)))) (|safety| (*1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|GuessOption|)))) (|check| (*1 *1 *2) (AND (|isDomain| *2 (|Union| "skip" "MonteCarlo" "deterministic")) (|isDomain| *1 (|GuessOption|)))) (|checkExtraValues| (*1 *1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GuessOption|)))) (|one| (*1 *1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GuessOption|)))) (|debug| (*1 *1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GuessOption|)))) (|functionName| (*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|GuessOption|)))) (|functionNames| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *1 (|GuessOption|)))) (|variableName| (*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|GuessOption|)))) (|indexName| (*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|GuessOption|)))) (|displayKind| (*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|GuessOption|)))) (|option| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|GuessOption|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |maxDerivative| ($ (|Union| (|NonNegativeInteger|) "arbitrary"))) (SIGNATURE |maxShift| ($ (|Union| (|NonNegativeInteger|) "arbitrary"))) (SIGNATURE |maxSubst| ($ (|Union| (|PositiveInteger|) "arbitrary"))) (SIGNATURE |maxPower| ($ (|Union| (|PositiveInteger|) "arbitrary"))) (SIGNATURE |homogeneous| ($ (|Union| (|PositiveInteger|) (|Boolean|)))) (SIGNATURE |Somos| ($ (|Union| (|PositiveInteger|) (|Boolean|)))) (SIGNATURE |maxLevel| ($ (|Union| (|NonNegativeInteger|) "arbitrary"))) (SIGNATURE |maxDegree| ($ (|Union| (|NonNegativeInteger|) "arbitrary"))) (SIGNATURE |maxMixedDegree| ($ (|NonNegativeInteger|))) (SIGNATURE |allDegrees| ($ (|Boolean|))) (SIGNATURE |safety| ($ (|NonNegativeInteger|))) (SIGNATURE |check| ($ (|Union| "skip" "MonteCarlo" "deterministic"))) (SIGNATURE |checkExtraValues| ($ (|Boolean|))) (SIGNATURE |one| ($ (|Boolean|))) (SIGNATURE |debug| ($ (|Boolean|))) (SIGNATURE |functionName| ($ (|Symbol|))) (SIGNATURE |functionNames| ($ (|List| (|Symbol|)))) (SIGNATURE |variableName| ($ (|Symbol|))) (SIGNATURE |indexName| ($ (|Symbol|))) (SIGNATURE |displayKind| ($ (|Symbol|))) (SIGNATURE |option| ((|Union| (|Any|) "failed") (|List| $) (|Symbol|))))) 
((|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) 35))) 
(((|GosperSummationMethod| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |GospersMethod| ((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|IntegralDomain|) (|PolynomialCategory| |#3| |#1| |#2|) (|Join| (|RetractableTo| (|Fraction| (|Integer|))) (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#4|)) (SIGNATURE |numer| (|#4| $)) (SIGNATURE |denom| (|#4| $))))) (T |GosperSummationMethod|)) 
((|GospersMethod| (*1 *2 *2 *3 *4) (|partial| AND (|isDomain| *4 (|Mapping| *3)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|IntegralDomain|)) (|ofCategory| *7 (|PolynomialCategory| *6 *5 *3)) (|isDomain| *1 (|GosperSummationMethod| *5 *3 *6 *7 *2)) (|ofCategory| *2 (|Join| (|RetractableTo| (|Fraction| (|Integer|))) (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ *7)) (SIGNATURE |numer| (*7 $)) (SIGNATURE |denom| (*7 $)))))))) 
(CATEGORY |package| (SIGNATURE |GospersMethod| ((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)))) 
((|theCurve| ((|#3|) 43)) (|singularPoints| (((|List| |#5|)) 47)) (|setSingularPoints| (((|List| |#5|) (|List| |#5|)) 129)) (|setCurve| ((|#3| |#3|) 107)) (|reset| (((|Void|)) 106)) (|rationalPoints| (((|List| |#5|)) 150 (|has| |#1| (|Finite|)))) (|rationalPlaces| (((|List| |#7|)) 153 (|has| |#1| (|Finite|)))) (|printInfo| (((|Void|) (|List| (|Boolean|))) 120)) (|pointDominateBy| ((|#5| |#7|) 94)) (|placesOfDegree| (((|List| |#7|) (|PositiveInteger|)) 149 (|has| |#1| (|Finite|)))) (|placesAbove| (((|List| |#7|) |#5|) 92)) (|parametrize| ((|#6| |#3| |#7|) 97)) (|numberRatPlacesExtDeg| (((|Integer|) (|PositiveInteger|)) 194 (|has| |#1| (|Finite|)))) (|numberPlacesDegExtDeg| (((|Integer|) (|PositiveInteger|) (|PositiveInteger|)) 193 (|has| |#1| (|Finite|)))) (|numberOfPlacesOfDegree| (((|Integer|) (|PositiveInteger|)) 176 (|has| |#1| (|Finite|)))) (|lBasis| (((|Record| (|:| |num| (|List| |#3|)) (|:| |den| |#3|)) |#8|) 69)) (|intersectionDivisor| ((|#8| |#3|) 50)) (|interpolateFormsForFact| (((|List| |#3|) |#8| (|List| |#3|)) 136)) (|interpolateForms| (((|List| |#3|) |#8| (|NonNegativeInteger|)) 65)) (|homogenize| ((|#3| |#3| (|Integer|)) 40)) (|genusNeg| (((|Integer|)) 74)) (|genus| (((|NonNegativeInteger|)) 73)) (|findOrderOfDivisor| (((|Record| (|:| |ord| (|Integer|)) (|:| |num| |#3|) (|:| |den| |#3|) (|:| |upTo| (|Integer|))) |#8| (|Integer|) (|Integer|)) 114)) (|evalIfCan| (((|Union| |#1| "failed") (|Fraction| |#3|) |#7|) 144) (((|Union| |#1| "failed") |#3| |#3| |#7|) 139) (((|Union| |#1| "failed") |#3| |#7|) 104)) (|eval| ((|#1| (|Fraction| |#3|) |#7|) 145) ((|#1| |#3| |#3| |#7|) 140) ((|#1| |#3| |#7|) 105)) (|desingTreeWoFullParam| (((|List| |#10|)) 70)) (|desingTree| (((|List| |#10|)) 45)) (|classNumber| (((|Integer|)) 204 (|has| |#1| (|Finite|)))) (|adjunctionDivisor| ((|#8|) 54)) (|ZetaFunction| (((|UnivariateTaylorSeriesCZero| (|Integer|) |t|) (|PositiveInteger|)) 155 (|has| |#1| (|Finite|))) (((|UnivariateTaylorSeriesCZero| (|Integer|) |t|)) 156 (|has| |#1| (|Finite|)))) (|LPolynomial| (((|SparseUnivariatePolynomial| (|Integer|)) (|PositiveInteger|)) 158 (|has| |#1| (|Finite|))) (((|SparseUnivariatePolynomial| (|Integer|))) 196 (|has| |#1| (|Finite|))))) 
(((|GeneralPackageForAlgebraicFunctionField| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8| |#9| |#10| |#11|) (CATEGORY |package| (SIGNATURE |reset| ((|Void|))) (SIGNATURE |setCurve| (|#3| |#3|)) (SIGNATURE |homogenize| (|#3| |#3| (|Integer|))) (SIGNATURE |printInfo| ((|Void|) (|List| (|Boolean|)))) (SIGNATURE |theCurve| (|#3|)) (SIGNATURE |genus| ((|NonNegativeInteger|))) (SIGNATURE |genusNeg| ((|Integer|))) (SIGNATURE |desingTree| ((|List| |#10|))) (SIGNATURE |desingTreeWoFullParam| ((|List| |#10|))) (SIGNATURE |setSingularPoints| ((|List| |#5|) (|List| |#5|))) (SIGNATURE |singularPoints| ((|List| |#5|))) (SIGNATURE |parametrize| (|#6| |#3| |#7|)) (SIGNATURE |lBasis| ((|Record| (|:| |num| (|List| |#3|)) (|:| |den| |#3|)) |#8|)) (SIGNATURE |findOrderOfDivisor| ((|Record| (|:| |ord| (|Integer|)) (|:| |num| |#3|) (|:| |den| |#3|) (|:| |upTo| (|Integer|))) |#8| (|Integer|) (|Integer|))) (SIGNATURE |interpolateForms| ((|List| |#3|) |#8| (|NonNegativeInteger|))) (SIGNATURE |interpolateFormsForFact| ((|List| |#3|) |#8| (|List| |#3|))) (SIGNATURE |eval| (|#1| |#3| |#7|)) (SIGNATURE |eval| (|#1| |#3| |#3| |#7|)) (SIGNATURE |eval| (|#1| (|Fraction| |#3|) |#7|)) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") |#3| |#7|)) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") |#3| |#3| |#7|)) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") (|Fraction| |#3|) |#7|)) (SIGNATURE |intersectionDivisor| (|#8| |#3|)) (SIGNATURE |adjunctionDivisor| (|#8|)) (SIGNATURE |placesAbove| ((|List| |#7|) |#5|)) (SIGNATURE |pointDominateBy| (|#5| |#7|)) (IF (|has| |#1| (|Finite|)) (PROGN (SIGNATURE |rationalPlaces| ((|List| |#7|))) (SIGNATURE |rationalPoints| ((|List| |#5|))) (SIGNATURE |LPolynomial| ((|SparseUnivariatePolynomial| (|Integer|)))) (SIGNATURE |LPolynomial| ((|SparseUnivariatePolynomial| (|Integer|)) (|PositiveInteger|))) (SIGNATURE |classNumber| ((|Integer|))) (SIGNATURE |placesOfDegree| ((|List| |#7|) (|PositiveInteger|))) (SIGNATURE |numberOfPlacesOfDegree| ((|Integer|) (|PositiveInteger|))) (SIGNATURE |numberRatPlacesExtDeg| ((|Integer|) (|PositiveInteger|))) (SIGNATURE |numberPlacesDegExtDeg| ((|Integer|) (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |ZetaFunction| ((|UnivariateTaylorSeriesCZero| (|Integer|) |t|))) (SIGNATURE |ZetaFunction| ((|UnivariateTaylorSeriesCZero| (|Integer|) |t|) (|PositiveInteger|)))) |noBranch|)) (|Field|) (|List| (|Symbol|)) (|PolynomialCategory| |#1| |#4| (|OrderedVariableList| |#2|)) (|DirectProductCategory| (|#| |#2|) (|NonNegativeInteger|)) (|ProjectiveSpaceCategory| |#1|) (|LocalPowerSeriesCategory| |#1|) (|PlacesCategory| |#1| |#6|) (|DivisorCategory| |#7|) (|InfinitlyClosePointCategory| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8| |#11|) (|DesingTreeCategory| |#9|) (|BlowUpMethodCategory|)) (T |GeneralPackageForAlgebraicFunctionField|)) 
((|ZetaFunction| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Finite|)) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|ofCategory| *11 (|DivisorCategory| *10)) (|ofCategory| *12 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *8 *9 *10 *11 *14)) (|ofCategory| *14 (|BlowUpMethodCategory|)) (|isDomain| *2 (|UnivariateTaylorSeriesCZero| (|Integer|) |t|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *4 *5 *6 *7 *8 *9 *10 *11 *12 *13 *14)) (|ofCategory| *13 (|DesingTreeCategory| *12)))) (|ZetaFunction| (*1 *2) (AND (|ofCategory| *3 (|Finite|)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|UnivariateTaylorSeriesCZero| (|Integer|) |t|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *3 *4 *5 *6 *7 *8 *9 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|numberPlacesDegExtDeg| (*1 *2 *3 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Finite|)) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|ofCategory| *11 (|DivisorCategory| *10)) (|ofCategory| *12 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *8 *9 *10 *11 *14)) (|ofCategory| *14 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *4 *5 *6 *7 *8 *9 *10 *11 *12 *13 *14)) (|ofCategory| *13 (|DesingTreeCategory| *12)))) (|numberRatPlacesExtDeg| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Finite|)) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|ofCategory| *11 (|DivisorCategory| *10)) (|ofCategory| *12 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *8 *9 *10 *11 *14)) (|ofCategory| *14 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *4 *5 *6 *7 *8 *9 *10 *11 *12 *13 *14)) (|ofCategory| *13 (|DesingTreeCategory| *12)))) (|numberOfPlacesOfDegree| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Finite|)) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|ofCategory| *11 (|DivisorCategory| *10)) (|ofCategory| *12 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *8 *9 *10 *11 *14)) (|ofCategory| *14 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *4 *5 *6 *7 *8 *9 *10 *11 *12 *13 *14)) (|ofCategory| *13 (|DesingTreeCategory| *12)))) (|placesOfDegree| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Finite|)) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|ofCategory| *11 (|DivisorCategory| *10)) (|ofCategory| *12 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *8 *9 *10 *11 *14)) (|ofCategory| *14 (|BlowUpMethodCategory|)) (|isDomain| *2 (|List| *10)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *4 *5 *6 *7 *8 *9 *10 *11 *12 *13 *14)) (|ofCategory| *13 (|DesingTreeCategory| *12)))) (|classNumber| (*1 *2) (AND (|ofCategory| *3 (|Finite|)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *3 *4 *5 *6 *7 *8 *9 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|LPolynomial| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Finite|)) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|ofCategory| *11 (|DivisorCategory| *10)) (|ofCategory| *12 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *8 *9 *10 *11 *14)) (|ofCategory| *14 (|BlowUpMethodCategory|)) (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *4 *5 *6 *7 *8 *9 *10 *11 *12 *13 *14)) (|ofCategory| *13 (|DesingTreeCategory| *12)))) (|LPolynomial| (*1 *2) (AND (|ofCategory| *3 (|Finite|)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *3 *4 *5 *6 *7 *8 *9 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|rationalPoints| (*1 *2) (AND (|ofCategory| *3 (|Finite|)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|List| *7)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *3 *4 *5 *6 *7 *8 *9 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|rationalPlaces| (*1 *2) (AND (|ofCategory| *3 (|Finite|)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|List| *9)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *3 *4 *5 *6 *7 *8 *9 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|pointDominateBy| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *8 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *3 (|PlacesCategory| *4 *8)) (|ofCategory| *9 (|DivisorCategory| *3)) (|ofCategory| *10 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *2 *8 *3 *9 *12)) (|ofCategory| *12 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|ProjectiveSpaceCategory| *4)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *4 *5 *6 *7 *2 *8 *3 *9 *10 *11 *12)) (|ofCategory| *11 (|DesingTreeCategory| *10)))) (|placesAbove| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *3 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *9 (|PlacesCategory| *4 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *3 *8 *9 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|List| *9)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *4 *5 *6 *7 *3 *8 *9 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|adjunctionDivisor| (*1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *2 *12)) (|ofCategory| *12 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|DivisorCategory| *9)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *3 *4 *5 *6 *7 *8 *9 *2 *10 *11 *12)) (|ofCategory| *11 (|DesingTreeCategory| *10)))) (|intersectionDivisor| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *3 (|PolynomialCategory| *4 *6 (|OrderedVariableList| *5))) (|ofCategory| *6 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *9 (|PlacesCategory| *4 *8)) (|ofCategory| *10 (|InfinitlyClosePointCategory| *4 *5 *3 *6 *7 *8 *9 *2 *12)) (|ofCategory| *12 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|DivisorCategory| *9)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *4 *5 *3 *6 *7 *8 *9 *2 *10 *11 *12)) (|ofCategory| *11 (|DesingTreeCategory| *10)))) (|evalIfCan| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Fraction| *6)) (|ofCategory| *6 (|PolynomialCategory| *2 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *2)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *2)) (|ofCategory| *4 (|PlacesCategory| *2 *9)) (|ofCategory| *10 (|DivisorCategory| *4)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *2 *5 *6 *7 *8 *9 *4 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *2 *5 *6 *7 *8 *9 *4 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|evalIfCan| (*1 *2 *3 *3 *4) (|partial| AND (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *3 (|PolynomialCategory| *2 *6 (|OrderedVariableList| *5))) (|ofCategory| *6 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *2)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *2)) (|ofCategory| *4 (|PlacesCategory| *2 *8)) (|ofCategory| *9 (|DivisorCategory| *4)) (|ofCategory| *10 (|InfinitlyClosePointCategory| *2 *5 *3 *6 *7 *8 *4 *9 *12)) (|ofCategory| *12 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *2 *5 *3 *6 *7 *8 *4 *9 *10 *11 *12)) (|ofCategory| *11 (|DesingTreeCategory| *10)))) (|evalIfCan| (*1 *2 *3 *4) (|partial| AND (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *3 (|PolynomialCategory| *2 *6 (|OrderedVariableList| *5))) (|ofCategory| *6 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *2)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *2)) (|ofCategory| *4 (|PlacesCategory| *2 *8)) (|ofCategory| *9 (|DivisorCategory| *4)) (|ofCategory| *10 (|InfinitlyClosePointCategory| *2 *5 *3 *6 *7 *8 *4 *9 *12)) (|ofCategory| *12 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *2 *5 *3 *6 *7 *8 *4 *9 *10 *11 *12)) (|ofCategory| *11 (|DesingTreeCategory| *10)))) (|eval| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| *6)) (|ofCategory| *6 (|PolynomialCategory| *2 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *2)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *2)) (|ofCategory| *4 (|PlacesCategory| *2 *9)) (|ofCategory| *10 (|DivisorCategory| *4)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *2 *5 *6 *7 *8 *9 *4 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *2 *5 *6 *7 *8 *9 *4 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|eval| (*1 *2 *3 *3 *4) (AND (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *3 (|PolynomialCategory| *2 *6 (|OrderedVariableList| *5))) (|ofCategory| *6 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *2)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *2)) (|ofCategory| *4 (|PlacesCategory| *2 *8)) (|ofCategory| *9 (|DivisorCategory| *4)) (|ofCategory| *10 (|InfinitlyClosePointCategory| *2 *5 *3 *6 *7 *8 *4 *9 *12)) (|ofCategory| *12 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *2 *5 *3 *6 *7 *8 *4 *9 *10 *11 *12)) (|ofCategory| *11 (|DesingTreeCategory| *10)))) (|eval| (*1 *2 *3 *4) (AND (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *3 (|PolynomialCategory| *2 *6 (|OrderedVariableList| *5))) (|ofCategory| *6 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *2)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *2)) (|ofCategory| *4 (|PlacesCategory| *2 *8)) (|ofCategory| *9 (|DivisorCategory| *4)) (|ofCategory| *10 (|InfinitlyClosePointCategory| *2 *5 *3 *6 *7 *8 *4 *9 *12)) (|ofCategory| *12 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *2 *5 *3 *6 *7 *8 *4 *9 *10 *11 *12)) (|ofCategory| *11 (|DesingTreeCategory| *10)))) (|interpolateFormsForFact| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|ofCategory| *3 (|DivisorCategory| *10)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *8 *9 *10 *3 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *4 *5 *6 *7 *8 *9 *10 *3 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|interpolateForms| (*1 *2 *3 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|PolynomialCategory| *5 *8 (|OrderedVariableList| *6))) (|ofCategory| *8 (|DirectProductCategory| (|#| *6) *4)) (|ofCategory| *9 (|ProjectiveSpaceCategory| *5)) (|ofCategory| *10 (|LocalPowerSeriesCategory| *5)) (|ofCategory| *11 (|PlacesCategory| *5 *10)) (|ofCategory| *3 (|DivisorCategory| *11)) (|ofCategory| *12 (|InfinitlyClosePointCategory| *5 *6 *7 *8 *9 *10 *11 *3 *14)) (|ofCategory| *14 (|BlowUpMethodCategory|)) (|isDomain| *2 (|List| *7)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *5 *6 *7 *8 *9 *10 *11 *3 *12 *13 *14)) (|ofCategory| *13 (|DesingTreeCategory| *12)))) (|findOrderOfDivisor| (*1 *2 *3 *4 *4) (AND (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|PolynomialCategory| *5 *8 (|OrderedVariableList| *6))) (|ofCategory| *8 (|DirectProductCategory| (|#| *6) (|NonNegativeInteger|))) (|ofCategory| *9 (|ProjectiveSpaceCategory| *5)) (|ofCategory| *10 (|LocalPowerSeriesCategory| *5)) (|ofCategory| *11 (|PlacesCategory| *5 *10)) (|ofCategory| *3 (|DivisorCategory| *11)) (|ofCategory| *12 (|InfinitlyClosePointCategory| *5 *6 *7 *8 *9 *10 *11 *3 *14)) (|ofCategory| *14 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Record| (|:| |ord| (|Integer|)) (|:| |num| *7) (|:| |den| *7) (|:| |upTo| (|Integer|)))) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *5 *6 *7 *8 *9 *10 *11 *3 *12 *13 *14)) (|isDomain| *4 (|Integer|)) (|ofCategory| *13 (|DesingTreeCategory| *12)))) (|lBasis| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|ofCategory| *3 (|DivisorCategory| *10)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *8 *9 *10 *3 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Record| (|:| |num| (|List| *6)) (|:| |den| *6))) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *4 *5 *6 *7 *8 *9 *10 *3 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|parametrize| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *3 (|PolynomialCategory| *5 *7 (|OrderedVariableList| *6))) (|ofCategory| *7 (|DirectProductCategory| (|#| *6) (|NonNegativeInteger|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *5)) (|ofCategory| *4 (|PlacesCategory| *5 *2)) (|ofCategory| *9 (|DivisorCategory| *4)) (|ofCategory| *10 (|InfinitlyClosePointCategory| *5 *6 *3 *7 *8 *2 *4 *9 *12)) (|ofCategory| *12 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|LocalPowerSeriesCategory| *5)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *5 *6 *3 *7 *8 *2 *4 *9 *10 *11 *12)) (|ofCategory| *11 (|DesingTreeCategory| *10)))) (|singularPoints| (*1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|List| *7)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *3 *4 *5 *6 *7 *8 *9 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|setSingularPoints| (*1 *2 *2) (AND (|isDomain| *2 (|List| *7)) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *3 *4 *5 *6 *7 *8 *9 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|desingTreeWoFullParam| (*1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|List| *12)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *3 *4 *5 *6 *7 *8 *9 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|desingTree| (*1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|List| *12)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *3 *4 *5 *6 *7 *8 *9 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|genusNeg| (*1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *3 *4 *5 *6 *7 *8 *9 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|genus| (*1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) *2)) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *3 *4 *5 *6 *7 *8 *9 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|theCurve| (*1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *6 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *7 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *8 (|PlacesCategory| *3 *7)) (|ofCategory| *9 (|DivisorCategory| *8)) (|ofCategory| *10 (|InfinitlyClosePointCategory| *3 *4 *2 *5 *6 *7 *8 *9 *12)) (|ofCategory| *12 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|PolynomialCategory| *3 *5 (|OrderedVariableList| *4))) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *3 *4 *2 *5 *6 *7 *8 *9 *10 *11 *12)) (|ofCategory| *11 (|DesingTreeCategory| *10)))) (|printInfo| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Boolean|))) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|ofCategory| *11 (|DivisorCategory| *10)) (|ofCategory| *12 (|InfinitlyClosePointCategory| *4 *5 *6 *7 *8 *9 *10 *11 *14)) (|ofCategory| *14 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *4 *5 *6 *7 *8 *9 *10 *11 *12 *13 *14)) (|ofCategory| *13 (|DesingTreeCategory| *12)))) (|homogenize| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *2 (|PolynomialCategory| *4 *6 (|OrderedVariableList| *5))) (|ofCategory| *6 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *9 (|PlacesCategory| *4 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *4 *5 *2 *6 *7 *8 *9 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *4 *5 *2 *6 *7 *8 *9 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11)))) (|setCurve| (*1 *2 *2) (AND (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *2 (|PolynomialCategory| *3 *5 (|OrderedVariableList| *4))) (|ofCategory| *5 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *6 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *7 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *8 (|PlacesCategory| *3 *7)) (|ofCategory| *9 (|DivisorCategory| *8)) (|ofCategory| *10 (|InfinitlyClosePointCategory| *3 *4 *2 *5 *6 *7 *8 *9 *12)) (|ofCategory| *12 (|BlowUpMethodCategory|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *3 *4 *2 *5 *6 *7 *8 *9 *10 *11 *12)) (|ofCategory| *11 (|DesingTreeCategory| *10)))) (|reset| (*1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *13)) (|ofCategory| *13 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GeneralPackageForAlgebraicFunctionField| *3 *4 *5 *6 *7 *8 *9 *10 *11 *12 *13)) (|ofCategory| *12 (|DesingTreeCategory| *11))))) 
(CATEGORY |package| (SIGNATURE |reset| ((|Void|))) (SIGNATURE |setCurve| (|#3| |#3|)) (SIGNATURE |homogenize| (|#3| |#3| (|Integer|))) (SIGNATURE |printInfo| ((|Void|) (|List| (|Boolean|)))) (SIGNATURE |theCurve| (|#3|)) (SIGNATURE |genus| ((|NonNegativeInteger|))) (SIGNATURE |genusNeg| ((|Integer|))) (SIGNATURE |desingTree| ((|List| |#10|))) (SIGNATURE |desingTreeWoFullParam| ((|List| |#10|))) (SIGNATURE |setSingularPoints| ((|List| |#5|) (|List| |#5|))) (SIGNATURE |singularPoints| ((|List| |#5|))) (SIGNATURE |parametrize| (|#6| |#3| |#7|)) (SIGNATURE |lBasis| ((|Record| (|:| |num| (|List| |#3|)) (|:| |den| |#3|)) |#8|)) (SIGNATURE |findOrderOfDivisor| ((|Record| (|:| |ord| (|Integer|)) (|:| |num| |#3|) (|:| |den| |#3|) (|:| |upTo| (|Integer|))) |#8| (|Integer|) (|Integer|))) (SIGNATURE |interpolateForms| ((|List| |#3|) |#8| (|NonNegativeInteger|))) (SIGNATURE |interpolateFormsForFact| ((|List| |#3|) |#8| (|List| |#3|))) (SIGNATURE |eval| (|#1| |#3| |#7|)) (SIGNATURE |eval| (|#1| |#3| |#3| |#7|)) (SIGNATURE |eval| (|#1| (|Fraction| |#3|) |#7|)) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") |#3| |#7|)) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") |#3| |#3| |#7|)) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") (|Fraction| |#3|) |#7|)) (SIGNATURE |intersectionDivisor| (|#8| |#3|)) (SIGNATURE |adjunctionDivisor| (|#8|)) (SIGNATURE |placesAbove| ((|List| |#7|) |#5|)) (SIGNATURE |pointDominateBy| (|#5| |#7|)) (IF (|has| |#1| (|Finite|)) (PROGN (SIGNATURE |rationalPlaces| ((|List| |#7|))) (SIGNATURE |rationalPoints| ((|List| |#5|))) (SIGNATURE |LPolynomial| ((|SparseUnivariatePolynomial| (|Integer|)))) (SIGNATURE |LPolynomial| ((|SparseUnivariatePolynomial| (|Integer|)) (|PositiveInteger|))) (SIGNATURE |classNumber| ((|Integer|))) (SIGNATURE |placesOfDegree| ((|List| |#7|) (|PositiveInteger|))) (SIGNATURE |numberOfPlacesOfDegree| ((|Integer|) (|PositiveInteger|))) (SIGNATURE |numberRatPlacesExtDeg| ((|Integer|) (|PositiveInteger|))) (SIGNATURE |numberPlacesDegExtDeg| ((|Integer|) (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |ZetaFunction| ((|UnivariateTaylorSeriesCZero| (|Integer|) |t|))) (SIGNATURE |ZetaFunction| ((|UnivariateTaylorSeriesCZero| (|Integer|) |t|) (|PositiveInteger|)))) |noBranch|)) 
((~= (((|Boolean|) $ $) NIL)) (|variables| (((|List| |#3|) $) 41)) (|trivialIdeal?| (((|Boolean|) $) NIL)) (|triangular?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|select| (($ (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) NIL T CONST)) (|roughUnitIdeal?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|roughSubIdeal?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|roughEqualIdeals?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|roughBase?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 47)) (|retract| (($ (|List| |#4|)) NIL)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|))))) (|remove| (($ |#4| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|)))) (($ (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) NIL (|has| |#1| (|IntegralDomain|)))) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|)))) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| (|Mapping| |#4| |#4| |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|parts| (((|List| |#4|) $) 18 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|mvar| ((|#3| $) 45)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#4|) $) 14 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#4| $) 26 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|))))) (|map!| (($ (|Mapping| |#4| |#4|) $) 23 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#4| |#4|) $) 21)) (|mainVariables| (((|List| |#3|) $) NIL)) (|mainVariable?| (((|Boolean|) |#3| $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) NIL (|has| |#1| (|IntegralDomain|)))) (|hash| (((|SingleInteger|) $) NIL)) (|find| (((|Union| |#4| "failed") (|Mapping| (|Boolean|) |#4|) $) NIL)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ |#4| |#4|) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|Equation| |#4|)) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|List| (|Equation| |#4|))) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) 39)) (|empty| (($) 17)) (|count| (((|NonNegativeInteger|) |#4| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) 16)) (|convert| (((|InputForm|) $) NIL (|has| |#4| (|ConvertibleTo| (|InputForm|)))) (($ (|List| |#4|)) 49)) (|construct| (($ (|List| |#4|)) 13)) (|collectUpper| (($ $ |#3|) NIL)) (|collectUnder| (($ $ |#3|) NIL)) (|collect| (($ $ |#3|) NIL)) (|coerce| (((|OutputForm|) $) 38) (((|List| |#4|) $) 48)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 30)) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|GeneralPolynomialSet| |#1| |#2| |#3| |#4|) (|Join| (|PolynomialSetCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |convert| ($ (|List| |#4|))) (ATTRIBUTE |finiteAggregate|) (ATTRIBUTE |shallowlyMutable|))) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|)) (T |GeneralPolynomialSet|)) 
((|convert| (*1 *1 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|GeneralPolynomialSet| *3 *4 *5 *6))))) 
(|Join| (|PolynomialSetCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |convert| ($ (|List| |#4|))) (ATTRIBUTE |finiteAggregate|) (ATTRIBUTE |shallowlyMutable|))) 
((|Zero| (($) 11)) (|One| (($) 13)) (* (($ |#2| $) 15) (($ $ |#2|) 16))) 
(((|GradedAlgebra&| |#1| |#2| |#3|) (CATEGORY |domain| (SIGNATURE |One| (|#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE |Zero| (|#1|))) (|GradedAlgebra| |#2| |#3|) (|CommutativeRing|) (|AbelianMonoid|)) (T |GradedAlgebra&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |One| (|#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE |Zero| (|#1|))) 
((~= (((|Boolean|) $ $) 7)) (|retractIfCan| (((|Union| |#1| "failed") $) 23)) (|retract| ((|#1| $) 22)) (|product| (($ $ $) 20)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|degree| ((|#2| $) 18)) (|coerce| (((|OutputForm|) $) 11) (($ |#1|) 24)) (|Zero| (($) 17 T CONST)) (|One| (($) 21 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 14) (($ $ $) 12)) (+ (($ $ $) 13)) (* (($ |#1| $) 16) (($ $ |#1|) 15))) 
(((|GradedAlgebra| |#1| |#2|) (|Category|) (|CommutativeRing|) (|AbelianMonoid|)) (T |GradedAlgebra|)) 
((|One| (*1 *1) (AND (|ofCategory| *1 (|GradedAlgebra| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (|product| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|GradedAlgebra| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|))))) 
(|Join| (|GradedModule| |t#1| |t#2|) (|RetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE (|One|) ($) |constant|) (SIGNATURE |product| ($ $ $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|GradedModule| |#1| |#2|) . T) ((|RetractableTo| |#1|) . T) ((|SetCategory|) . T)) 
((|writeDotGraph| (((|Void|) (|List| (|String|)) (|List| (|String|)) (|String|)) 19)) (|standardDotHeader| (((|List| (|String|))) 7)) (|sampleDotGraph| (((|List| (|String|))) 8)) (|dotview| (((|Void|) (|String|) (|String|)) 21)) (|dot2eps| (((|Void|) (|String|)) 20))) 
(((|Graphviz|) (CATEGORY |package| (SIGNATURE |standardDotHeader| ((|List| (|String|)))) (SIGNATURE |sampleDotGraph| ((|List| (|String|)))) (SIGNATURE |writeDotGraph| ((|Void|) (|List| (|String|)) (|List| (|String|)) (|String|))) (SIGNATURE |dot2eps| ((|Void|) (|String|))) (SIGNATURE |dotview| ((|Void|) (|String|) (|String|))))) (T |Graphviz|)) 
((|dotview| (*1 *2 *3 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Graphviz|)))) (|dot2eps| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Graphviz|)))) (|writeDotGraph| (*1 *2 *3 *3 *4) (AND (|isDomain| *3 (|List| (|String|))) (|isDomain| *4 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Graphviz|)))) (|sampleDotGraph| (*1 *2) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|Graphviz|)))) (|standardDotHeader| (*1 *2) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|Graphviz|))))) 
(CATEGORY |package| (SIGNATURE |standardDotHeader| ((|List| (|String|)))) (SIGNATURE |sampleDotGraph| ((|List| (|String|)))) (SIGNATURE |writeDotGraph| ((|Void|) (|List| (|String|)) (|List| (|String|)) (|String|))) (SIGNATURE |dot2eps| ((|Void|) (|String|))) (SIGNATURE |dotview| ((|Void|) (|String|) (|String|)))) 
((|nextSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) 18)) (|firstSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) 16))) 
(((|GrayCode|) (CATEGORY |package| (SIGNATURE |nextSubsetGray| ((|Vector| (|Vector| (|Integer|))) (|Vector| (|Vector| (|Integer|))) (|PositiveInteger|))) (SIGNATURE |firstSubsetGray| ((|Vector| (|Vector| (|Integer|))) (|PositiveInteger|))))) (T |GrayCode|)) 
((|firstSubsetGray| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Vector| (|Vector| (|Integer|)))) (|isDomain| *1 (|GrayCode|)))) (|nextSubsetGray| (*1 *2 *2 *3) (AND (|isDomain| *2 (|Vector| (|Vector| (|Integer|)))) (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *1 (|GrayCode|))))) 
(CATEGORY |package| (SIGNATURE |nextSubsetGray| ((|Vector| (|Vector| (|Integer|))) (|Vector| (|Vector| (|Integer|))) (|PositiveInteger|))) (SIGNATURE |firstSubsetGray| ((|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)))) 
((|screenResolution| (((|Integer|) (|Integer|)) 30) (((|Integer|)) 22)) (|minPoints| (((|Integer|) (|Integer|)) 26) (((|Integer|)) 18)) (|maxPoints| (((|Integer|) (|Integer|)) 28) (((|Integer|)) 20)) (|drawToScale| (((|Boolean|) (|Boolean|)) 12) (((|Boolean|)) 10)) (|clipPointsDefault| (((|Boolean|) (|Boolean|)) 11) (((|Boolean|)) 9)) (|adaptive| (((|Boolean|) (|Boolean|)) 24) (((|Boolean|)) 15))) 
(((|GraphicsDefaults|) (CATEGORY |package| (SIGNATURE |clipPointsDefault| ((|Boolean|))) (SIGNATURE |drawToScale| ((|Boolean|))) (SIGNATURE |clipPointsDefault| ((|Boolean|) (|Boolean|))) (SIGNATURE |drawToScale| ((|Boolean|) (|Boolean|))) (SIGNATURE |adaptive| ((|Boolean|))) (SIGNATURE |maxPoints| ((|Integer|))) (SIGNATURE |minPoints| ((|Integer|))) (SIGNATURE |screenResolution| ((|Integer|))) (SIGNATURE |adaptive| ((|Boolean|) (|Boolean|))) (SIGNATURE |maxPoints| ((|Integer|) (|Integer|))) (SIGNATURE |minPoints| ((|Integer|) (|Integer|))) (SIGNATURE |screenResolution| ((|Integer|) (|Integer|))))) (T |GraphicsDefaults|)) 
((|screenResolution| (*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GraphicsDefaults|)))) (|minPoints| (*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GraphicsDefaults|)))) (|maxPoints| (*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GraphicsDefaults|)))) (|adaptive| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GraphicsDefaults|)))) (|screenResolution| (*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GraphicsDefaults|)))) (|minPoints| (*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GraphicsDefaults|)))) (|maxPoints| (*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GraphicsDefaults|)))) (|adaptive| (*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GraphicsDefaults|)))) (|drawToScale| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GraphicsDefaults|)))) (|clipPointsDefault| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GraphicsDefaults|)))) (|drawToScale| (*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GraphicsDefaults|)))) (|clipPointsDefault| (*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GraphicsDefaults|))))) 
(CATEGORY |package| (SIGNATURE |clipPointsDefault| ((|Boolean|))) (SIGNATURE |drawToScale| ((|Boolean|))) (SIGNATURE |clipPointsDefault| ((|Boolean|) (|Boolean|))) (SIGNATURE |drawToScale| ((|Boolean|) (|Boolean|))) (SIGNATURE |adaptive| ((|Boolean|))) (SIGNATURE |maxPoints| ((|Integer|))) (SIGNATURE |minPoints| ((|Integer|))) (SIGNATURE |screenResolution| ((|Integer|))) (SIGNATURE |adaptive| ((|Boolean|) (|Boolean|))) (SIGNATURE |maxPoints| ((|Integer|) (|Integer|))) (SIGNATURE |minPoints| ((|Integer|) (|Integer|))) (SIGNATURE |screenResolution| ((|Integer|) (|Integer|)))) 
((~= (((|Boolean|) $ $) NIL)) (|units| (((|List| (|Float|)) $) 27) (((|List| (|Float|)) $ (|List| (|Float|))) 90)) (|ranges| (((|List| (|Segment| (|Float|))) $) 14) (((|List| (|Segment| (|Float|))) $ (|List| (|Segment| (|Float|)))) 87)) (|putColorInfo| (((|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|))) 42)) (|pointLists| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) 83)) (|point| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|)) 103)) (|makeGraphImage| (($ $) 82) (($ (|List| (|List| (|Point| (|DoubleFloat|))))) 93) (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|))) 92) (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|)) (|List| (|DrawOption|))) 94)) (|latex| (((|String|) $) NIL)) (|key| (((|Integer|) $) 65)) (|hash| (((|SingleInteger|) $) NIL)) (|graphImage| (($) 91)) (|figureUnits| (((|List| (|DoubleFloat|)) (|List| (|List| (|Point| (|DoubleFloat|))))) 52)) (|component| (((|Void|) $ (|List| (|Point| (|DoubleFloat|))) (|Palette|) (|Palette|) (|PositiveInteger|)) 97) (((|Void|) $ (|Point| (|DoubleFloat|))) 99) (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|) (|Palette|) (|PositiveInteger|)) 98)) (|coerce| (((|OutputForm|) $) 109) (($ (|List| (|List| (|Point| (|DoubleFloat|))))) 104)) (|appendPoint| (((|Void|) $ (|Point| (|DoubleFloat|))) 102)) (= (((|Boolean|) $ $) NIL))) 
(((|GraphImage|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |graphImage| ($)) (SIGNATURE |makeGraphImage| ($ $)) (SIGNATURE |makeGraphImage| ($ (|List| (|List| (|Point| (|DoubleFloat|)))))) (SIGNATURE |makeGraphImage| ($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|)))) (SIGNATURE |makeGraphImage| ($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|)) (|List| (|DrawOption|)))) (SIGNATURE |pointLists| ((|List| (|List| (|Point| (|DoubleFloat|)))) $)) (SIGNATURE |key| ((|Integer|) $)) (SIGNATURE |ranges| ((|List| (|Segment| (|Float|))) $)) (SIGNATURE |ranges| ((|List| (|Segment| (|Float|))) $ (|List| (|Segment| (|Float|))))) (SIGNATURE |units| ((|List| (|Float|)) $)) (SIGNATURE |units| ((|List| (|Float|)) $ (|List| (|Float|)))) (SIGNATURE |component| ((|Void|) $ (|List| (|Point| (|DoubleFloat|))) (|Palette|) (|Palette|) (|PositiveInteger|))) (SIGNATURE |component| ((|Void|) $ (|Point| (|DoubleFloat|)))) (SIGNATURE |component| ((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|) (|Palette|) (|PositiveInteger|))) (SIGNATURE |appendPoint| ((|Void|) $ (|Point| (|DoubleFloat|)))) (SIGNATURE |point| ((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|))) (SIGNATURE |coerce| ($ (|List| (|List| (|Point| (|DoubleFloat|)))))) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE |putColorInfo| ((|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)))) (SIGNATURE |figureUnits| ((|List| (|DoubleFloat|)) (|List| (|List| (|Point| (|DoubleFloat|))))))))) (T |GraphImage|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|GraphImage|)))) (|graphImage| (*1 *1) (|isDomain| *1 (|GraphImage|))) (|makeGraphImage| (*1 *1 *1) (|isDomain| *1 (|GraphImage|))) (|makeGraphImage| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|))))) (|isDomain| *1 (|GraphImage|)))) (|makeGraphImage| (*1 *1 *2 *3 *3 *4) (AND (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|))))) (|isDomain| *3 (|List| (|Palette|))) (|isDomain| *4 (|List| (|PositiveInteger|))) (|isDomain| *1 (|GraphImage|)))) (|makeGraphImage| (*1 *1 *2 *3 *3 *4 *5) (AND (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|))))) (|isDomain| *3 (|List| (|Palette|))) (|isDomain| *4 (|List| (|PositiveInteger|))) (|isDomain| *5 (|List| (|DrawOption|))) (|isDomain| *1 (|GraphImage|)))) (|pointLists| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|))))) (|isDomain| *1 (|GraphImage|)))) (|key| (*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GraphImage|)))) (|ranges| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Segment| (|Float|)))) (|isDomain| *1 (|GraphImage|)))) (|ranges| (*1 *2 *1 *2) (AND (|isDomain| *2 (|List| (|Segment| (|Float|)))) (|isDomain| *1 (|GraphImage|)))) (|units| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Float|))) (|isDomain| *1 (|GraphImage|)))) (|units| (*1 *2 *1 *2) (AND (|isDomain| *2 (|List| (|Float|))) (|isDomain| *1 (|GraphImage|)))) (|component| (*1 *2 *1 *3 *4 *4 *5) (AND (|isDomain| *3 (|List| (|Point| (|DoubleFloat|)))) (|isDomain| *4 (|Palette|)) (|isDomain| *5 (|PositiveInteger|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GraphImage|)))) (|component| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Point| (|DoubleFloat|))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GraphImage|)))) (|component| (*1 *2 *1 *3 *4 *4 *5) (AND (|isDomain| *3 (|Point| (|DoubleFloat|))) (|isDomain| *4 (|Palette|)) (|isDomain| *5 (|PositiveInteger|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GraphImage|)))) (|appendPoint| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Point| (|DoubleFloat|))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GraphImage|)))) (|point| (*1 *2 *1 *3 *4) (AND (|isDomain| *3 (|Point| (|DoubleFloat|))) (|isDomain| *4 (|Palette|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GraphImage|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|))))) (|isDomain| *1 (|GraphImage|)))) (|putColorInfo| (*1 *2 *2 *3) (AND (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|))))) (|isDomain| *3 (|List| (|Palette|))) (|isDomain| *1 (|GraphImage|)))) (|figureUnits| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|List| (|Point| (|DoubleFloat|))))) (|isDomain| *2 (|List| (|DoubleFloat|))) (|isDomain| *1 (|GraphImage|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |graphImage| ($)) (SIGNATURE |makeGraphImage| ($ $)) (SIGNATURE |makeGraphImage| ($ (|List| (|List| (|Point| (|DoubleFloat|)))))) (SIGNATURE |makeGraphImage| ($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|)))) (SIGNATURE |makeGraphImage| ($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|)) (|List| (|DrawOption|)))) (SIGNATURE |pointLists| ((|List| (|List| (|Point| (|DoubleFloat|)))) $)) (SIGNATURE |key| ((|Integer|) $)) (SIGNATURE |ranges| ((|List| (|Segment| (|Float|))) $)) (SIGNATURE |ranges| ((|List| (|Segment| (|Float|))) $ (|List| (|Segment| (|Float|))))) (SIGNATURE |units| ((|List| (|Float|)) $)) (SIGNATURE |units| ((|List| (|Float|)) $ (|List| (|Float|)))) (SIGNATURE |component| ((|Void|) $ (|List| (|Point| (|DoubleFloat|))) (|Palette|) (|Palette|) (|PositiveInteger|))) (SIGNATURE |component| ((|Void|) $ (|Point| (|DoubleFloat|)))) (SIGNATURE |component| ((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|) (|Palette|) (|PositiveInteger|))) (SIGNATURE |appendPoint| ((|Void|) $ (|Point| (|DoubleFloat|)))) (SIGNATURE |point| ((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|))) (SIGNATURE |coerce| ($ (|List| (|List| (|Point| (|DoubleFloat|)))))) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE |putColorInfo| ((|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)))) (SIGNATURE |figureUnits| ((|List| (|DoubleFloat|)) (|List| (|List| (|Point| (|DoubleFloat|)))))))) 
((- (($ $) NIL) (($ $ $) 11))) 
(((|GradedModule&| |#1| |#2| |#3|) (CATEGORY |domain| (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|))) (|GradedModule| |#2| |#3|) (|CommutativeRing|) (|AbelianMonoid|)) (T |GradedModule&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|degree| ((|#2| $) 18)) (|coerce| (((|OutputForm|) $) 11)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 14) (($ $ $) 12)) (+ (($ $ $) 13)) (* (($ |#1| $) 16) (($ $ |#1|) 15))) 
(((|GradedModule| |#1| |#2|) (|Category|) (|CommutativeRing|) (|AbelianMonoid|)) (T |GradedModule|)) 
((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|GradedModule| *3 *2)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *2 (|AbelianMonoid|)))) (|Zero| (*1 *1) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (* (*1 *1 *1 *2) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (- (*1 *1 *1) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (+ (*1 *1 *1 *1) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (- (*1 *1 *1 *1) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |degree| (|t#2| $)) (SIGNATURE (|Zero|) ($) |constant|) (SIGNATURE * ($ |t#1| $)) (SIGNATURE * ($ $ |t#1|)) (SIGNATURE - ($ $)) (SIGNATURE + ($ $ $)) (SIGNATURE - ($ $ $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) 88)) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) 86)) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) 58))) 
(((|GroebnerSolve| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |groebSolve| ((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|)))) (SIGNATURE |testDim| ((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|)))) (SIGNATURE |genericPosition| ((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))))) (|List| (|Symbol|)) (|GcdDomain|) (|GcdDomain|)) (T |GroebnerSolve|)) 
((|genericPosition| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| (|OrderedVariableList| *5))) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|GcdDomain|)) (|isDomain| *2 (|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| *5 *6))) (|:| |coords| (|List| (|Integer|))))) (|isDomain| *1 (|GroebnerSolve| *5 *6 *7)) (|isDomain| *3 (|List| (|DistributedMultivariatePolynomial| *5 *6))) (|ofCategory| *7 (|GcdDomain|)))) (|testDim| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| (|HomogeneousDistributedMultivariatePolynomial| *4 *5))) (|isDomain| *3 (|List| (|OrderedVariableList| *4))) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|GcdDomain|)) (|isDomain| *1 (|GroebnerSolve| *4 *5 *6)) (|ofCategory| *6 (|GcdDomain|)))) (|groebSolve| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| (|OrderedVariableList| *5))) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|GcdDomain|)) (|isDomain| *2 (|List| (|List| (|DistributedMultivariatePolynomial| *5 *6)))) (|isDomain| *1 (|GroebnerSolve| *5 *6 *7)) (|isDomain| *3 (|List| (|DistributedMultivariatePolynomial| *5 *6))) (|ofCategory| *7 (|GcdDomain|))))) 
(CATEGORY |package| (SIGNATURE |groebSolve| ((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|)))) (SIGNATURE |testDim| ((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|)))) (SIGNATURE |genericPosition| ((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))))) 
((|recip| (((|Union| $ "failed") $) 11)) (|conjugate| (($ $ $) 20)) (|commutator| (($ $ $) 21)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) 14)) (/ (($ $ $) 9)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) 19))) 
(((|Group&| |#1|) (CATEGORY |domain| (SIGNATURE |commutator| (|#1| |#1| |#1|)) (SIGNATURE |conjugate| (|#1| |#1| |#1|)) (SIGNATURE ^ (|#1| |#1| (|Integer|))) (SIGNATURE ** (|#1| |#1| (|Integer|))) (SIGNATURE / (|#1| |#1| |#1|)) (SIGNATURE |recip| ((|Union| |#1| "failed") |#1|)) (SIGNATURE ^ (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE ^ (|#1| |#1| (|PositiveInteger|))) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|)))) (|Group|)) (T |Group&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |commutator| (|#1| |#1| |#1|)) (SIGNATURE |conjugate| (|#1| |#1| |#1|)) (SIGNATURE ^ (|#1| |#1| (|Integer|))) (SIGNATURE ** (|#1| |#1| (|Integer|))) (SIGNATURE / (|#1| |#1| |#1|)) (SIGNATURE |recip| ((|Union| |#1| "failed") |#1|)) (SIGNATURE ^ (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE ^ (|#1| |#1| (|PositiveInteger|))) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|)))) 
((~= (((|Boolean|) $ $) 7)) (|sample| (($) 19 T CONST)) (|recip| (((|Union| $ "failed") $) 15)) (|one?| (((|Boolean|) $) 18)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 26)) (|hash| (((|SingleInteger|) $) 10)) (|conjugate| (($ $ $) 22)) (|commutator| (($ $ $) 21)) (|coerce| (((|OutputForm|) $) 11)) (^ (($ $ (|PositiveInteger|)) 12) (($ $ (|NonNegativeInteger|)) 16) (($ $ (|Integer|)) 23)) (|One| (($) 20 T CONST)) (= (((|Boolean|) $ $) 6)) (/ (($ $ $) 25)) (** (($ $ (|PositiveInteger|)) 13) (($ $ (|NonNegativeInteger|)) 17) (($ $ (|Integer|)) 24)) (* (($ $ $) 14))) 
(((|Group|) (|Category|)) (T |Group|)) 
((|inv| (*1 *1 *1) (|ofCategory| *1 (|Group|))) (/ (*1 *1 *1 *1) (|ofCategory| *1 (|Group|))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Group|)) (|isDomain| *2 (|Integer|)))) (^ (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Group|)) (|isDomain| *2 (|Integer|)))) (|conjugate| (*1 *1 *1 *1) (|ofCategory| *1 (|Group|))) (|commutator| (*1 *1 *1 *1) (|ofCategory| *1 (|Group|)))) 
(|Join| (|Monoid|) (CATEGORY |domain| (SIGNATURE |inv| ($ $)) (SIGNATURE / ($ $ $)) (SIGNATURE ** ($ $ (|Integer|))) (SIGNATURE ^ ($ $ (|Integer|))) (ATTRIBUTE |unitsKnown|) (SIGNATURE |conjugate| ($ $ $)) (SIGNATURE |commutator| ($ $ $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Monoid|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) NIL)) (|variable| (((|Symbol|) $) 17)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|truncate| (($ $ (|Fraction| (|Integer|))) NIL) (($ $ (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) NIL)) (|terms| (((|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|))) $) NIL)) (|tanh| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|tan| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL (|has| |#1| (|Field|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#1| (|Field|)))) (|sqrt| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sizeLess?| (((|Boolean|) $ $) NIL (|has| |#1| (|Field|)))) (|sinh| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sin| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) NIL)) (|sech| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sec| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sample| (($) NIL T CONST)) (|rem| (($ $ $) NIL (|has| |#1| (|Field|)))) (|reductum| (($ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|quo| (($ $ $) NIL (|has| |#1| (|Field|)))) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL (|has| |#1| (|Field|)))) (|prime?| (((|Boolean|) $) NIL (|has| |#1| (|Field|)))) (|pole?| (((|Boolean|) $) NIL)) (|pi| (($) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|order| (((|Fraction| (|Integer|)) $) NIL) (((|Fraction| (|Integer|)) $ (|Fraction| (|Integer|))) 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|#2|)))) NIL (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ $ (|List| |#2|) (|List| |#2|)) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ |#2| |#2|) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|Equation| |#2|)) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|List| (|Equation| |#2|))) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|entry?| (((|Boolean|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|entries| (((|List| |#2|) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#2| $ |#1|) 13) ((|#2| $ |#1| |#2|) NIL)) (|dictionary| (($) NIL) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (((|NonNegativeInteger|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) NIL (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL)) (|coerce| (((|OutputForm|) $) NIL (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))))) (|bag| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) NIL (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|GeneralSparseTable| |#1| |#2| |#3| |#4|) (|TableAggregate| |#1| |#2|) (|SetCategory|) (|SetCategory|) (|TableAggregate| |#1| |#2|) |#2|) (T |GeneralSparseTable|)) 
NIL 
(|TableAggregate| |#1| |#2|) 
((~= (((|Boolean|) $ $) NIL)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) NIL)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) NIL)) (|variables| (((|List| |#3|) $) NIL)) (|trivialIdeal?| (((|Boolean|) $) NIL)) (|triangular?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|stronglyReduced?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|stronglyReduce| ((|#4| |#4| $) NIL)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|select| (($ (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| |#4| "failed") $ |#3|) NIL)) (|sample| (($) NIL T CONST)) (|roughUnitIdeal?| (((|Boolean|) $) 26 (|has| |#1| (|IntegralDomain|)))) (|roughSubIdeal?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|roughEqualIdeals?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|roughBase?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) NIL)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) NIL)) (|retract| (($ (|List| |#4|)) NIL)) (|rest| (((|Union| $ "failed") $) 39)) (|removeZero| ((|#4| |#4| $) NIL)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|))))) (|remove| (($ |#4| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|)))) (($ (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) NIL (|has| |#1| (|IntegralDomain|)))) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) NIL)) (|reduceByQuasiMonic| ((|#4| |#4| $) NIL)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|)))) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| (|Mapping| |#4| |#4| |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) NIL)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) NIL)) (|parts| (((|List| |#4|) $) 16 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|normalized?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|mvar| ((|#3| $) 33)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#4|) $) 17 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#4| $) 25 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|))))) (|map!| (($ (|Mapping| |#4| |#4|) $) 23 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#4| |#4|) $) 21)) (|mainVariables| (((|List| |#3|) $) NIL)) (|mainVariable?| (((|Boolean|) |#3| $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL)) (|last| (((|Union| |#4| "failed") $) 37)) (|initials| (((|List| |#4|) $) NIL)) (|initiallyReduced?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|initiallyReduce| ((|#4| |#4| $) NIL)) (|infRittWu?| (((|Boolean|) $ $) NIL)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) NIL (|has| |#1| (|IntegralDomain|)))) (|headReduced?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|headReduce| ((|#4| |#4| $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|first| (((|Union| |#4| "failed") $) 35)) (|find| (((|Union| |#4| "failed") (|Mapping| (|Boolean|) |#4|) $) NIL)) (|extendIfCan| (((|Union| $ "failed") $ |#4|) 46)) (|extend| (($ $ |#4|) NIL)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ |#4| |#4|) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|Equation| |#4|)) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|List| (|Equation| |#4|))) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) 15)) (|empty| (($) 13)) (|degree| (((|NonNegativeInteger|) $) NIL)) (|count| (((|NonNegativeInteger|) |#4| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) 12)) (|convert| (((|InputForm|) $) NIL (|has| |#4| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#4|)) 20)) (|collectUpper| (($ $ |#3|) 42)) (|collectUnder| (($ $ |#3|) 43)) (|collectQuasiMonic| (($ $) NIL)) (|collect| (($ $ |#3|) NIL)) (|coerce| (((|OutputForm|) $) 31) (((|List| |#4|) $) 40)) (|coHeight| (((|NonNegativeInteger|) $) NIL (|has| |#3| (|Finite|)))) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) NIL) (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) NIL)) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|algebraicVariables| (((|List| |#3|) $) NIL)) (|algebraic?| (((|Boolean|) |#3| $) NIL)) (= (((|Boolean|) $ $) NIL)) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|GeneralTriangularSet| |#1| |#2| |#3| |#4|) (|TriangularSetCategory| |#1| |#2| |#3| |#4|) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|)) (T |GeneralTriangularSet|)) 
NIL 
(|TriangularSetCategory| |#1| |#2| |#3| |#4|) 
((|shiftHP| (((|Mapping| (|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|AlgebraicNumber|))) (|UnivariateFormalPowerSeries| (|AlgebraicNumber|)))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|)))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))))) (|:| |exprStream| (|Mapping| (|Stream| (|Expression| (|Integer|))) (|Expression| (|Integer|)) (|Symbol|))) (|:| A (|Mapping| (|AlgebraicNumber|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|AlgebraicNumber|)))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|AlgebraicNumber|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) (|Symbol|) (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| (|AlgebraicNumber|)) (|NonNegativeInteger|)))) (|List| (|GuessOption|))) (|Symbol|)) NIL (|has| (|AlgebraicNumber|) (|RetractableTo| (|Symbol|)))) (((|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|AlgebraicNumber|))) (|UnivariateFormalPowerSeries| (|AlgebraicNumber|)))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|)))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))))) (|:| |exprStream| (|Mapping| (|Stream| (|Expression| (|Integer|))) (|Expression| (|Integer|)) (|Symbol|))) (|:| A (|Mapping| (|AlgebraicNumber|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|AlgebraicNumber|)))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|AlgebraicNumber|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) (|Symbol|) (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| (|AlgebraicNumber|)) (|NonNegativeInteger|)))) (|List| (|GuessOption|))) NIL)) (|guessRec| (((|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|))) (|Symbol|)) NIL (|has| (|AlgebraicNumber|) (|RetractableTo| (|Symbol|)))) (((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|))) NIL) (((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|))) NIL)) (|guessRat| (((|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|))) (|Symbol|)) NIL (|has| (|AlgebraicNumber|) (|RetractableTo| (|Symbol|)))) (((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|))) NIL) (((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|))) NIL)) (|guessPade| (((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|))) NIL) (((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|))) NIL)) (|guessPRec| (((|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|))) (|Symbol|)) NIL (|has| (|AlgebraicNumber|) (|RetractableTo| (|Symbol|)))) (((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|))) NIL) (((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|))) NIL)) (|guessHolo| (((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|))) NIL) (((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|))) NIL)) (|guessHP| (((|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|))) (|Mapping| (|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|AlgebraicNumber|))) (|UnivariateFormalPowerSeries| (|AlgebraicNumber|)))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|)))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))))) (|:| |exprStream| (|Mapping| (|Stream| (|Expression| (|Integer|))) (|Expression| (|Integer|)) (|Symbol|))) (|:| A (|Mapping| (|AlgebraicNumber|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|AlgebraicNumber|)))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|AlgebraicNumber|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) (|Symbol|) (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| (|AlgebraicNumber|)) (|NonNegativeInteger|)))) (|List| (|GuessOption|)))) NIL)) (|guessExpRat| (((|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| 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(|Symbol|))) (|:| A (|Mapping| (|AlgebraicNumber|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|AlgebraicNumber|)))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|AlgebraicNumber|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) (|Symbol|) (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| (|AlgebraicNumber|)) (|NonNegativeInteger|)))) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessRec| ((|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessPRec| ((|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessRat| 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(|isDomain| *1 (|GuessAlgebraicNumber|)))) (|diffHP| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|AlgebraicNumber|))) (|UnivariateFormalPowerSeries| (|AlgebraicNumber|)))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|)))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))))) (|:| |exprStream| (|Mapping| (|Stream| (|Expression| (|Integer|))) (|Expression| (|Integer|)) (|Symbol|))) (|:| A (|Mapping| (|AlgebraicNumber|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|AlgebraicNumber|)))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|AlgebraicNumber|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) (|Symbol|) (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| (|AlgebraicNumber|)) (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessRat| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessRat| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessPRec| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessPRec| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessRec| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessRec| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessPade| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessPade| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessHolo| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessHolo| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessAlg| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessAlg| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessADE| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessADE| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessHP| (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| (|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|AlgebraicNumber|))) (|UnivariateFormalPowerSeries| (|AlgebraicNumber|)))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|)))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))))) (|:| |exprStream| (|Mapping| (|Stream| (|Expression| (|Integer|))) (|Expression| (|Integer|)) (|Symbol|))) (|:| A (|Mapping| (|AlgebraicNumber|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|AlgebraicNumber|)))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|AlgebraicNumber|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) (|Symbol|) (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| (|AlgebraicNumber|)) (|NonNegativeInteger|)))) (|List| (|GuessOption|)))) (|isDomain| *2 (|Mapping| (|List| (|Record| (|:| |function| 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(|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessBinRat| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessExpRat| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guessExpRat| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guess| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *4 (|List| (|Mapping| (|List| (|Record| (|:| |function| (|Expression| 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(|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|)))) (|guess| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|AlgebraicNumber|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessAlgebraicNumber|))))) 
(CATEGORY |package| (SIGNATURE |guess| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)))) (SIGNATURE |guess| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|)))) (SIGNATURE |guess| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|)))) (|List| (|Symbol|)))) (SIGNATURE |guess| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|)))) (|List| (|Symbol|)) (|List| (|GuessOption|)))) (SIGNATURE |guessExpRat| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)))) (SIGNATURE |guessExpRat| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|)))) (SIGNATURE |guessBinRat| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)))) (SIGNATURE |guessBinRat| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|)))) (IF (|has| (|AlgebraicNumber|) (|RetractableTo| (|Symbol|))) (IF (|has| (|AlgebraicNumber|) (|RetractableTo| (|Symbol|))) (PROGN (SIGNATURE |guessExpRat| ((|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessBinRat| ((|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|))) (|Symbol|)))) |noBranch|) |noBranch|) (SIGNATURE |guessHP| ((|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|))) (|Mapping| (|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|AlgebraicNumber|))) (|UnivariateFormalPowerSeries| (|AlgebraicNumber|)))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|)))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))))) (|:| |exprStream| (|Mapping| (|Stream| (|Expression| (|Integer|))) (|Expression| (|Integer|)) (|Symbol|))) (|:| A (|Mapping| (|AlgebraicNumber|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|AlgebraicNumber|)))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|AlgebraicNumber|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) (|Symbol|) (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| (|AlgebraicNumber|)) (|NonNegativeInteger|)))) (|List| (|GuessOption|))))) (SIGNATURE |guessADE| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)))) (SIGNATURE |guessADE| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|)))) (SIGNATURE |guessAlg| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)))) (SIGNATURE |guessAlg| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|)))) (SIGNATURE |guessHolo| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)))) (SIGNATURE |guessHolo| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|)))) (SIGNATURE |guessPade| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|)))) (SIGNATURE |guessPade| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)))) (SIGNATURE |guessRec| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)))) (SIGNATURE |guessRec| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|)))) (SIGNATURE |guessPRec| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|)))) (SIGNATURE |guessPRec| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)))) (SIGNATURE |guessRat| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)) (|List| (|GuessOption|)))) (SIGNATURE |guessRat| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|AlgebraicNumber|)))) (SIGNATURE |diffHP| ((|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|AlgebraicNumber|))) (|UnivariateFormalPowerSeries| (|AlgebraicNumber|)))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|)))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))))) (|:| |exprStream| (|Mapping| (|Stream| (|Expression| (|Integer|))) (|Expression| (|Integer|)) (|Symbol|))) (|:| A (|Mapping| (|AlgebraicNumber|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|AlgebraicNumber|)))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|AlgebraicNumber|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) (|Symbol|) (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| 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((F2EXPRR (((|Expression| (|Integer|)) |#1|) 11))) 
(((|GuessFiniteFunctions| |#1|) (CATEGORY |package| (SIGNATURE F2EXPRR ((|Expression| (|Integer|)) |#1|))) (|Join| (|FiniteFieldCategory|) (|ConvertibleTo| (|Integer|)))) (T |GuessFiniteFunctions|)) 
((F2EXPRR (*1 *2 *3) (AND (|isDomain| *2 (|Expression| (|Integer|))) (|isDomain| *1 (|GuessFiniteFunctions| *3)) (|ofCategory| *3 (|Join| (|FiniteFieldCategory|) (|ConvertibleTo| (|Integer|))))))) 
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|#1|)) (|UnivariateFormalPowerSeries| |#1|))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|)))) (|:| |exprStream| (|Mapping| (|Stream| (|Expression| (|Integer|))) (|Expression| (|Integer|)) (|Symbol|))) (|:| A (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| |#1|))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|)))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) (|Symbol|) (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| |#1|) (|NonNegativeInteger|)))) (|List| (|GuessOption|))) NIL))) 
(((|GuessFinite| |#1|) (CATEGORY |package| (SIGNATURE |guess| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|))) (SIGNATURE |guess| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|)))) (SIGNATURE |guess| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|)))) (|List| (|Symbol|)))) (SIGNATURE |guess| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|)))) (|List| (|Symbol|)) (|List| 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(|guessBinRat| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *7 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|ofType| *8 (|Mapping| *4 *7)) (|isDomain| *2 (|Mapping| (|List| (|Record| (|:| |function| *6) (|:| |order| (|NonNegativeInteger|)))) (|List| *4) (|List| (|GuessOption|)))) (|isDomain| *1 (|Guess| *4 *5 *6 *7 *8 *9)) (|ofCategory| *4 (|RetractableTo| *3)) (|ofCategory| *5 (|RetractableTo| *3)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|Join| (|FunctionSpace| (|Integer|)) (|IntegralDomain|) (|RetractableTo| *7) (|RetractableTo| *3) (|RetractableTo| (|Integer|)) (|CombinatorialOpsCategory|) (|PartialDifferentialRing| *3) (CATEGORY |domain| (SIGNATURE * ($ $ $)) (SIGNATURE / ($ $ $)) (SIGNATURE ** ($ $ $)) (SIGNATURE |numerator| ($ $)) (SIGNATURE |denominator| ($ $)) (SIGNATURE |ground?| ((|Boolean|) $))))) (|ofType| *9 (|Mapping| *6 *4)))) (|guessExpRat| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *7 (|Join| 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(|SparseUnivariatePolynomial| |#1|))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|)))) (|:| |exprStream| (|Mapping| (|Stream| |#3|) |#3| (|Symbol|))) (|:| A (|Mapping| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| |#2|))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|)))) (|:| AX (|Mapping| |#3| (|NonNegativeInteger|) (|Symbol|) |#3|)) (|:| C (|Mapping| (|List| |#2|) (|NonNegativeInteger|)))) (|List| (|GuessOption|)))) (SIGNATURE |shiftHP| ((|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| |#1|)) (|UnivariateFormalPowerSeries| |#1|))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|)))) (|:| |exprStream| (|Mapping| (|Stream| |#3|) |#3| (|Symbol|))) (|:| A (|Mapping| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| |#2|))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|)))) (|:| AX (|Mapping| |#3| (|NonNegativeInteger|) (|Symbol|) |#3|)) (|:| C (|Mapping| (|List| |#2|) (|NonNegativeInteger|)))) (|List| (|GuessOption|)))) (IF (|has| |#1| (|RetractableTo| (|Symbol|))) (IF (|has| |#2| (|RetractableTo| (|Symbol|))) (PROGN (SIGNATURE |shiftHP| ((|Mapping| (|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| |#1|)) (|UnivariateFormalPowerSeries| |#1|))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|)))) (|:| |exprStream| (|Mapping| 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(|List| (|GuessOption|))) (|Symbol|)))) |noBranch|) |noBranch|)) 
((|shiftHP| (((|Mapping| (|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|Fraction| (|Polynomial| (|Integer|))))) (|UnivariateFormalPowerSeries| (|Fraction| (|Polynomial| (|Integer|)))))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|)))))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| |exprStream| (|Mapping| (|Stream| (|Expression| (|Integer|))) (|Expression| (|Integer|)) (|Symbol|))) (|:| A (|Mapping| (|Polynomial| (|Integer|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|Polynomial| (|Integer|))))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|)))) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) (|Symbol|) (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| (|Polynomial| (|Integer|))) (|NonNegativeInteger|)))) (|List| (|GuessOption|))) (|Symbol|)) NIL (AND (|has| (|Fraction| (|Polynomial| (|Integer|))) (|RetractableTo| (|Symbol|))) (|has| (|Polynomial| (|Integer|)) (|RetractableTo| (|Symbol|))))) (((|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|Fraction| (|Polynomial| (|Integer|))))) (|UnivariateFormalPowerSeries| (|Fraction| (|Polynomial| (|Integer|)))))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|)))))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| |exprStream| (|Mapping| (|Stream| (|Expression| (|Integer|))) (|Expression| (|Integer|)) (|Symbol|))) (|:| A (|Mapping| (|Polynomial| (|Integer|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|Polynomial| (|Integer|))))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|)))) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) (|Symbol|) (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| (|Polynomial| (|Integer|))) (|NonNegativeInteger|)))) (|List| (|GuessOption|))) NIL)) (|guessRec| (((|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)) NIL (AND (|has| (|Fraction| (|Polynomial| (|Integer|))) (|RetractableTo| (|Symbol|))) (|has| (|Polynomial| (|Integer|)) (|RetractableTo| 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(|Polynomial| (|Integer|)))))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| |exprStream| (|Mapping| (|Stream| (|Expression| (|Integer|))) (|Expression| (|Integer|)) (|Symbol|))) (|:| A (|Mapping| (|Polynomial| (|Integer|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|Polynomial| (|Integer|))))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|)))) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) (|Symbol|) (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| (|Polynomial| (|Integer|))) (|NonNegativeInteger|)))) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessRec| ((|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessPRec| ((|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessRat| ((|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessADE| ((|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)))) |noBranch|) |noBranch|))) (T |GuessPolynomial|)) 
((|guessADE| (*1 *2 *3) (AND (|ofCategory| (|Fraction| (|Polynomial| (|Integer|))) (|RetractableTo| *3)) (|ofCategory| (|Polynomial| (|Integer|)) (|RetractableTo| *3)) (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|GuessOption|)))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessRat| (*1 *2 *3) (AND (|ofCategory| (|Fraction| (|Polynomial| (|Integer|))) (|RetractableTo| *3)) (|ofCategory| (|Polynomial| (|Integer|)) (|RetractableTo| *3)) (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|GuessOption|)))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessPRec| (*1 *2 *3) (AND (|ofCategory| (|Fraction| (|Polynomial| (|Integer|))) (|RetractableTo| *3)) (|ofCategory| (|Polynomial| (|Integer|)) (|RetractableTo| *3)) (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|GuessOption|)))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessRec| (*1 *2 *3) (AND (|ofCategory| (|Fraction| (|Polynomial| (|Integer|))) (|RetractableTo| *3)) (|ofCategory| (|Polynomial| (|Integer|)) (|RetractableTo| *3)) (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|GuessOption|)))) (|isDomain| *1 (|GuessPolynomial|)))) (|diffHP| (*1 *2 *3) (AND (|ofCategory| (|Fraction| (|Polynomial| (|Integer|))) (|RetractableTo| *3)) (|ofCategory| (|Polynomial| (|Integer|)) (|RetractableTo| *3)) (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| (|Record| (|:| |guessStream| 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(|Expression| (|Integer|)) *3)) (|:| A (|Mapping| (|Polynomial| (|Integer|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|Polynomial| (|Integer|))))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|)))) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) *3 (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| (|Polynomial| (|Integer|))) (|NonNegativeInteger|)))) (|List| (|GuessOption|)))) (|isDomain| *1 (|GuessPolynomial|)))) (|shiftHP| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|Fraction| (|Polynomial| (|Integer|))))) (|UnivariateFormalPowerSeries| (|Fraction| (|Polynomial| (|Integer|)))))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|)))))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| |exprStream| (|Mapping| (|Stream| (|Expression| (|Integer|))) (|Expression| (|Integer|)) (|Symbol|))) (|:| A (|Mapping| (|Polynomial| (|Integer|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|Polynomial| (|Integer|))))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|)))) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) (|Symbol|) (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| (|Polynomial| (|Integer|))) (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|diffHP| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 (|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|Fraction| (|Polynomial| (|Integer|))))) (|UnivariateFormalPowerSeries| (|Fraction| (|Polynomial| (|Integer|)))))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|)))))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| |exprStream| (|Mapping| (|Stream| (|Expression| (|Integer|))) (|Expression| (|Integer|)) (|Symbol|))) (|:| A (|Mapping| (|Polynomial| (|Integer|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|Polynomial| (|Integer|))))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|)))) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) (|Symbol|) (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| (|Polynomial| (|Integer|))) (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessRat| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessRat| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessPRec| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessPRec| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessRec| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessRec| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessPade| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessPade| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessHolo| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessHolo| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessAlg| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessAlg| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessADE| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessADE| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessHP| (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| (|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|Fraction| (|Polynomial| (|Integer|))))) (|UnivariateFormalPowerSeries| (|Fraction| (|Polynomial| (|Integer|)))))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|)))))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| |exprStream| (|Mapping| (|Stream| (|Expression| (|Integer|))) (|Expression| (|Integer|)) (|Symbol|))) (|:| A (|Mapping| (|Polynomial| (|Integer|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|Polynomial| (|Integer|))))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|)))) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) (|Symbol|) (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| (|Polynomial| (|Integer|))) (|NonNegativeInteger|)))) (|List| (|GuessOption|)))) (|isDomain| *2 (|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|GuessOption|)))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessBinRat| (*1 *2 *3) (AND (|ofCategory| (|Fraction| (|Polynomial| (|Integer|))) (|RetractableTo| *3)) (|ofCategory| (|Polynomial| (|Integer|)) (|RetractableTo| *3)) (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|GuessOption|)))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessExpRat| (*1 *2 *3) (AND (|ofCategory| (|Fraction| (|Polynomial| (|Integer|))) (|RetractableTo| *3)) (|ofCategory| (|Polynomial| (|Integer|)) (|RetractableTo| *3)) (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|GuessOption|)))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessBinRat| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessBinRat| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessExpRat| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guessExpRat| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guess| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *4 (|List| (|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|GuessOption|))))) (|isDomain| *5 (|List| (|Symbol|))) (|isDomain| *6 (|List| (|GuessOption|))) (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guess| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|List| (|Mapping| (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|GuessOption|))))) (|isDomain| *5 (|List| (|Symbol|))) (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guess| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|)))) (|guess| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessPolynomial|))))) 
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|guessHolo| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessPade| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessPade| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))))) (SIGNATURE |guessRec| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))))) (SIGNATURE |guessRec| ((|List| (|Record| (|:| |function| (|Expression| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessPRec| ((|List| (|Record| (|:| |function| 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(|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|)))))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| |exprStream| (|Mapping| (|Stream| (|Expression| (|Integer|))) (|Expression| (|Integer|)) (|Symbol|))) (|:| A (|Mapping| (|Polynomial| (|Integer|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|Polynomial| (|Integer|))))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|)))) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) (|Symbol|) (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| (|Polynomial| (|Integer|))) (|NonNegativeInteger|)))) (|List| (|GuessOption|)))) (SIGNATURE |shiftHP| ((|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|Fraction| (|Polynomial| (|Integer|))))) (|UnivariateFormalPowerSeries| (|Fraction| (|Polynomial| (|Integer|)))))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|)))))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| |exprStream| (|Mapping| (|Stream| (|Expression| (|Integer|))) (|Expression| (|Integer|)) (|Symbol|))) (|:| A (|Mapping| (|Polynomial| (|Integer|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|Polynomial| (|Integer|))))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|)))) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| AX (|Mapping| (|Expression| 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(|Polynomial| (|Integer|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| (|Polynomial| (|Integer|))))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|)))) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| (|Integer|))))))) (|:| AX (|Mapping| (|Expression| (|Integer|)) (|NonNegativeInteger|) (|Symbol|) (|Expression| (|Integer|)))) (|:| C (|Mapping| (|List| (|Polynomial| (|Integer|))) (|NonNegativeInteger|)))) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |diffHP| ((|Mapping| (|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|Fraction| (|Polynomial| (|Integer|))))) (|UnivariateFormalPowerSeries| (|Fraction| (|Polynomial| (|Integer|)))))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| (|Fraction| 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(|GuessOption|))) (|Symbol|)) NIL) (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) NIL) (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) NIL)) (|guessHolo| (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) NIL) (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) NIL)) (|guessHP| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Mapping| HPSPEC (|List| (|GuessOption|)))) NIL)) (|guessExpRat| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)) NIL) (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) NIL) (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) NIL)) (|guessBinRat| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)) NIL) (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) NIL) (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) NIL)) (|guessAlg| (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) NIL) (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) NIL)) (|guessADE| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)) NIL) (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) NIL) (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) NIL)) (|guess| (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (|List| (|Symbol|)) (|List| (|GuessOption|))) NIL) (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (|List| (|Symbol|))) NIL) (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) NIL) (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) NIL)) (|diffHP| (((|Mapping| HPSPEC (|List| (|GuessOption|))) (|Symbol|)) NIL) ((HPSPEC (|List| (|GuessOption|))) NIL))) 
(((|GuessUnivariatePolynomial| |#1|) (CATEGORY |package| (SIGNATURE |guess| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guess| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guess| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (|List| (|Symbol|)))) (SIGNATURE |guess| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (|List| (|Symbol|)) (|List| (|GuessOption|)))) (SIGNATURE |guessExpRat| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guessExpRat| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessBinRat| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guessBinRat| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessExpRat| ((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessBinRat| ((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessHP| ((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Mapping| HPSPEC (|List| (|GuessOption|))))) (SIGNATURE |guessADE| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guessADE| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessAlg| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guessAlg| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessHolo| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guessHolo| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessPade| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessPade| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guessRec| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guessRec| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessPRec| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessPRec| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guessRat| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessRat| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |diffHP| (HPSPEC (|List| (|GuessOption|)))) (SIGNATURE |shiftHP| (HPSPEC (|List| (|GuessOption|)))) (SIGNATURE |shiftHP| ((|Mapping| HPSPEC (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |diffHP| ((|Mapping| HPSPEC (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessRec| ((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessPRec| ((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessRat| ((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessADE| ((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)))) (|Symbol|)) (T |GuessUnivariatePolynomial|)) 
((|guessADE| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| *4 (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| *4 (|Integer|)))) (|List| (|GuessOption|)))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)) (|ofType| *4 *3))) (|guessRat| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| *4 (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| *4 (|Integer|)))) (|List| (|GuessOption|)))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)) (|ofType| *4 *3))) (|guessPRec| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| *4 (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| *4 (|Integer|)))) (|List| (|GuessOption|)))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)) (|ofType| *4 *3))) (|guessRec| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| *4 (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| *4 (|Integer|)))) (|List| (|GuessOption|)))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)) (|ofType| *4 *3))) (|diffHP| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| HPSPEC (|List| (|GuessOption|)))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)) (|ofType| *4 *3))) (|shiftHP| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| HPSPEC (|List| (|GuessOption|)))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)) (|ofType| *4 *3))) (|shiftHP| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 HPSPEC) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)) (|ofType| *4 (|Symbol|)))) (|diffHP| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|GuessOption|))) (|isDomain| *2 HPSPEC) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)) (|ofType| *4 (|Symbol|)))) (|guessRat| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *4 (|Integer|))))) (|ofType| *4 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *4 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)))) (|guessRat| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *5 (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|ofType| *5 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *5 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *5)))) (|guessPRec| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *4 (|Integer|))))) (|ofType| *4 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *4 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)))) (|guessPRec| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *5 (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|ofType| *5 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *5 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *5)))) (|guessRec| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *5 (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|ofType| *5 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *5 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *5)))) (|guessRec| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *4 (|Integer|))))) (|ofType| *4 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *4 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)))) (|guessPade| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *4 (|Integer|))))) (|ofType| *4 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *4 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)))) (|guessPade| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *5 (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|ofType| *5 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *5 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *5)))) (|guessHolo| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *5 (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|ofType| *5 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *5 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *5)))) (|guessHolo| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *4 (|Integer|))))) (|ofType| *4 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *4 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)))) (|guessAlg| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *5 (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|ofType| *5 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *5 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *5)))) (|guessAlg| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *4 (|Integer|))))) (|ofType| *4 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *4 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)))) (|guessADE| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *5 (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|ofType| *5 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *5 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *5)))) (|guessADE| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *4 (|Integer|))))) (|ofType| *4 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *4 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)))) (|guessHP| (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| HPSPEC (|List| (|GuessOption|)))) (|isDomain| *2 (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| *4 (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| *4 (|Integer|)))) (|List| (|GuessOption|)))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)) (|ofType| *4 (|Symbol|)))) (|guessBinRat| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| *4 (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| *4 (|Integer|)))) (|List| (|GuessOption|)))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)) (|ofType| *4 *3))) (|guessExpRat| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| *4 (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| *4 (|Integer|)))) (|List| (|GuessOption|)))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)) (|ofType| *4 *3))) (|guessBinRat| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *5 (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|ofType| *5 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *5 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *5)))) (|guessBinRat| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *4 (|Integer|))))) (|ofType| *4 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *4 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)))) (|guessExpRat| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *5 (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|ofType| *5 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *5 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *5)))) (|guessExpRat| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *4 (|Integer|))))) (|ofType| *4 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *4 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4)))) (|guess| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *4 (|List| (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| *7 (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| *7 (|Integer|)))) (|List| (|GuessOption|))))) (|isDomain| *5 (|List| (|Symbol|))) (|isDomain| *6 (|List| (|GuessOption|))) (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *7 (|Integer|))))) (|ofType| *7 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *7 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *7)))) (|guess| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|List| (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| *6 (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| *6 (|Integer|)))) (|List| (|GuessOption|))))) (|isDomain| *5 (|List| (|Symbol|))) (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *6 (|Integer|))))) (|ofType| *6 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *6 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *6)))) (|guess| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *5 (|Integer|))))) (|isDomain| *4 (|List| (|GuessOption|))) (|ofType| *5 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *5 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *5)))) (|guess| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|MyUnivariatePolynomial| *4 (|Integer|))))) (|ofType| *4 (|Symbol|)) (|isDomain| *2 (|List| (|Record| (|:| |function| (|MyExpression| *4 (|Integer|))) (|:| |order| (|NonNegativeInteger|))))) (|isDomain| *1 (|GuessUnivariatePolynomial| *4))))) 
(CATEGORY |package| (SIGNATURE |guess| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guess| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guess| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (|List| (|Symbol|)))) (SIGNATURE |guess| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (|List| (|Symbol|)) (|List| (|GuessOption|)))) (SIGNATURE |guessExpRat| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guessExpRat| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessBinRat| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guessBinRat| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessExpRat| ((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessBinRat| ((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessHP| ((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Mapping| HPSPEC (|List| (|GuessOption|))))) (SIGNATURE |guessADE| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guessADE| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessAlg| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guessAlg| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessHolo| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guessHolo| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessPade| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessPade| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guessRec| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guessRec| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessPRec| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessPRec| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |guessRat| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (SIGNATURE |guessRat| ((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))))) (SIGNATURE |diffHP| (HPSPEC (|List| (|GuessOption|)))) (SIGNATURE |shiftHP| (HPSPEC (|List| (|GuessOption|)))) (SIGNATURE |shiftHP| ((|Mapping| HPSPEC (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |diffHP| ((|Mapping| HPSPEC (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessRec| ((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessPRec| ((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessRat| ((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|))) (SIGNATURE |guessADE| ((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL)) (|retract| (((|Integer|) $) NIL) (((|Fraction| (|Integer|)) $) NIL)) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|pi| (($) 18)) (|one?| (((|Boolean|) $) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|convert| (((|Float|) $) 22) (((|DoubleFloat|) $) 25) (((|Fraction| (|SparseUnivariatePolynomial| (|Integer|))) $) 19) (((|InputForm|) $) 52)) (|coerce| (((|OutputForm|) $) 50) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) (((|DoubleFloat|) $) 24) (((|Float|) $) 21)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|associates?| (((|Boolean|) $ $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) 36 T CONST)) (|One| (($) 11 T CONST)) (= (((|Boolean|) $ $) NIL)) (/ (($ $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL))) 
(((|Pi|) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))) (|RealConstant|) (|CoercibleTo| (|DoubleFloat|)) (|CoercibleTo| (|Float|)) (|ConvertibleTo| (|Fraction| (|SparseUnivariatePolynomial| (|Integer|)))) (|ConvertibleTo| (|InputForm|)) (CATEGORY |domain| (SIGNATURE |pi| ($))))) (T |Pi|)) 
((|pi| (*1 *1) (|isDomain| *1 (|Pi|)))) 
(|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))) (|RealConstant|) (|CoercibleTo| (|DoubleFloat|)) (|CoercibleTo| (|Float|)) (|ConvertibleTo| (|Fraction| (|SparseUnivariatePolynomial| (|Integer|)))) (|ConvertibleTo| (|InputForm|)) (CATEGORY |domain| (SIGNATURE |pi| ($)))) 
((~= (((|Boolean|) $ $) NIL (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))))) (|table| (($) NIL) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL)) (|swap!| (((|Void|) $ |#1| |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setelt| ((|#2| $ |#1| |#2|) 16)) (|select!| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|select| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|search| (((|Union| |#2| "failed") |#1| $) 20)) (|sample| (($) NIL T CONST)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))))) (|remove!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| |#2| "failed") |#1| $) 18)) (|remove| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| ((|#2| $ |#1| |#2|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#2| $ |#1|) NIL)) (|parts| (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|List| |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| ((|#1| $) NIL (|has| |#1| (|OrderedSet|)))) (|members| (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|List| |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (((|Boolean|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|maxIndex| ((|#1| $) NIL (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ (|Mapping| |#2| |#2|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL) (($ (|Mapping| |#2| |#2|) $) NIL) (($ (|Mapping| |#2| |#2| |#2|) $ $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))))) (|keys| (((|List| |#1|) $) 13)) (|key?| (((|Boolean|) |#1| $) NIL)) (|inspect| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL)) (|insert!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL)) (|indices| (((|List| |#1|) $) NIL)) (|index?| (((|Boolean|) |#1| $) NIL)) (|hash| (((|SingleInteger|) $) NIL (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))))) (|first| ((|#2| $) NIL (|has| |#1| (|OrderedSet|)))) (|find| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL)) (|fill!| (($ $ |#2|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|extract!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) NIL (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ $ (|Equation| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ $ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ $ (|List| |#2|) (|List| |#2|)) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ |#2| |#2|) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|Equation| |#2|)) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|List| (|Equation| |#2|))) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|entry?| (((|Boolean|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|entries| (((|List| |#2|) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) 19)) (|elt| ((|#2| $ |#1|) NIL) ((|#2| $ |#1| |#2|) NIL)) (|dictionary| (($) NIL) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (((|NonNegativeInteger|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) NIL (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL)) (|coerce| (((|OutputForm|) $) NIL (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))))) (|bag| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 11 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))))) (|#| (((|NonNegativeInteger|) $) 15 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|HashTable| |#1| |#2| |#3|) (|Join| (|TableAggregate| |#1| |#2|) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|))) (|SetCategory|) (|SetCategory|) (|String|)) (T |HashTable|)) 
NIL 
(|Join| (|TableAggregate| |#1| |#2|) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|))) 
((|lfunc| (((|Integer|) (|Integer|) (|Integer|)) 7)) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) 11)) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) 22))) 
(((|HallBasis|) (CATEGORY |package| (SIGNATURE |lfunc| ((|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |inHallBasis?| ((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |generate| ((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|))))) (T |HallBasis|)) 
((|generate| (*1 *2 *3 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Vector| (|List| (|Integer|)))) (|isDomain| *1 (|HallBasis|)))) (|inHallBasis?| (*1 *2 *3 *3 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|HallBasis|)))) (|lfunc| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|HallBasis|))))) 
(CATEGORY |package| (SIGNATURE |lfunc| ((|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |inHallBasis?| ((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |generate| ((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|variables| (((|List| (|OrderedVariableList| |#1|)) $) NIL)) (|univariate| (((|SparseUnivariatePolynomial| $) $ (|OrderedVariableList| |#1|)) NIL) (((|SparseUnivariatePolynomial| |#2|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#2| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#2| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#2| (|IntegralDomain|)))) (|totalDegree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|List| (|OrderedVariableList| |#1|))) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL (|has| |#2| (|GcdDomain|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#2| (|GcdDomain|)))) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Integer|) "failed") $) NIL (|has| |#2| (|RetractableTo| (|Integer|)))) (((|Union| (|OrderedVariableList| |#1|) "failed") $) NIL)) (|retract| ((|#2| $) NIL) (((|Fraction| (|Integer|)) $) NIL (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Integer|) $) NIL (|has| |#2| (|RetractableTo| (|Integer|)))) (((|OrderedVariableList| |#1|) $) NIL)) (|resultant| (($ $ $ (|OrderedVariableList| |#1|)) NIL (|has| |#2| (|CommutativeRing|)))) (|reorder| (($ $ (|List| (|Integer|))) NIL)) (|reductum| (($ $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| |#2| 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(|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (AND (|has| (|OrderedVariableList| |#1|) (|PatternMatchable| (|Integer|))) (|has| |#2| (|PatternMatchable| (|Integer|)))))) (|one?| (((|Boolean|) $) NIL)) (|numberOfMonomials| (((|NonNegativeInteger|) $) NIL)) (|multivariate| (($ (|SparseUnivariatePolynomial| |#2|) (|OrderedVariableList| |#1|)) NIL) (($ (|SparseUnivariatePolynomial| $) (|OrderedVariableList| |#1|)) NIL)) (|monomials| (((|List| $) $) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monomial| (($ |#2| (|HomogeneousDirectProduct| (|#| |#1|) (|NonNegativeInteger|))) NIL) (($ $ (|OrderedVariableList| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| (|NonNegativeInteger|))) NIL)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ (|OrderedVariableList| |#1|)) NIL)) (|minimumDegree| (((|HomogeneousDirectProduct| (|#| |#1|) (|NonNegativeInteger|)) $) NIL) (((|NonNegativeInteger|) $ (|OrderedVariableList| |#1|)) NIL) (((|List| (|NonNegativeInteger|)) $ (|List| (|OrderedVariableList| |#1|))) NIL)) (|min| (($ $ $) NIL (|has| |#2| (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#2| (|OrderedSet|)))) (|mapExponents| (($ (|Mapping| (|HomogeneousDirectProduct| (|#| |#1|) (|NonNegativeInteger|)) (|HomogeneousDirectProduct| (|#| |#1|) (|NonNegativeInteger|))) $) NIL)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL)) (|mainVariable| (((|Union| (|OrderedVariableList| |#1|) "failed") $) NIL)) (|leadingMonomial| (($ $) NIL)) (|leadingCoefficient| ((|#2| $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| |#2| (|GcdDomain|)))) (|lcm| (($ (|List| $)) NIL (|has| |#2| (|GcdDomain|))) (($ $ $) NIL (|has| |#2| (|GcdDomain|)))) (|latex| (((|String|) $) NIL)) (|isTimes| (((|Union| (|List| $) "failed") $) NIL)) (|isPlus| (((|Union| (|List| $) "failed") $) NIL)) (|isExpt| (((|Union| (|Record| (|:| |var| (|OrderedVariableList| |#1|)) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|ground?| (((|Boolean|) $) NIL)) (|ground| ((|#2| $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|GcdDomain|)))) (|gcd| (($ (|List| $)) NIL (|has| |#2| (|GcdDomain|))) (($ $ $) NIL (|has| |#2| (|GcdDomain|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|exquo| (((|Union| $ "failed") $ |#2|) NIL (|has| |#2| (|IntegralDomain|))) (((|Union| $ "failed") $ $) NIL (|has| |#2| (|IntegralDomain|)))) (|eval| (($ $ (|List| (|Equation| $))) NIL) (($ $ (|Equation| $)) NIL) (($ $ $ $) NIL) (($ $ (|List| $) (|List| $)) NIL) (($ $ (|OrderedVariableList| |#1|) |#2|) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| |#2|)) NIL) (($ $ (|OrderedVariableList| |#1|) $) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| $)) NIL)) (|discriminant| (($ $ (|OrderedVariableList| |#1|)) NIL (|has| |#2| (|CommutativeRing|)))) (|differentiate| (($ $ (|OrderedVariableList| |#1|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|))) NIL) (($ $ (|OrderedVariableList| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| (|NonNegativeInteger|))) NIL)) (|degree| (((|HomogeneousDirectProduct| (|#| |#1|) (|NonNegativeInteger|)) $) NIL) (((|NonNegativeInteger|) $ (|OrderedVariableList| |#1|)) NIL) (((|List| (|NonNegativeInteger|)) $ (|List| (|OrderedVariableList| |#1|))) NIL)) (|convert| (((|Pattern| (|Float|)) $) NIL (AND (|has| (|OrderedVariableList| |#1|) (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Float|)))))) (((|Pattern| (|Integer|)) $) NIL (AND (|has| (|OrderedVariableList| |#1|) (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Integer|)))))) (((|InputForm|) $) NIL (AND (|has| (|OrderedVariableList| |#1|) (|ConvertibleTo| (|InputForm|))) (|has| |#2| (|ConvertibleTo| (|InputForm|)))))) (|content| ((|#2| $) NIL (|has| |#2| (|GcdDomain|))) (($ $ (|OrderedVariableList| |#1|)) NIL (|has| |#2| (|GcdDomain|)))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#2| (|PolynomialFactorizationExplicit|))))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ |#2|) NIL) (($ (|OrderedVariableList| |#1|)) NIL) (($ (|Fraction| (|Integer|))) NIL (OR (|has| |#2| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))))) (($ $) NIL (|has| |#2| (|IntegralDomain|)))) (|coefficients| (((|List| |#2|) $) NIL)) (|coefficient| ((|#2| $ (|HomogeneousDirectProduct| (|#| |#1|) (|NonNegativeInteger|))) NIL) (($ $ (|OrderedVariableList| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| (|NonNegativeInteger|))) NIL)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#2| (|PolynomialFactorizationExplicit|))) (|has| |#2| (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|CommutativeRing|)))) (|associates?| (((|Boolean|) $ $) NIL (|has| |#2| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($ $ (|OrderedVariableList| |#1|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|))) NIL) (($ $ (|OrderedVariableList| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| (|NonNegativeInteger|))) NIL)) (>= (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (/ (($ $ |#2|) NIL (|has| |#2| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#2| (|Algebra| (|Fraction| (|Integer|))))) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#2| (|Algebra| (|Fraction| (|Integer|))))) (($ |#2| $) NIL) (($ $ |#2|) NIL))) 
(((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Join| (|PolynomialCategory| |#2| (|HomogeneousDirectProduct| (|#| |#1|) (|NonNegativeInteger|)) (|OrderedVariableList| |#1|)) (CATEGORY |domain| (SIGNATURE |reorder| ($ $ (|List| (|Integer|)))))) (|List| (|Symbol|)) (|Ring|)) (T |HomogeneousDistributedMultivariatePolynomial|)) 
((|reorder| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|HomogeneousDistributedMultivariatePolynomial| *3 *4)) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|Ring|))))) 
(|Join| (|PolynomialCategory| |#2| (|HomogeneousDirectProduct| (|#| |#1|) (|NonNegativeInteger|)) (|OrderedVariableList| |#1|)) (CATEGORY |domain| (SIGNATURE |reorder| ($ $ (|List| (|Integer|)))))) 
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|#2| (|SetCategory|)))) (((|Union| |#2| "failed") $) NIL (|has| |#2| (|SetCategory|)))) (|retract| (((|Integer|) $) NIL (AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#2| (|SetCategory|)))) (((|Fraction| (|Integer|)) $) NIL (AND (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|)))) ((|#2| $) NIL (|has| |#2| (|SetCategory|)))) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|)))) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| $) (|Vector| $)) NIL (|has| |#2| (|Ring|))) (((|Matrix| |#2|) (|Matrix| $)) NIL (|has| |#2| (|Ring|)))) (|recip| (((|Union| $ "failed") $) NIL (|has| |#2| (|Monoid|)))) (|random| (($) NIL (|has| |#2| (|Finite|)))) (|qsetelt!| ((|#2| $ (|Integer|) |#2|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#2| $ (|Integer|)) 11)) (|positive?| (((|Boolean|) $) NIL (|has| |#2| (|OrderedRing|)))) (|parts| (((|List| |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|one?| (((|Boolean|) $) NIL (|has| |#2| (|Monoid|)))) (|negative?| (((|Boolean|) $) NIL (|has| |#2| (|OrderedRing|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL (OR (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedRing|))))) (|members| (((|List| |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|maxIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (OR (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedRing|))))) (|map!| (($ (|Mapping| |#2| |#2|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#2| |#2|) $) NIL)) (|lookup| (((|PositiveInteger|) $) NIL (|has| |#2| (|Finite|)))) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| |#2| (|SetCategory|)))) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|index| (($ (|PositiveInteger|)) NIL (|has| |#2| (|Finite|)))) (|hash| (((|SingleInteger|) $) NIL (|has| |#2| (|SetCategory|)))) (|first| ((|#2| $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|fill!| (($ $ |#2|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#2|))) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|Equation| |#2|)) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ |#2| |#2|) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|List| |#2|) (|List| |#2|)) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|enumerate| (((|List| $)) NIL (|has| |#2| (|Finite|)))) (|entry?| (((|Boolean|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|entries| (((|List| |#2|) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#2| $ (|Integer|) |#2|) NIL) ((|#2| $ (|Integer|)) NIL)) (|dot| ((|#2| $ $) NIL (|has| |#2| (|Ring|)))) (|directProduct| (($ (|Vector| |#2|)) NIL)) (|dimension| (((|CardinalNumber|)) NIL (|has| |#2| (|Field|)))) (|differentiate| (($ $) NIL (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) (($ $ (|NonNegativeInteger|)) NIL (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) (($ $ (|Symbol|)) NIL (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) NIL (|has| |#2| (|Ring|))) (($ $ (|Mapping| |#2| |#2|)) NIL (|has| |#2| (|Ring|)))) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|copy| (($ $) NIL)) (|coerce| (((|Vector| |#2|) $) NIL) (((|OutputForm|) $) NIL (|has| |#2| (|SetCategory|))) (($ (|Integer|)) NIL (OR (AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#2| (|SetCategory|))) (|has| |#2| (|Ring|)))) (($ (|Fraction| (|Integer|))) NIL (AND (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|)))) (($ |#2|) NIL (|has| |#2| (|SetCategory|)))) (|characteristic| (((|NonNegativeInteger|)) NIL (|has| |#2| (|Ring|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|abs| (($ $) NIL (|has| |#2| (|OrderedRing|)))) (^ (($ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|Monoid|))) (($ $ (|PositiveInteger|)) NIL (|has| |#2| (|Monoid|)))) (|Zero| (($) NIL (|has| |#2| (|CancellationAbelianMonoid|)) CONST)) (|One| (($) NIL (|has| |#2| (|Monoid|)) CONST)) (D (($ $) NIL (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) (($ $ (|NonNegativeInteger|)) NIL (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) (($ $ (|Symbol|)) NIL (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND 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(($ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|Monoid|))) (($ $ (|PositiveInteger|)) NIL (|has| |#2| (|Monoid|)))) (* (($ (|Integer|) $) NIL (|has| |#2| (|Ring|))) (($ $ $) NIL (|has| |#2| (|Monoid|))) (($ $ |#2|) NIL (|has| |#2| (|Monoid|))) (($ |#2| $) NIL (|has| |#2| (|Monoid|))) (($ (|NonNegativeInteger|) $) NIL (|has| |#2| (|CancellationAbelianMonoid|))) (($ (|PositiveInteger|) $) NIL (|has| |#2| (|AbelianSemiGroup|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|HomogeneousDirectProduct| |#1| |#2|) (|DirectProductCategory| |#1| |#2|) (|NonNegativeInteger|) (|OrderedAbelianMonoidSup|)) (T |HomogeneousDirectProduct|)) 
NIL 
(|DirectProductCategory| |#1| |#2|) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|sample| (($) NIL T CONST)) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|merge!| (($ $ $) 32)) (|merge| (($ $ $) 31)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|max| ((|#1| $) 26)) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|inspect| ((|#1| $) 27)) (|insert!| (($ |#1| $) 10)) (|heap| (($ (|List| |#1|)) 12)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|extract!| ((|#1| $) 23)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) 9)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|)))) (|bag| (($ (|List| |#1|)) 29)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 21 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|Heap| |#1|) (|Join| (|PriorityQueueAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |heap| ($ (|List| |#1|))) (SIGNATURE |bag| ($ (|List| |#1|))) (SIGNATURE |copy| ($ $)) (SIGNATURE |empty?| ((|Boolean|) $)) (SIGNATURE |empty| ($)) (SIGNATURE |eq?| ((|Boolean|) $ $)) (SIGNATURE |extract!| (|#1| $)) (SIGNATURE |insert!| ($ |#1| $)) (SIGNATURE |inspect| (|#1| $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (SIGNATURE |max| (|#1| $)) (SIGNATURE |merge| ($ $ $)) (SIGNATURE |merge!| ($ $ $)) (SIGNATURE |sample| ($)) (SIGNATURE |less?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |size?| ((|Boolean|) $ (|NonNegativeInteger|))) (IF (|has| $ (ATTRIBUTE |shallowlyMutable|)) (SIGNATURE |map!| ($ (|Mapping| |#1| |#1|) $)) |noBranch|) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |latex| ((|String|) $)) (SIGNATURE |hash| ((|SingleInteger|) $)) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE = ((|Boolean|) $ $)) (SIGNATURE ~= ((|Boolean|) $ $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (PROGN (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |#| ((|NonNegativeInteger|) $)) (SIGNATURE |parts| ((|List| |#1|) $)) (SIGNATURE |members| ((|List| |#1|) $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |member?| ((|Boolean|) |#1| $)) (SIGNATURE |count| ((|NonNegativeInteger|) |#1| $))) |noBranch|) |noBranch|))) (|OrderedSet|)) (T |Heap|)) 
((|eq?| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Heap| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|copy| (*1 *1 *1) (AND (|isDomain| *1 (|Heap| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|empty| (*1 *1) (AND (|isDomain| *1 (|Heap| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|empty?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Heap| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|less?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Heap| *4)) (|ofCategory| *4 (|OrderedSet|)))) (|more?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Heap| *4)) (|ofCategory| *4 (|OrderedSet|)))) (|size?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Heap| *4)) (|ofCategory| *4 (|OrderedSet|)))) (|sample| (*1 *1) (AND (|isDomain| *1 (|Heap| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|#| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Heap| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|Heap| *3)))) (|map!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|Heap| *3)))) (|any?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Heap| *4)))) (|every?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Heap| *4)))) (|count| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Heap| *4)))) (|parts| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|Heap| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|members| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|Heap| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|count| (*1 *2 *3 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Heap| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|OrderedSet|)))) (|member?| (*1 *2 *3 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Heap| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|OrderedSet|)))) (|latex| (*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|Heap| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|OrderedSet|)))) (|hash| (*1 *2 *1) (AND (|isDomain| *2 (|SingleInteger|)) (|isDomain| *1 (|Heap| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|OrderedSet|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|Heap| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|OrderedSet|)))) (= (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Heap| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|OrderedSet|)))) (~= (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Heap| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|OrderedSet|)))) (|bag| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|Heap| *3)))) (|extract!| (*1 *2 *1) (AND (|isDomain| *1 (|Heap| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|insert!| (*1 *1 *2 *1) (AND (|isDomain| *1 (|Heap| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|inspect| (*1 *2 *1) (AND (|isDomain| *1 (|Heap| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|max| (*1 *2 *1) (AND (|isDomain| *1 (|Heap| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|merge| (*1 *1 *1 *1) (AND (|isDomain| *1 (|Heap| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|merge!| (*1 *1 *1 *1) (AND (|isDomain| *1 (|Heap| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|heap| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|Heap| *3))))) 
(|Join| (|PriorityQueueAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |heap| ($ (|List| |#1|))) (SIGNATURE |bag| ($ (|List| |#1|))) (SIGNATURE |copy| ($ $)) (SIGNATURE |empty?| ((|Boolean|) $)) (SIGNATURE |empty| ($)) (SIGNATURE |eq?| ((|Boolean|) $ $)) (SIGNATURE |extract!| (|#1| $)) (SIGNATURE |insert!| ($ |#1| $)) (SIGNATURE |inspect| (|#1| $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (SIGNATURE |max| (|#1| $)) (SIGNATURE |merge| ($ $ $)) (SIGNATURE |merge!| ($ $ $)) (SIGNATURE |sample| ($)) (SIGNATURE |less?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |size?| ((|Boolean|) $ (|NonNegativeInteger|))) (IF (|has| $ (ATTRIBUTE |shallowlyMutable|)) (SIGNATURE |map!| ($ (|Mapping| |#1| |#1|) $)) |noBranch|) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |latex| ((|String|) $)) (SIGNATURE |hash| ((|SingleInteger|) $)) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE = ((|Boolean|) $ $)) (SIGNATURE ~= ((|Boolean|) $ $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (PROGN (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |#| ((|NonNegativeInteger|) $)) (SIGNATURE |parts| ((|List| |#1|) $)) (SIGNATURE |members| ((|List| |#1|) $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |member?| ((|Boolean|) |#1| $)) (SIGNATURE |count| ((|NonNegativeInteger|) |#1| $))) |noBranch|) |noBranch|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|reduce| (($ $) 69)) (|principal?| (((|Boolean|) $) NIL)) (|latex| (((|String|) $) NIL)) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) 43)) (|hash| (((|SingleInteger|) $) NIL)) (|generator| (((|Union| |#4| "failed") $) 105)) (|divisor| (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) 76) (($ |#4|) 32) (($ |#1| |#1|) 113) (($ |#1| |#1| (|Integer|)) NIL) (($ |#4| |#2| |#2| |#2| |#1|) 125)) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) 45)) (|coerce| (((|OutputForm|) $) 100)) (|Zero| (($) 33 T CONST)) (= (((|Boolean|) $ $) 107)) (- (($ $) 72) (($ $ $) NIL)) (+ (($ $ $) 70)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 73))) 
(((|HyperellipticFiniteDivisor| |#1| |#2| |#3| |#4|) (|FiniteDivisorCategory| |#1| |#2| |#3| |#4|) (|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|)) (T |HyperellipticFiniteDivisor|)) 
NIL 
(|FiniteDivisorCategory| |#1| |#2| |#3| |#4|) 
((|lintgcd| (((|Integer|) (|List| (|Integer|))) 28)) (|gcdprim| ((|#1| (|List| |#1|)) 56)) (|gcdcofactprim| (((|List| |#1|) (|List| |#1|)) 57)) (|gcdcofact| (((|List| |#1|) (|List| |#1|)) 59)) (|gcd| ((|#1| (|List| |#1|)) 58)) (|content| (((|List| (|Integer|)) (|List| |#1|)) 31))) 
(((|HeuGcd| |#1|) (CATEGORY |package| (SIGNATURE |gcd| (|#1| (|List| |#1|))) (SIGNATURE |gcdprim| (|#1| (|List| |#1|))) (SIGNATURE |gcdcofact| ((|List| |#1|) (|List| |#1|))) (SIGNATURE |gcdcofactprim| ((|List| |#1|) (|List| |#1|))) (SIGNATURE |content| ((|List| (|Integer|)) (|List| |#1|))) (SIGNATURE |lintgcd| ((|Integer|) (|List| (|Integer|))))) (|UnivariatePolynomialCategory| (|Integer|))) (T |HeuGcd|)) 
((|lintgcd| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|HeuGcd| *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)))) (|content| (*1 *2 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Integer|))) (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|HeuGcd| *4)))) (|gcdcofactprim| (*1 *2 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))) (|isDomain| *1 (|HeuGcd| *3)))) (|gcdcofact| (*1 *2 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))) (|isDomain| *1 (|HeuGcd| *3)))) (|gcdprim| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|isDomain| *1 (|HeuGcd| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Integer|))))) (|gcd| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|isDomain| *1 (|HeuGcd| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(CATEGORY |package| (SIGNATURE |gcd| (|#1| (|List| |#1|))) (SIGNATURE |gcdprim| (|#1| (|List| |#1|))) (SIGNATURE |gcdcofact| ((|List| |#1|) (|List| |#1|))) (SIGNATURE |gcdcofactprim| ((|List| |#1|) (|List| |#1|))) (SIGNATURE |content| ((|List| (|Integer|)) (|List| |#1|))) (SIGNATURE |lintgcd| ((|Integer|) (|List| (|Integer|))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|wholePart| (((|Integer|) $) NIL (|has| (|Integer|) (|EuclideanDomain|)))) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|toint| (((|Integer|) (|String|)) 19)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Integer|) (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Integer|) (|PolynomialFactorizationExplicit|)))) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sign| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedIntegralDomain|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL) (((|Union| (|Symbol|) "failed") $) NIL (|has| (|Integer|) (|RetractableTo| (|Symbol|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| (|Integer|) (|RetractableTo| (|Integer|)))) (((|Union| (|Integer|) "failed") $) NIL (|has| (|Integer|) (|RetractableTo| (|Integer|))))) (|retract| (((|Integer|) $) NIL) (((|Symbol|) $) NIL (|has| (|Integer|) (|RetractableTo| (|Symbol|)))) (((|Fraction| (|Integer|)) $) NIL (|has| (|Integer|) (|RetractableTo| (|Integer|)))) (((|Integer|) $) NIL (|has| (|Integer|) (|RetractableTo| (|Integer|))))) (|rem| (($ $ $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| (|Integer|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| (|Integer|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| (|Integer|)) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) NIL (|has| (|Integer|) (|IntegerNumberSystem|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|positive?| (((|Boolean|) $) NIL (|has| (|Integer|) (|OrderedIntegralDomain|)))) (|patternMatch| (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (|has| (|Integer|) (|PatternMatchable| (|Integer|)))) (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (|has| (|Integer|) (|PatternMatchable| (|Float|))))) (|one?| (((|Boolean|) $) NIL)) (|numerator| (($ $) NIL)) (|numer| (((|Integer|) $) NIL)) (|nextItem| (((|Union| $ "failed") $) NIL (|has| (|Integer|) (|StepThrough|)))) (|negative?| (((|Boolean|) $) NIL (|has| (|Integer|) (|OrderedIntegralDomain|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|min| (($ $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|map| (($ (|Mapping| (|Integer|) (|Integer|)) $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|init| (($) NIL (|has| (|Integer|) (|StepThrough|)) CONST)) (|hex| (($ (|Fraction| (|Integer|))) 8)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|fractionPart| (($ $) NIL (|has| (|Integer|) (|EuclideanDomain|))) (((|Fraction| (|Integer|)) $) NIL)) (|floor| (((|Integer|) $) NIL (|has| (|Integer|) (|IntegerNumberSystem|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Integer|) (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Integer|) (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|eval| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) NIL (|has| (|Integer|) (|Evalable| (|Integer|)))) (($ $ (|Integer|) (|Integer|)) NIL (|has| (|Integer|) (|Evalable| (|Integer|)))) (($ $ (|Equation| (|Integer|))) NIL (|has| (|Integer|) (|Evalable| (|Integer|)))) (($ $ (|List| (|Equation| (|Integer|)))) NIL (|has| (|Integer|) (|Evalable| (|Integer|)))) (($ $ (|List| (|Symbol|)) (|List| (|Integer|))) NIL (|has| (|Integer|) (|InnerEvalable| (|Symbol|) (|Integer|)))) (($ $ (|Symbol|) (|Integer|)) NIL (|has| (|Integer|) (|InnerEvalable| (|Symbol|) (|Integer|))))) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|elt| (($ $ (|Integer|)) NIL (|has| (|Integer|) (|Eltable| (|Integer|) (|Integer|))))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|differentiate| (($ $) NIL (|has| (|Integer|) (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|Integer|) (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| (|Integer|) (|Integer|)) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| (|Integer|) (|Integer|))) NIL)) (|denominator| (($ $) NIL)) (|denom| (((|Integer|) $) NIL)) (|convert| (((|Pattern| (|Integer|)) $) NIL (|has| (|Integer|) (|ConvertibleTo| (|Pattern| (|Integer|))))) (((|Pattern| (|Float|)) $) NIL (|has| (|Integer|) (|ConvertibleTo| (|Pattern| (|Float|))))) (((|InputForm|) $) NIL (|has| (|Integer|) (|ConvertibleTo| (|InputForm|)))) (((|Float|) $) NIL (|has| (|Integer|) (|RealConstant|))) (((|DoubleFloat|) $) NIL (|has| (|Integer|) (|RealConstant|)))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| (|Integer|) (|PolynomialFactorizationExplicit|))))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) 7) (($ (|Integer|)) NIL) (($ (|Symbol|)) NIL (|has| (|Integer|) (|RetractableTo| (|Symbol|)))) (((|Fraction| (|Integer|)) $) NIL) (((|RadixExpansion| 16) $) 9)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| (|Integer|) (|PolynomialFactorizationExplicit|))) (|has| (|Integer|) (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|ceiling| (((|Integer|) $) NIL (|has| (|Integer|) (|IntegerNumberSystem|)))) (|associates?| (((|Boolean|) $ $) NIL)) (|abs| (($ $) NIL (|has| (|Integer|) (|OrderedIntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($ $) NIL (|has| (|Integer|) (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|Integer|) (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| (|Integer|) (|Integer|)) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| (|Integer|) (|Integer|))) NIL)) (>= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (/ (($ $ $) NIL) (($ (|Integer|) (|Integer|)) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ (|Integer|) $) NIL) (($ $ (|Integer|)) NIL))) 
(((|HexadecimalExpansion|) (|Join| (|QuotientFieldCategory| (|Integer|)) (CATEGORY |domain| (SIGNATURE |coerce| ((|Fraction| (|Integer|)) $)) (SIGNATURE |coerce| ((|RadixExpansion| 16) $)) (SIGNATURE |fractionPart| ((|Fraction| (|Integer|)) $)) (SIGNATURE |hex| ($ (|Fraction| (|Integer|)))) (SIGNATURE |toint| ((|Integer|) (|String|)))))) (T |HexadecimalExpansion|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|HexadecimalExpansion|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|RadixExpansion| 16)) (|isDomain| *1 (|HexadecimalExpansion|)))) (|fractionPart| (*1 *2 *1) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|HexadecimalExpansion|)))) (|hex| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|HexadecimalExpansion|)))) (|toint| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|HexadecimalExpansion|))))) 
(|Join| (|QuotientFieldCategory| (|Integer|)) (CATEGORY |domain| (SIGNATURE |coerce| ((|Fraction| (|Integer|)) $)) (SIGNATURE |coerce| ((|RadixExpansion| 16) $)) (SIGNATURE |fractionPart| ((|Fraction| (|Integer|)) $)) (SIGNATURE |hex| ($ (|Fraction| (|Integer|)))) (SIGNATURE |toint| ((|Integer|) (|String|))))) 
((|members| (((|List| |#2|) $) 22)) (|member?| (((|Boolean|) |#2| $) 27)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 20)) (|eval| (($ $ (|List| (|Equation| |#2|))) 12) (($ $ (|Equation| |#2|)) NIL) (($ $ |#2| |#2|) NIL) (($ $ (|List| |#2|) (|List| |#2|)) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) 21) (((|NonNegativeInteger|) |#2| $) 25)) (|coerce| (((|OutputForm|) $) 36)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 19)) (= (((|Boolean|) $ $) 30)) (|#| (((|NonNegativeInteger|) $) 16))) 
(((|HomogeneousAggregate&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE = ((|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#2|) (|List| |#2|))) (SIGNATURE |eval| (|#1| |#1| |#2| |#2|)) (SIGNATURE |eval| (|#1| |#1| (|Equation| |#2|))) (SIGNATURE |eval| (|#1| |#1| (|List| (|Equation| |#2|)))) (SIGNATURE |member?| ((|Boolean|) |#2| |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) |#2| |#1|)) (SIGNATURE |members| ((|List| |#2|) |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) |#1|))) (|HomogeneousAggregate| |#2|) (|Type|)) (T |HomogeneousAggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE = ((|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#2|) (|List| |#2|))) (SIGNATURE |eval| (|#1| |#1| |#2| |#2|)) (SIGNATURE |eval| (|#1| |#1| (|Equation| |#2|))) (SIGNATURE |eval| (|#1| |#1| (|List| (|Equation| |#2|)))) (SIGNATURE |member?| ((|Boolean|) |#2| |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) |#2| |#1|)) (SIGNATURE |members| ((|List| |#2|) |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) |#1|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|sample| (($) 7 T CONST)) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|HomogeneousAggregate| |#1|) (|Category|) (|Type|)) (T |HomogeneousAggregate|)) 
((|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|HomogeneousAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|map!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|HomogeneousAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|any?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|HomogeneousAggregate| *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|every?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|HomogeneousAggregate| *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|count| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|HomogeneousAggregate| *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|parts| (*1 *2 *1) (AND (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|HomogeneousAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|List| *3)))) (|members| (*1 *2 *1) (AND (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|HomogeneousAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|List| *3)))) (|count| (*1 *2 *3 *1) (AND (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|HomogeneousAggregate| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|member?| (*1 *2 *3 *1) (AND (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|HomogeneousAggregate| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) 
(|Join| (|Aggregate|) (CATEGORY |domain| (IF (|has| |t#1| (|SetCategory|)) (ATTRIBUTE (|SetCategory|)) |noBranch|) (IF (|has| |t#1| (|SetCategory|)) (IF (|has| |t#1| (|Evalable| |t#1|)) (ATTRIBUTE (|Evalable| |t#1|)) |noBranch|) |noBranch|) (SIGNATURE |map| ($ (|Mapping| |t#1| |t#1|) $)) (IF (|has| $ (ATTRIBUTE |shallowlyMutable|)) (SIGNATURE |map!| ($ (|Mapping| |t#1| |t#1|) $)) |noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (PROGN (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |t#1|) $)) (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |t#1|) $)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |t#1|) $)) (SIGNATURE |parts| ((|List| |t#1|) $)) (SIGNATURE |members| ((|List| |t#1|) $)) (IF (|has| |t#1| (|SetCategory|)) (PROGN (SIGNATURE |count| ((|NonNegativeInteger|) |t#1| $)) (SIGNATURE |member?| ((|Boolean|) |t#1| $))) |noBranch|)) |noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|exprex| (((|String|) (|OutputForm|)) 40)) (|display| (((|Void|) (|String|)) 29)) (|coerceS| (((|String|) (|OutputForm|)) 25)) (|coerceL| (((|String|) (|OutputForm|)) 26)) (|coerce| (((|OutputForm|) $) NIL) (((|String|) (|OutputForm|)) 24)) (= (((|Boolean|) $ $) NIL))) 
(((|HTMLFormat|) (|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE |coerce| ((|String|) (|OutputForm|))) (SIGNATURE |coerceS| ((|String|) (|OutputForm|))) (SIGNATURE |coerceL| ((|String|) (|OutputForm|))) (SIGNATURE |exprex| ((|String|) (|OutputForm|))) (SIGNATURE |display| ((|Void|) (|String|)))))) (T |HTMLFormat|)) 
((|coerce| (*1 *2 *3) (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|String|)) (|isDomain| *1 (|HTMLFormat|)))) (|coerceS| (*1 *2 *3) (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|String|)) (|isDomain| *1 (|HTMLFormat|)))) (|coerceL| (*1 *2 *3) (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|String|)) (|isDomain| *1 (|HTMLFormat|)))) (|exprex| (*1 *2 *3) (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|String|)) (|isDomain| *1 (|HTMLFormat|)))) (|display| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|HTMLFormat|))))) 
(|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE |coerce| ((|String|) (|OutputForm|))) (SIGNATURE |coerceS| ((|String|) (|OutputForm|))) (SIGNATURE |coerceL| ((|String|) (|OutputForm|))) (SIGNATURE |exprex| ((|String|) (|OutputForm|))) (SIGNATURE |display| ((|Void|) (|String|))))) 
((|tanh| (($ $) 15)) (|sinh| (($ $) 24)) (|sech| (($ $) 12)) (|csch| (($ $) 10)) (|coth| (($ $) 17)) (|cosh| (($ $) 22))) 
(((|HyperbolicFunctionCategory&| |#1|) (CATEGORY |domain| (SIGNATURE |cosh| (|#1| |#1|)) (SIGNATURE |coth| (|#1| |#1|)) (SIGNATURE |csch| (|#1| |#1|)) (SIGNATURE |sech| (|#1| |#1|)) (SIGNATURE |sinh| (|#1| |#1|)) (SIGNATURE |tanh| (|#1| |#1|))) (|HyperbolicFunctionCategory|)) (T |HyperbolicFunctionCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |cosh| (|#1| |#1|)) (SIGNATURE |coth| (|#1| |#1|)) (SIGNATURE |csch| (|#1| |#1|)) (SIGNATURE |sech| (|#1| |#1|)) (SIGNATURE |sinh| (|#1| |#1|)) (SIGNATURE |tanh| (|#1| |#1|))) 
((|tanh| (($ $) 11)) (|sinh| (($ $) 10)) (|sech| (($ $) 9)) (|csch| (($ $) 8)) (|coth| (($ $) 7)) (|cosh| (($ $) 6))) 
(((|HyperbolicFunctionCategory|) (|Category|)) (T |HyperbolicFunctionCategory|)) 
((|tanh| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|))) (|sinh| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|))) (|sech| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|))) (|csch| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|))) (|coth| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|))) (|cosh| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|)))) 
(|Join| (CATEGORY |domain| (SIGNATURE |cosh| ($ $)) (SIGNATURE |coth| ($ $)) (SIGNATURE |csch| ($ $)) (SIGNATURE |sech| ($ $)) (SIGNATURE |sinh| ($ $)) (SIGNATURE |tanh| ($ $)))) 
((|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) 42))) 
(((|InnerAlgFactor| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)))) (|Field|) (|UnivariatePolynomialCategory| |#1|) (|Join| (|Field|) (|CharacteristicZero|) (|MonogenicAlgebra| |#1| |#2|)) (|UnivariatePolynomialCategory| |#3|)) (T |InnerAlgFactor|)) 
((|factor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| (|Factored| *6) *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Field|)) (|ofCategory| *7 (|Join| (|Field|) (|CharacteristicZero|) (|MonogenicAlgebra| *5 *6))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|InnerAlgFactor| *5 *6 *7 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *7))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) NIL) (((|List| $) (|SparseUnivariatePolynomial| $)) NIL) (((|List| $) (|Polynomial| $)) NIL)) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) NIL) (($ (|SparseUnivariatePolynomial| $)) NIL) (($ (|Polynomial| $)) NIL)) (|zero?| (((|Boolean|) $) 36)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|trueEqual| (((|Boolean|) $ $) 62)) (|tower| (((|List| (|Kernel| $)) $) 46)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|subst| (($ $ (|Equation| $)) NIL) (($ $ (|List| (|Equation| $))) NIL) (($ $ (|List| (|Kernel| $)) (|List| $)) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sqrt| (($ $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sample| (($) NIL T CONST)) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) NIL) (((|List| $) (|SparseUnivariatePolynomial| $)) NIL) (((|List| $) (|Polynomial| $)) NIL)) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) NIL) (($ (|SparseUnivariatePolynomial| $)) NIL) (($ (|Polynomial| $)) NIL)) (|retractIfCan| (((|Union| (|Kernel| $) "failed") $) NIL) (((|Union| (|Integer|) "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL)) (|retract| (((|Kernel| $) $) NIL) (((|Integer|) $) NIL) (((|Fraction| (|Integer|)) $) 48)) (|rem| (($ $ $) NIL)) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| (|Integer|)) (|Matrix| $)) NIL) (((|Record| (|:| |mat| (|Matrix| (|Fraction| (|Integer|)))) (|:| |vec| (|Vector| (|Fraction| (|Integer|))))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| (|Fraction| (|Integer|))) (|Matrix| $)) NIL)) (|reduce| (($ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|paren| (($ $) NIL) (($ (|List| $)) NIL)) (|operators| (((|List| (|BasicOperator|)) $) NIL)) (|operator| (((|BasicOperator|) (|BasicOperator|)) NIL)) (|one?| (((|Boolean|) $) 39)) (|odd?| (((|Boolean|) $) NIL (|has| $ (|RetractableTo| (|Integer|))))) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) 34)) (|nthRoot| (($ $ (|Integer|)) NIL)) (|norm| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) 77) (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) 53) (($ $ (|Kernel| $)) 66) (($ $ (|List| (|Kernel| $))) 67)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) 64 (|has| $ (|Ring|)))) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|map| (($ (|Mapping| $ $) (|Kernel| $)) NIL)) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) NIL)) 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(((|InnerAlgebraicNumber|) (|Join| (|ExpressionSpace|) (|AlgebraicallyClosedField|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))) (|LinearlyExplicitRingOver| (|Integer|)) (|RealConstant|) (|LinearlyExplicitRingOver| (|Fraction| (|Integer|))) (|CharacteristicZero|) (|ConvertibleTo| (|Complex| (|Float|))) (|DifferentialRing|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)))) (SIGNATURE |numer| ((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $)) (SIGNATURE |denom| ((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $)) (SIGNATURE |reduce| ($ $)) (SIGNATURE |trueEqual| ((|Boolean|) $ $)) (SIGNATURE |norm| ((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $))) (SIGNATURE |norm| ((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $)))) (SIGNATURE |norm| ($ $ (|Kernel| $))) (SIGNATURE |norm| ($ $ (|List| (|Kernel| $))))))) (T |InnerAlgebraicNumber|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| (|InnerAlgebraicNumber|)))) (|isDomain| *1 (|InnerAlgebraicNumber|)))) (|numer| (*1 *2 *1) (AND (|isDomain| *2 (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| (|InnerAlgebraicNumber|)))) (|isDomain| *1 (|InnerAlgebraicNumber|)))) (|denom| (*1 *2 *1) (AND (|isDomain| *2 (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| (|InnerAlgebraicNumber|)))) (|isDomain| *1 (|InnerAlgebraicNumber|)))) (|reduce| (*1 *1 *1) (|isDomain| *1 (|InnerAlgebraicNumber|))) (|trueEqual| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|InnerAlgebraicNumber|)))) (|norm| (*1 *2 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|InnerAlgebraicNumber|))) (|isDomain| *3 (|Kernel| (|InnerAlgebraicNumber|))) (|isDomain| *1 (|InnerAlgebraicNumber|)))) (|norm| (*1 *2 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|InnerAlgebraicNumber|))) (|isDomain| *3 (|List| (|Kernel| (|InnerAlgebraicNumber|)))) (|isDomain| *1 (|InnerAlgebraicNumber|)))) (|norm| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Kernel| (|InnerAlgebraicNumber|))) (|isDomain| *1 (|InnerAlgebraicNumber|)))) (|norm| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Kernel| (|InnerAlgebraicNumber|)))) (|isDomain| *1 (|InnerAlgebraicNumber|))))) 
(|Join| (|ExpressionSpace|) (|AlgebraicallyClosedField|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))) (|LinearlyExplicitRingOver| (|Integer|)) (|RealConstant|) (|LinearlyExplicitRingOver| (|Fraction| (|Integer|))) (|CharacteristicZero|) (|ConvertibleTo| (|Complex| (|Float|))) (|DifferentialRing|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)))) (SIGNATURE |numer| ((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $)) (SIGNATURE |denom| ((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $)) (SIGNATURE |reduce| ($ $)) (SIGNATURE |trueEqual| ((|Boolean|) $ $)) (SIGNATURE |norm| ((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $))) (SIGNATURE |norm| ((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $)))) (SIGNATURE |norm| ($ $ (|Kernel| $))) (SIGNATURE |norm| ($ $ (|List| (|Kernel| $)))))) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) NIL) (((|Boolean|) $) NIL (|has| |#1| (|OrderedSet|)))) (|sort!| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $) NIL (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|has| |#1| (|OrderedSet|))))) (|sort| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) NIL) (($ $) NIL (|has| |#1| (|OrderedSet|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setelt| ((|#1| $ (|Integer|) |#1|) 25 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) NIL T CONST)) (|reverse!| (($ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) NIL)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|remove| (($ |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| ((|#1| $ (|Integer|) |#1|) 22 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#1| $ (|Integer|)) 21)) (|position| (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) NIL) (((|Integer|) |#1| $) NIL (|has| |#1| (|SetCategory|))) (((|Integer|) |#1| $ (|Integer|)) NIL (|has| |#1| (|SetCategory|)))) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|new| (($ 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NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|first| ((|#1| $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) NIL)) (|fill!| (($ $ |#1|) 10 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|entry?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|entries| (((|List| |#1|) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) 13)) (|elt| ((|#1| $ (|Integer|) |#1|) NIL) ((|#1| $ (|Integer|)) 24) (($ $ (|UniversalSegment| (|Integer|))) NIL)) (|delete| (($ $ (|Integer|)) NIL) (($ $ (|UniversalSegment| (|Integer|))) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copyInto!| (($ $ $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) NIL)) (|concat| (($ $ |#1|) NIL) (($ |#1| $) NIL) (($ $ $) NIL) (($ (|List| $)) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (|#| (((|NonNegativeInteger|) $) 9 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|IndexedOneDimensionalArray| |#1| |#2|) (|OneDimensionalArrayAggregate| |#1|) (|Type|) (|Integer|)) (T |IndexedOneDimensionalArray|)) 
NIL 
(|OneDimensionalArrayAggregate| |#1|) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) NIL)) (|setRow!| (($ $ (|Integer|) (|IndexedOneDimensionalArray| |#1| |#3|)) NIL)) (|setColumn!| (($ $ (|Integer|) (|IndexedOneDimensionalArray| |#1| |#2|)) NIL)) (|sample| (($) NIL T CONST)) (|row| (((|IndexedOneDimensionalArray| |#1| |#3|) $ (|Integer|)) NIL)) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) NIL)) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) NIL)) (|parts| (((|List| |#1|) $) NIL)) (|nrows| (((|NonNegativeInteger|) $) NIL)) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) NIL)) (|ncols| (((|NonNegativeInteger|) $) NIL)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minRowIndex| (((|Integer|) $) NIL)) (|minColIndex| (((|Integer|) $) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|maxRowIndex| (((|Integer|) $) NIL)) (|maxColIndex| (((|Integer|) $) NIL)) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|fill!| (($ $ |#1|) NIL)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#1| $ (|Integer|) (|Integer|)) NIL) ((|#1| $ (|Integer|) (|Integer|) |#1|) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) NIL)) (|column| (((|IndexedOneDimensionalArray| |#1| |#2|) $ (|Integer|)) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|IndexedTwoDimensionalArray| |#1| |#2| |#3|) (|TwoDimensionalArrayCategory| |#1| (|IndexedOneDimensionalArray| |#1| |#3|) (|IndexedOneDimensionalArray| |#1| |#2|)) (|Type|) (|Integer|) (|Integer|)) (T |IndexedTwoDimensionalArray|)) 
NIL 
(|TwoDimensionalArrayCategory| |#1| (|IndexedOneDimensionalArray| |#1| |#3|) (|IndexedOneDimensionalArray| |#1| |#2|)) 
((|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) 27)) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) 34)) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) 83))) 
(((|ChineseRemainderToolsForIntegralBases| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |factorList| ((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |listConjugateBases| ((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |chineseRemainder| ((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)))) (|FiniteFieldCategory|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| |#2|)) (T |ChineseRemainderToolsForIntegralBases|)) 
((|chineseRemainder| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|List| (|Record| (|:| |basis| (|Matrix| *7)) (|:| |basisDen| *7) (|:| |basisInv| (|Matrix| *7))))) (|isDomain| *5 (|NonNegativeInteger|)) (|ofCategory| *8 (|UnivariatePolynomialCategory| *7)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|ofCategory| *6 (|FiniteFieldCategory|)) (|isDomain| *2 (|Record| (|:| |basis| (|Matrix| *7)) (|:| |basisDen| *7) (|:| |basisInv| (|Matrix| *7)))) (|isDomain| *1 (|ChineseRemainderToolsForIntegralBases| *6 *7 *8)))) (|listConjugateBases| (*1 *2 *3 *4 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|FiniteFieldCategory|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|List| (|Record| (|:| |basis| (|Matrix| *6)) (|:| |basisDen| *6) (|:| |basisInv| (|Matrix| *6))))) (|isDomain| *1 (|ChineseRemainderToolsForIntegralBases| *5 *6 *7)) (|isDomain| *3 (|Record| (|:| |basis| (|Matrix| *6)) (|:| |basisDen| *6) (|:| |basisInv| (|Matrix| *6)))) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)))) (|factorList| (*1 *2 *3 *4 *4 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *3))) (|isDomain| *1 (|ChineseRemainderToolsForIntegralBases| *3 *5 *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |factorList| ((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |listConjugateBases| ((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |chineseRemainder| ((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)))) 
((|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) 60)) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) 25)) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) 30)) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) 42)) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) 50) (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) 47)) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) 29)) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) 18))) 
(((|IntegralBasisTools| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |diagonalProduct| (|#1| (|Matrix| |#1|))) (SIGNATURE |matrixGcd| (|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|))) (SIGNATURE |divideIfCan!| (|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|))) (SIGNATURE |leastPower| ((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |idealiser| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |idealiser| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|)) (SIGNATURE |idealiserMatrix| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |moduleSum| ((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))))) (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $)))) (|UnivariatePolynomialCategory| |#1|) (|FramedAlgebra| |#1| |#2|)) (T |IntegralBasisTools|)) 
((|moduleSum| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Record| (|:| |basis| (|Matrix| *3)) (|:| |basisDen| *3) (|:| |basisInv| (|Matrix| *3)))) (|ofCategory| *3 (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $))))) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *1 (|IntegralBasisTools| *3 *4 *5)) (|ofCategory| *5 (|FramedAlgebra| *3 *4)))) (|idealiserMatrix| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $))))) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *1 (|IntegralBasisTools| *3 *4 *5)) (|ofCategory| *5 (|FramedAlgebra| *3 *4)))) (|idealiser| (*1 *2 *2 *2 *3) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $))))) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *1 (|IntegralBasisTools| *3 *4 *5)) (|ofCategory| *5 (|FramedAlgebra| *3 *4)))) (|idealiser| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $))))) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *1 (|IntegralBasisTools| *3 *4 *5)) (|ofCategory| *5 (|FramedAlgebra| *3 *4)))) (|leastPower| (*1 *2 *2 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *3 (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $))))) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *1 (|IntegralBasisTools| *3 *4 *5)) (|ofCategory| *5 (|FramedAlgebra| *3 *4)))) (|divideIfCan!| (*1 *2 *3 *3 *2 *4) (AND (|isDomain| *3 (|Matrix| *2)) (|isDomain| *4 (|Integer|)) (|ofCategory| *2 (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $))))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *2)) (|isDomain| *1 (|IntegralBasisTools| *2 *5 *6)) (|ofCategory| *6 (|FramedAlgebra| *2 *5)))) (|matrixGcd| (*1 *2 *3 *2 *4) (AND (|isDomain| *3 (|Matrix| *2)) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *2 (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $))))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *2)) (|isDomain| *1 (|IntegralBasisTools| *2 *5 *6)) (|ofCategory| *6 (|FramedAlgebra| *2 *5)))) (|diagonalProduct| (*1 *2 *3) (AND (|isDomain| *3 (|Matrix| *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $))))) (|isDomain| *1 (|IntegralBasisTools| *2 *4 *5)) (|ofCategory| *5 (|FramedAlgebra| *2 *4))))) 
(CATEGORY |package| (SIGNATURE |diagonalProduct| (|#1| (|Matrix| |#1|))) (SIGNATURE |matrixGcd| (|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|))) (SIGNATURE |divideIfCan!| (|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|))) (SIGNATURE |leastPower| ((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |idealiser| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |idealiser| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|)) (SIGNATURE |idealiserMatrix| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |moduleSum| ((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))))) 
((~= (((|Boolean|) $ $) NIL)) (~ (($ $) NIL)) (|xor| (($ $ $) 35)) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) $) NIL (|has| (|Boolean|) (|OrderedSet|))) (((|Boolean|) (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $) NIL)) (|sort!| (($ $) NIL (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|has| (|Boolean|) (|OrderedSet|)))) (($ (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sort| (($ $) NIL (|has| (|Boolean|) (|OrderedSet|))) (($ (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setelt| (((|Boolean|) $ (|UniversalSegment| (|Integer|)) (|Boolean|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Boolean|) $ (|Integer|) (|Boolean|)) 36 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select| (($ (|Mapping| (|Boolean|) (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) NIL T CONST)) (|reverse!| (($ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) NIL)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Boolean|) (|SetCategory|))))) (|remove| (($ (|Mapping| (|Boolean|) (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Boolean|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Boolean|) (|SetCategory|))))) (|reduce| (((|Boolean|) (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Boolean|) (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $ (|Boolean|)) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Boolean|) (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $ (|Boolean|) (|Boolean|)) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Boolean|) (|SetCategory|))))) (|qsetelt!| (((|Boolean|) $ (|Integer|) (|Boolean|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| (((|Boolean|) $ (|Integer|)) NIL)) (|position| (((|Integer|) (|Boolean|) $ (|Integer|)) NIL (|has| (|Boolean|) (|SetCategory|))) (((|Integer|) (|Boolean|) $) NIL (|has| (|Boolean|) (|SetCategory|))) (((|Integer|) (|Mapping| (|Boolean|) (|Boolean|)) $) NIL)) (|parts| (((|List| (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|or| (($ $ $) 33)) (|not| (($ $) NIL)) (|nor| (($ $ $) NIL)) (|new| (($ (|NonNegativeInteger|) (|Boolean|)) 23)) (|nand| (($ $ $) NIL)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) 8 (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL)) (|merge| (($ $ $) NIL (|has| (|Boolean|) (|OrderedSet|))) (($ (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $ $) NIL)) (|members| (((|List| (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|Boolean|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Boolean|) (|SetCategory|))))) (|maxIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL)) (|map!| (($ (|Mapping| (|Boolean|) (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| (|Boolean|) (|Boolean|) (|Boolean|)) $ $) 30) (($ (|Mapping| (|Boolean|) (|Boolean|)) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL)) (|insert| (($ $ $ (|Integer|)) NIL) (($ (|Boolean|) $ (|Integer|)) NIL)) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|first| (((|Boolean|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|find| (((|Union| (|Boolean|) "failed") (|Mapping| (|Boolean|) (|Boolean|)) $) NIL)) (|fill!| (($ $ (|Boolean|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Boolean|)) (|List| (|Boolean|))) NIL (AND (|has| (|Boolean|) (|Evalable| (|Boolean|))) (|has| (|Boolean|) (|SetCategory|)))) (($ $ (|Boolean|) (|Boolean|)) NIL (AND (|has| (|Boolean|) (|Evalable| (|Boolean|))) (|has| (|Boolean|) (|SetCategory|)))) (($ $ (|Equation| (|Boolean|))) NIL (AND (|has| (|Boolean|) (|Evalable| (|Boolean|))) (|has| (|Boolean|) (|SetCategory|)))) (($ $ (|List| (|Equation| (|Boolean|)))) NIL (AND (|has| (|Boolean|) (|Evalable| (|Boolean|))) (|has| (|Boolean|) (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|entry?| (((|Boolean|) (|Boolean|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Boolean|) (|SetCategory|))))) (|entries| (((|List| (|Boolean|)) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) 24)) (|elt| (($ $ (|UniversalSegment| (|Integer|))) NIL) (((|Boolean|) $ (|Integer|)) 18) (((|Boolean|) $ (|Integer|) (|Boolean|)) NIL)) (|delete| (($ $ (|UniversalSegment| (|Integer|))) NIL) (($ $ (|Integer|)) NIL)) (|count| (((|NonNegativeInteger|) (|Boolean|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Boolean|) (|SetCategory|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copyInto!| (($ $ $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) 25)) (|convert| (((|InputForm|) $) NIL (|has| (|Boolean|) (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| (|Boolean|))) NIL)) (|concat| (($ (|List| $)) NIL) (($ $ $) NIL) (($ (|Boolean|) $) NIL) (($ $ (|Boolean|)) NIL)) (|coerce| (((|OutputForm|) $) 22)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|Boolean|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|and| (($ $ $) 31)) (^ (($ $) NIL)) (|\\/| (($ $ $) NIL)) (|Or| (($ $ $) 39)) (|Not| (($ $) 37)) (|And| (($ $ $) 38)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 26)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 27)) (|/\\| (($ $ $) NIL)) (|#| (((|NonNegativeInteger|) $) 10 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|IndexedBits| |#1|) (|Join| (|BitAggregate|) (CATEGORY |domain| (SIGNATURE |Not| ($ $)) (SIGNATURE |Or| ($ $ $)) (SIGNATURE |And| ($ $ $)))) (|Integer|)) (T |IndexedBits|)) 
((|Not| (*1 *1 *1) (AND (|isDomain| *1 (|IndexedBits| *2)) (|ofType| *2 (|Integer|)))) (|Or| (*1 *1 *1 *1) (AND (|isDomain| *1 (|IndexedBits| *2)) (|ofType| *2 (|Integer|)))) (|And| (*1 *1 *1 *1) (AND (|isDomain| *1 (|IndexedBits| *2)) (|ofType| *2 (|Integer|))))) 
(|Join| (|BitAggregate|) (CATEGORY |domain| (SIGNATURE |Not| ($ $)) (SIGNATURE |Or| ($ $ $)) (SIGNATURE |And| ($ $ $)))) 
((|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) 34)) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) 30) ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) 21)) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) 45)) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) 54))) 
(((|IntegralBasisPolynomialTools| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |mapUnivariate| (|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |mapUnivariate| ((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|)) (SIGNATURE |mapUnivariateIfCan| ((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |mapMatrixIfCan| ((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|)))) (SIGNATURE |mapBivariate| ((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|))) (|Ring|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| |#2|) (|Ring|)) (T |IntegralBasisPolynomialTools|)) 
((|mapBivariate| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *7 *5)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *7 (|Ring|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *7))) (|isDomain| *1 (|IntegralBasisPolynomialTools| *5 *6 *4 *7)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *6)))) (|mapMatrixIfCan| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Mapping| (|Union| *5 "failed") *8)) (|isDomain| *4 (|Matrix| (|SparseUnivariatePolynomial| *8))) (|ofCategory| *5 (|Ring|)) (|ofCategory| *8 (|Ring|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|Matrix| *6)) (|isDomain| *1 (|IntegralBasisPolynomialTools| *5 *6 *7 *8)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)))) (|mapUnivariateIfCan| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Mapping| (|Union| *5 "failed") *7)) (|isDomain| *4 (|SparseUnivariatePolynomial| *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *7 (|Ring|)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *5)) (|isDomain| *1 (|IntegralBasisPolynomialTools| *5 *2 *6 *7)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *2)))) (|mapUnivariate| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *7 *5)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *7 (|Ring|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|SparseUnivariatePolynomial| *7)) (|isDomain| *1 (|IntegralBasisPolynomialTools| *5 *4 *6 *7)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *4)))) (|mapUnivariate| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *5 *7)) (|isDomain| *4 (|SparseUnivariatePolynomial| *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *7 (|Ring|)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *5)) (|isDomain| *1 (|IntegralBasisPolynomialTools| *5 *2 *6 *7)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *2))))) 
(CATEGORY |package| (SIGNATURE |mapUnivariate| (|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |mapUnivariate| ((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|)) (SIGNATURE |mapUnivariateIfCan| ((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |mapMatrixIfCan| ((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|)))) (SIGNATURE |mapBivariate| ((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|))) 
((~= (((|Boolean|) $ $) NIL)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|fullDisplay| (((|Void|) $) 18)) (|elt| (((|String|) $ (|Symbol|)) 22)) (|display| (((|Void|) $) 14)) (|coerce| (((|OutputForm|) $) 20) (($ (|String|)) 19)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 8)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 7))) 
(((|IndexCard|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |elt| ((|String|) $ (|Symbol|))) (SIGNATURE |display| ((|Void|) $)) (SIGNATURE |fullDisplay| ((|Void|) $)) (SIGNATURE |coerce| ($ (|String|)))))) (T |IndexCard|)) 
((|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|String|)) (|isDomain| *1 (|IndexCard|)))) (|display| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|IndexCard|)))) (|fullDisplay| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|IndexCard|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|IndexCard|))))) 
(|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |elt| ((|String|) $ (|Symbol|))) (SIGNATURE |display| ((|Void|) $)) (SIGNATURE |fullDisplay| ((|Void|) $)) (SIGNATURE |coerce| ($ (|String|))))) 
((|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) 19)) (|commonDenominator| ((|#1| |#4|) 10)) (|clearDenominator| ((|#3| |#4|) 17))) 
(((|InnerCommonDenominator| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |commonDenominator| (|#1| |#4|)) (SIGNATURE |clearDenominator| (|#3| |#4|)) (SIGNATURE |splitDenominator| ((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|))) (|IntegralDomain|) (|QuotientFieldCategory| |#1|) (|FiniteLinearAggregate| |#1|) (|FiniteLinearAggregate| |#2|)) (T |InnerCommonDenominator|)) 
((|splitDenominator| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|QuotientFieldCategory| *4)) (|isDomain| *2 (|Record| (|:| |num| *6) (|:| |den| *4))) (|isDomain| *1 (|InnerCommonDenominator| *4 *5 *6 *3)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|ofCategory| *3 (|FiniteLinearAggregate| *5)))) (|clearDenominator| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|QuotientFieldCategory| *4)) (|ofCategory| *2 (|FiniteLinearAggregate| *4)) (|isDomain| *1 (|InnerCommonDenominator| *4 *5 *2 *3)) (|ofCategory| *3 (|FiniteLinearAggregate| *5)))) (|commonDenominator| (*1 *2 *3) (AND (|ofCategory| *4 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|isDomain| *1 (|InnerCommonDenominator| *2 *4 *5 *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *2)) (|ofCategory| *3 (|FiniteLinearAggregate| *4))))) 
(CATEGORY |package| (SIGNATURE |commonDenominator| (|#1| |#4|)) (SIGNATURE |clearDenominator| (|#3| |#4|)) (SIGNATURE |splitDenominator| ((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|))) 
((~= (((|Boolean|) $ $) NIL)) (|symbNameV| (((|Symbol|) $) NIL)) (|subMultV| (((|NonNegativeInteger|) $) NIL)) (|setsymbName!| (((|Symbol|) $ (|Symbol|)) NIL)) (|setsubmult!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) NIL)) (|setpoint!| (((|ProjectivePlane| |#1|) $ (|ProjectivePlane| |#1|)) NIL)) (|setmult!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) NIL)) (|setlocalPoint!| (((|AffinePlane| |#1|) $ (|AffinePlane| |#1|)) NIL)) (|setlocalParam!| (((|List| (|NeitherSparseOrDensePowerSeries| |#1|)) $ (|List| (|NeitherSparseOrDensePowerSeries| |#1|))) NIL)) (|setexcpDiv!| (((|Divisor| (|Places| |#1|)) $ (|Divisor| (|Places| |#1|))) NIL)) (|setcurve!| (((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) $ (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|)) NIL)) (|setchart!| ((|#3| $ |#3|) NIL)) (|pointV| (((|ProjectivePlane| |#1|) $) NIL)) (|multV| (((|NonNegativeInteger|) $) NIL)) (|localPointV| (((|AffinePlane| |#1|) $) NIL)) (|localParamV| (((|List| (|NeitherSparseOrDensePowerSeries| |#1|)) $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|fullOutput| (((|Boolean|) (|Boolean|)) NIL) (((|Boolean|)) NIL)) (|fullOut| (((|OutputForm|) $) NIL)) (|excpDivV| (((|Divisor| (|Places| |#1|)) $) NIL)) (|degree| (((|PositiveInteger|) $) NIL)) (|curveV| (((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) $) NIL)) (|create| (($ (|ProjectivePlane| |#1|) (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) (|AffinePlane| |#1|) (|NonNegativeInteger|) |#3| (|NonNegativeInteger|) (|Divisor| (|Places| |#1|)) |#1| (|Symbol|)) NIL) (($ (|ProjectivePlane| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|)) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (|chartV| ((|#3| $) NIL)) (|actualExtensionV| ((|#1| $) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|InfClsPt| |#1| |#2| |#3|) (|Join| (|InfinitlyClosePointCategory| |#1| |#2| (|DistributedMultivariatePolynomial| |#2| |#1|) (|DirectProduct| (|#| |#2|) (|NonNegativeInteger|)) (|ProjectivePlane| |#1|) (|NeitherSparseOrDensePowerSeries| |#1|) (|Places| |#1|) (|Divisor| (|Places| |#1|)) |#3|) (CATEGORY |domain| (SIGNATURE |fullOut| ((|OutputForm|) $)) (SIGNATURE |fullOutput| ((|Boolean|) (|Boolean|))) (SIGNATURE |fullOutput| ((|Boolean|))))) (|Field|) (|List| (|Symbol|)) (|BlowUpMethodCategory|)) (T |InfClsPt|)) 
((|fullOut| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|InfClsPt| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|fullOutput| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|InfClsPt| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|fullOutput| (*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|InfClsPt| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|))))) 
(|Join| (|InfinitlyClosePointCategory| |#1| |#2| (|DistributedMultivariatePolynomial| |#2| |#1|) (|DirectProduct| (|#| |#2|) (|NonNegativeInteger|)) (|ProjectivePlane| |#1|) (|NeitherSparseOrDensePowerSeries| |#1|) (|Places| |#1|) (|Divisor| (|Places| |#1|)) |#3|) (CATEGORY |domain| (SIGNATURE |fullOut| ((|OutputForm|) $)) (SIGNATURE |fullOutput| ((|Boolean|) (|Boolean|))) (SIGNATURE |fullOutput| ((|Boolean|))))) 
((~= (((|Boolean|) $ $) NIL)) (|zeroDim?| (((|Boolean|) $ (|List| |#3|)) 101) (((|Boolean|) $) 102)) (|zero?| (((|Boolean|) $) 144)) (|saturate| (($ $ |#4|) 93) (($ $ |#4| (|List| |#3|)) 97)) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) 137 (|has| |#3| (|ConvertibleTo| (|Symbol|))))) (|quotient| (($ $ $) 87) (($ $ |#4|) 85)) (|one?| (((|Boolean|) $) 143)) (|leadingIdeal| (($ $) 105)) (|latex| (((|String|) $) NIL)) (|intersect| (($ $ $) 79) (($ (|List| $)) 81)) (|inRadical?| (((|Boolean|) |#4| $) 104)) (|in?| (((|Boolean|) $ $) 68)) (|ideal| (($ (|List| |#4|)) 86)) (|hash| (((|SingleInteger|) $) NIL)) (|groebnerIdeal| (($ (|List| |#4|)) 141)) (|groebner?| (((|Boolean|) $) 142)) (|groebner| (($ $) 70)) (|generators| (((|List| |#4|) $) 55)) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) NIL)) (|element?| (((|Boolean|) |#4| $) 73)) (|dimension| (((|Integer|) $ (|List| |#3|)) 106) (((|Integer|) $) 107)) (|coerce| (((|OutputForm|) $) 140) (($ (|List| |#4|)) 82)) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) NIL)) (= (((|Boolean|) $ $) 69)) (+ (($ $ $) 89)) (** (($ $ (|NonNegativeInteger|)) 92)) (* (($ $ $) 91))) 
(((|PolynomialIdeals| |#1| |#2| |#3| |#4|) (|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE * ($ $ $)) (SIGNATURE ** ($ $ (|NonNegativeInteger|))) (SIGNATURE + ($ $ $)) (SIGNATURE |one?| ((|Boolean|) $)) (SIGNATURE |zero?| ((|Boolean|) $)) (SIGNATURE |element?| ((|Boolean|) |#4| $)) (SIGNATURE |in?| ((|Boolean|) $ $)) (SIGNATURE |inRadical?| ((|Boolean|) |#4| $)) (SIGNATURE |zeroDim?| ((|Boolean|) $ (|List| |#3|))) (SIGNATURE |zeroDim?| ((|Boolean|) $)) (SIGNATURE |intersect| ($ $ $)) (SIGNATURE |intersect| ($ (|List| $))) (SIGNATURE |quotient| ($ $ $)) (SIGNATURE |quotient| ($ $ |#4|)) (SIGNATURE |groebner| ($ $)) (SIGNATURE |generalPosition| ((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|))) (SIGNATURE |backOldPos| ($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)))) (SIGNATURE |dimension| ((|Integer|) $ (|List| |#3|))) (SIGNATURE |dimension| ((|Integer|) $)) (SIGNATURE |leadingIdeal| ($ $)) (SIGNATURE |ideal| ($ (|List| |#4|))) (SIGNATURE |groebnerIdeal| ($ (|List| |#4|))) (SIGNATURE |groebner?| ((|Boolean|) $)) (SIGNATURE |generators| ((|List| |#4|) $)) (SIGNATURE |coerce| ($ (|List| |#4|))) (SIGNATURE |saturate| ($ $ |#4|)) (SIGNATURE |saturate| ($ $ |#4| (|List| |#3|))) (IF (|has| |#3| (|ConvertibleTo| (|Symbol|))) (SIGNATURE |relationsIdeal| ((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|))) |noBranch|))) (|Field|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |PolynomialIdeals|)) 
((* (*1 *1 *1 *1) (AND (|ofCategory| *2 (|Field|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|PolynomialIdeals| *2 *3 *4 *5)) (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4)))) (** (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)))) (+ (*1 *1 *1 *1) (AND (|ofCategory| *2 (|Field|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|PolynomialIdeals| *2 *3 *4 *5)) (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4)))) (|one?| (*1 *2 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)))) (|zero?| (*1 *2 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)))) (|element?| (*1 *2 *3 *1) (AND (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *4 *5 *6)))) (|in?| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)))) (|inRadical?| (*1 *2 *3 *1) (AND (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *4 *5 *6)))) (|zeroDim?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *7)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)))) (|zeroDim?| (*1 *2 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)))) (|intersect| (*1 *1 *1 *1) (AND (|ofCategory| *2 (|Field|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|PolynomialIdeals| *2 *3 *4 *5)) (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4)))) (|intersect| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|PolynomialIdeals| *3 *4 *5 *6))) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)))) (|quotient| (*1 *1 *1 *1) (AND (|ofCategory| *2 (|Field|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|PolynomialIdeals| *2 *3 *4 *5)) (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4)))) (|quotient| (*1 *1 *1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *2)) (|ofCategory| *2 (|PolynomialCategory| *3 *4 *5)))) (|groebner| (*1 *1 *1) (AND (|ofCategory| *2 (|Field|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|PolynomialIdeals| *2 *3 *4 *5)) (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4)))) (|generalPosition| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Record| (|:| |mval| (|Matrix| *4)) (|:| |invmval| (|Matrix| *4)) (|:| |genIdeal| (|PolynomialIdeals| *4 *5 *6 *7)))) (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *7)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)))) (|backOldPos| (*1 *1 *2) (AND (|isDomain| *2 (|Record| (|:| |mval| (|Matrix| *3)) (|:| |invmval| (|Matrix| *3)) (|:| |genIdeal| (|PolynomialIdeals| *3 *4 *5 *6)))) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)))) (|dimension| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *7)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)))) (|dimension| (*1 *2 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)))) (|leadingIdeal| (*1 *1 *1) (AND (|ofCategory| *2 (|Field|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|PolynomialIdeals| *2 *3 *4 *5)) (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4)))) (|ideal| (*1 *1 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6)))) (|groebnerIdeal| (*1 *1 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6)))) (|groebner?| (*1 *2 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)))) (|generators| (*1 *2 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *6)) (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6)))) (|saturate| (*1 *1 *1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *2)) (|ofCategory| *2 (|PolynomialCategory| *3 *4 *5)))) (|saturate| (*1 *1 *1 *2 *3) (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *2)) (|ofCategory| *2 (|PolynomialCategory| *4 *5 *6)))) (|relationsIdeal| (*1 *2 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *6 (|ConvertibleTo| (|Symbol|))) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|SuchThat| (|List| (|Polynomial| *4)) (|List| (|Equation| (|Polynomial| *4))))) (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *7))))) 
(|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE * ($ $ $)) (SIGNATURE ** ($ $ (|NonNegativeInteger|))) (SIGNATURE + ($ $ $)) (SIGNATURE |one?| ((|Boolean|) $)) (SIGNATURE |zero?| ((|Boolean|) $)) (SIGNATURE |element?| ((|Boolean|) |#4| $)) (SIGNATURE |in?| ((|Boolean|) $ $)) (SIGNATURE |inRadical?| ((|Boolean|) |#4| $)) (SIGNATURE |zeroDim?| ((|Boolean|) $ (|List| |#3|))) (SIGNATURE |zeroDim?| ((|Boolean|) $)) (SIGNATURE |intersect| ($ $ $)) (SIGNATURE |intersect| ($ (|List| $))) (SIGNATURE |quotient| ($ $ $)) (SIGNATURE |quotient| ($ $ |#4|)) (SIGNATURE |groebner| ($ $)) (SIGNATURE |generalPosition| ((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|))) (SIGNATURE |backOldPos| ($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)))) (SIGNATURE |dimension| ((|Integer|) $ (|List| |#3|))) (SIGNATURE |dimension| ((|Integer|) $)) (SIGNATURE |leadingIdeal| ($ $)) (SIGNATURE |ideal| ($ (|List| |#4|))) (SIGNATURE |groebnerIdeal| ($ (|List| |#4|))) (SIGNATURE |groebner?| ((|Boolean|) $)) (SIGNATURE |generators| ((|List| |#4|) $)) (SIGNATURE |coerce| ($ (|List| |#4|))) (SIGNATURE |saturate| ($ $ |#4|)) (SIGNATURE |saturate| ($ $ |#4| (|List| |#3|))) (IF (|has| |#3| (|ConvertibleTo| (|Symbol|))) (SIGNATURE |relationsIdeal| ((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|))) |noBranch|))) 
((|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) 144)) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) 145)) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) 103)) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) NIL)) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) 147)) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) 159))) 
(((|IdealDecompositionPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |zeroDimPrime?| ((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))))) (SIGNATURE |zeroDimPrimary?| ((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))))) (SIGNATURE |prime?| ((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))))) (SIGNATURE |radical| ((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))))) (SIGNATURE |primaryDecomp| ((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))))) (SIGNATURE |contract| ((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))))) (|List| (|Symbol|)) (|NonNegativeInteger|)) (T |IdealDecompositionPackage|)) 
((|contract| (*1 *2 *2 *3) (AND (|isDomain| *2 (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| *5 (|NonNegativeInteger|)) (|OrderedVariableList| *4) (|DistributedMultivariatePolynomial| *4 (|Fraction| (|Integer|))))) (|isDomain| *3 (|List| (|OrderedVariableList| *4))) (|ofType| *4 (|List| (|Symbol|))) (|ofType| *5 (|NonNegativeInteger|)) (|isDomain| *1 (|IdealDecompositionPackage| *4 *5)))) (|primaryDecomp| (*1 *2 *3) (AND (|ofType| *4 (|List| (|Symbol|))) (|ofType| *5 (|NonNegativeInteger|)) (|isDomain| *2 (|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| *5 (|NonNegativeInteger|)) (|OrderedVariableList| *4) (|DistributedMultivariatePolynomial| *4 (|Fraction| (|Integer|)))))) (|isDomain| *1 (|IdealDecompositionPackage| *4 *5)) (|isDomain| *3 (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| *5 (|NonNegativeInteger|)) (|OrderedVariableList| *4) (|DistributedMultivariatePolynomial| *4 (|Fraction| (|Integer|))))))) (|radical| (*1 *2 *2) (AND (|isDomain| *2 (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| *4 (|NonNegativeInteger|)) (|OrderedVariableList| *3) (|DistributedMultivariatePolynomial| *3 (|Fraction| (|Integer|))))) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|NonNegativeInteger|)) (|isDomain| *1 (|IdealDecompositionPackage| *3 *4)))) (|prime?| (*1 *2 *3) (AND (|isDomain| *3 (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| *5 (|NonNegativeInteger|)) (|OrderedVariableList| *4) (|DistributedMultivariatePolynomial| *4 (|Fraction| (|Integer|))))) (|ofType| *4 (|List| (|Symbol|))) (|ofType| *5 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|IdealDecompositionPackage| *4 *5)))) (|zeroDimPrimary?| (*1 *2 *3) (AND (|isDomain| *3 (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| *5 (|NonNegativeInteger|)) (|OrderedVariableList| *4) (|DistributedMultivariatePolynomial| *4 (|Fraction| (|Integer|))))) (|ofType| *4 (|List| (|Symbol|))) (|ofType| *5 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|IdealDecompositionPackage| *4 *5)))) (|zeroDimPrime?| (*1 *2 *3) (AND (|isDomain| *3 (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| *5 (|NonNegativeInteger|)) (|OrderedVariableList| *4) (|DistributedMultivariatePolynomial| *4 (|Fraction| (|Integer|))))) (|ofType| *4 (|List| (|Symbol|))) (|ofType| *5 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|IdealDecompositionPackage| *4 *5))))) 
(CATEGORY |package| (SIGNATURE |zeroDimPrime?| ((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))))) (SIGNATURE |zeroDimPrimary?| ((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))))) (SIGNATURE |prime?| ((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))))) (SIGNATURE |radical| ((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))))) (SIGNATURE |primaryDecomp| ((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))))) (SIGNATURE |contract| ((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|reductum| (($ $) NIL)) (|monomial| (($ |#1| |#2|) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|leadingSupport| ((|#2| $) NIL)) (|leadingCoefficient| ((|#1| $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (|Zero| (($) 12 T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) 11) (($ $ $) 23)) (+ (($ $ $) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 18))) 
(((|IndexedDirectProductAbelianGroup| |#1| |#2|) (|Join| (|AbelianGroup|) (|IndexedDirectProductCategory| |#1| |#2|)) (|AbelianGroup|) (|OrderedSet|)) (T |IndexedDirectProductAbelianGroup|)) 
NIL 
(|Join| (|AbelianGroup|) (|IndexedDirectProductCategory| |#1| |#2|)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 12)) (|sample| (($) NIL T CONST)) (|reductum| (($ $) 26)) (|monomial| (($ |#1| |#2|) 23)) (|map| (($ (|Mapping| |#1| |#1|) $) 25)) (|leadingSupport| ((|#2| $) NIL)) (|leadingCoefficient| ((|#1| $) 27)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (|Zero| (($) 10 T CONST)) (= (((|Boolean|) $ $) NIL)) (+ (($ $ $) 17)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) 22))) 
(((|IndexedDirectProductAbelianMonoid| |#1| |#2|) (|Join| (|AbelianMonoid|) (|IndexedDirectProductCategory| |#1| |#2|)) (|AbelianMonoid|) (|OrderedSet|)) (T |IndexedDirectProductAbelianMonoid|)) 
NIL 
(|Join| (|AbelianMonoid|) (|IndexedDirectProductCategory| |#1| |#2|)) 
((~= (((|Boolean|) $ $) 7)) (|reductum| (($ $) 12)) (|monomial| (($ |#1| |#2|) 15)) (|map| (($ (|Mapping| |#1| |#1|) $) 16)) (|leadingSupport| ((|#2| $) 13)) (|leadingCoefficient| ((|#1| $) 14)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (= (((|Boolean|) $ $) 6))) 
(((|IndexedDirectProductCategory| |#1| |#2|) (|Category|) (|SetCategory|) (|OrderedSet|)) (T |IndexedDirectProductCategory|)) 
((|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|IndexedDirectProductCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|OrderedSet|)))) (|monomial| (*1 *1 *2 *3) (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|OrderedSet|)))) (|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *2 *3)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *2 (|SetCategory|)))) (|leadingSupport| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|OrderedSet|)))) (|reductum| (*1 *1 *1) (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|OrderedSet|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |map| ($ (|Mapping| |t#1| |t#1|) $)) (SIGNATURE |monomial| ($ |t#1| |t#2|)) (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |leadingSupport| (|t#2| $)) (SIGNATURE |reductum| ($ $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|sample| (($) NIL T CONST)) (|reductum| (($ $) NIL)) (|monomial| (($ |#1| |#2|) NIL)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|leadingSupport| ((|#2| $) NIL)) (|leadingCoefficient| ((|#1| $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (|Zero| (($) NIL T CONST)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 13)) (+ (($ $ $) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL))) 
(((|IndexedDirectProductOrderedAbelianMonoid| |#1| |#2|) (|Join| (|OrderedAbelianMonoid|) (|IndexedDirectProductCategory| |#1| |#2|)) (|OrderedAbelianMonoid|) (|OrderedSet|)) (T |IndexedDirectProductOrderedAbelianMonoid|)) 
NIL 
(|Join| (|OrderedAbelianMonoid|) (|IndexedDirectProductCategory| |#1| |#2|)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|sup| (($ $ $) 16)) (|subtractIfCan| (((|Union| $ "failed") $ $) 13)) (|sample| (($) NIL T CONST)) (|reductum| (($ $) NIL)) (|monomial| (($ |#1| |#2|) NIL)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|leadingSupport| ((|#2| $) NIL)) (|leadingCoefficient| ((|#1| $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (|Zero| (($) NIL T CONST)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) NIL)) (+ (($ $ $) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL))) 
(((|IndexedDirectProductOrderedAbelianMonoidSup| |#1| |#2|) (|Join| (|OrderedAbelianMonoidSup|) (|IndexedDirectProductCategory| |#1| |#2|)) (|OrderedAbelianMonoidSup|) (|OrderedSet|)) (T |IndexedDirectProductOrderedAbelianMonoidSup|)) 
NIL 
(|Join| (|OrderedAbelianMonoidSup|) (|IndexedDirectProductCategory| |#1| |#2|)) 
((~= (((|Boolean|) $ $) NIL)) (|reductum| (($ $) 24)) (|monomial| (($ |#1| |#2|) 21)) (|map| (($ (|Mapping| |#1| |#1|) $) 23)) (|leadingSupport| ((|#2| $) 26)) (|leadingCoefficient| ((|#1| $) 25)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 20)) (= (((|Boolean|) $ $) 13))) 
(((|IndexedDirectProductObject| |#1| |#2|) (|IndexedDirectProductCategory| |#1| |#2|) (|SetCategory|) (|OrderedSet|)) (T |IndexedDirectProductObject|)) 
NIL 
(|IndexedDirectProductCategory| |#1| |#2|) 
((|eval| (($ $ (|List| |#2|) (|List| |#3|)) NIL) (($ $ |#2| |#3|) 12))) 
(((|InnerEvalable&| |#1| |#2| |#3|) (CATEGORY |domain| (SIGNATURE |eval| (|#1| |#1| |#2| |#3|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#2|) (|List| |#3|)))) (|InnerEvalable| |#2| |#3|) (|SetCategory|) (|Type|)) (T |InnerEvalable&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |eval| (|#1| |#1| |#2| |#3|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#2|) (|List| |#3|)))) 
((|eval| (($ $ (|List| |#1|) (|List| |#2|)) 7) (($ $ |#1| |#2|) 6))) 
(((|InnerEvalable| |#1| |#2|) (|Category|) (|SetCategory|) (|Type|)) (T |InnerEvalable|)) 
((|eval| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *4)) (|isDomain| *3 (|List| *5)) (|ofCategory| *1 (|InnerEvalable| *4 *5)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|Type|)))) (|eval| (*1 *1 *1 *2 *3) (AND (|ofCategory| *1 (|InnerEvalable| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|Type|))))) 
(|Join| (CATEGORY |domain| (SIGNATURE |eval| ($ $ |t#1| |t#2|)) (SIGNATURE |eval| ($ $ (|List| |t#1|) (|List| |t#2|))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 16)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) 18)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|size| (((|NonNegativeInteger|) $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL)) (|retract| ((|#1| $) NIL)) (|nthFactor| ((|#1| $ (|Integer|)) 23)) (|nthCoef| ((|#2| $ (|Integer|)) 21)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 46)) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) 43)) (|latex| (((|String|) $) NIL)) (|highCommonTerms| (($ $ $) 53 (|has| |#2| (|OrderedAbelianMonoid|)))) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 42) (($ |#1|) NIL)) (|coefficient| ((|#2| |#1| $) 49)) (|Zero| (($) 11 T CONST)) (= (((|Boolean|) $ $) 29)) (+ (($ $ $) 27) (($ |#1| $) 25)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) 36) (($ |#2| |#1|) 31))) 
(((|InnerFreeAbelianMonoid| |#1| |#2| |#3|) (|FreeAbelianMonoidCategory| |#1| |#2|) (|SetCategory|) (|CancellationAbelianMonoid|) |#2|) (T |InnerFreeAbelianMonoid|)) 
NIL 
(|FreeAbelianMonoidCategory| |#1| |#2|) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) NIL) (((|Boolean|) $) NIL (|has| |#1| (|OrderedSet|)))) (|sort!| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $) NIL (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|has| |#1| (|OrderedSet|))))) (|sort| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) NIL) (($ $) NIL (|has| |#1| (|OrderedSet|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|shrinkable| (((|Boolean|) (|Boolean|)) 24)) (|setelt| ((|#1| $ (|Integer|) |#1|) 27 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) 51)) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) NIL T CONST)) (|reverse!| (($ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) NIL)) (|removeDuplicates!| (($ $) 54 (|has| |#1| (|SetCategory|)))) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|remove!| (($ |#1| $) NIL (|has| |#1| (|SetCategory|))) (($ (|Mapping| (|Boolean|) |#1|) $) 43)) (|remove| (($ |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| ((|#1| $ (|Integer|) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#1| $ (|Integer|)) NIL)) (|position| (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) NIL) (((|Integer|) |#1| $) NIL (|has| |#1| (|SetCategory|))) (((|Integer|) |#1| $ (|Integer|)) NIL (|has| |#1| (|SetCategory|)))) (|physicalLength!| (($ $ (|Integer|)) 13)) (|physicalLength| (((|NonNegativeInteger|) $) 11)) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|new| (($ (|NonNegativeInteger|) |#1|) 22)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) 20 (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|merge!| (($ $ $) NIL (|has| |#1| (|OrderedSet|))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) 34)) (|merge| (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) 35) (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|maxIndex| (((|Integer|) $) 19 (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|insert!| (($ $ $ (|Integer|)) 50) (($ |#1| $ (|Integer|)) 36)) (|insert| (($ |#1| $ (|Integer|)) NIL) (($ $ $ (|Integer|)) NIL)) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|flexibleArray| (($ (|List| |#1|)) 28)) (|first| ((|#1| $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) NIL)) (|fill!| (($ $ |#1|) 18 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 39)) (|entry?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|entries| (((|List| |#1|) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) 14)) (|elt| ((|#1| $ (|Integer|) |#1|) NIL) ((|#1| $ (|Integer|)) 32) (($ $ (|UniversalSegment| (|Integer|))) NIL)) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) 49) (($ $ (|Integer|)) 44)) (|delete| (($ $ (|Integer|)) NIL) (($ $ (|UniversalSegment| (|Integer|))) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copyInto!| (($ $ $ (|Integer|)) 40 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) 31)) (|convert| (((|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) NIL)) (|concat!| (($ $ $) 41) (($ $ |#1|) 38)) (|concat| (($ $ |#1|) NIL) (($ |#1| $) 37) (($ $ $) NIL) (($ (|List| $)) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (|#| (((|NonNegativeInteger|) $) 15 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|IndexedFlexibleArray| |#1| |#2|) (|Join| (|OneDimensionalArrayAggregate| |#1|) (|ExtensibleLinearAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |flexibleArray| ($ (|List| |#1|))) (SIGNATURE |physicalLength| ((|NonNegativeInteger|) $)) (SIGNATURE |physicalLength!| ($ $ (|Integer|))) (SIGNATURE |shrinkable| ((|Boolean|) (|Boolean|))))) (|Type|) (|Integer|)) (T |IndexedFlexibleArray|)) 
((|flexibleArray| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|IndexedFlexibleArray| *3 *4)) (|ofType| *4 (|Integer|)))) (|physicalLength| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|IndexedFlexibleArray| *3 *4)) (|ofCategory| *3 (|Type|)) (|ofType| *4 (|Integer|)))) (|physicalLength!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IndexedFlexibleArray| *3 *4)) (|ofCategory| *3 (|Type|)) (|ofType| *4 *2))) (|shrinkable| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|IndexedFlexibleArray| *3 *4)) (|ofCategory| *3 (|Type|)) (|ofType| *4 (|Integer|))))) 
(|Join| (|OneDimensionalArrayAggregate| |#1|) (|ExtensibleLinearAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |flexibleArray| ($ (|List| |#1|))) (SIGNATURE |physicalLength| ((|NonNegativeInteger|) $)) (SIGNATURE |physicalLength!| ($ $ (|Integer|))) (SIGNATURE |shrinkable| ((|Boolean|) (|Boolean|))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|transcendent?| (((|Boolean|) $) NIL)) (|transcendenceDegree| (((|NonNegativeInteger|)) NIL)) (|trace| (((|InnerPrimeField| |#1|) $) NIL) (($ $ (|PositiveInteger|)) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|size| (((|NonNegativeInteger|)) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|InnerPrimeField| |#1|) "failed") $) NIL)) (|retract| (((|InnerPrimeField| |#1|) $) NIL)) (|represents| (($ (|Vector| (|InnerPrimeField| |#1|))) NIL)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|primitiveElement| (($) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|primitive?| (((|Boolean|) $) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) NIL (OR (|has| (|InnerPrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (($ $) NIL (OR (|has| (|InnerPrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|InnerPrimeField| |#1|) (|Finite|))))) (|prime?| (((|Boolean|) $) NIL)) (|order| (((|PositiveInteger|) $) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|))) (((|OnePointCompletion| (|PositiveInteger|)) $) NIL (OR (|has| (|InnerPrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|InnerPrimeField| |#1|) (|Finite|))))) (|one?| (((|Boolean|) $) NIL)) (|normalElement| (($) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|normal?| (((|Boolean|) $) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|norm| (((|InnerPrimeField| |#1|) $) NIL) (($ $ (|PositiveInteger|)) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|nextItem| (((|Union| $ "failed") $) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| (|InnerPrimeField| |#1|)) $) NIL) (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|lookup| (((|PositiveInteger|) $) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| (|InnerPrimeField| |#1|)) $) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|linearAssociatedLog| (((|SparseUnivariatePolynomial| (|InnerPrimeField| |#1|)) $) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|))) (((|Union| (|SparseUnivariatePolynomial| (|InnerPrimeField| |#1|)) "failed") $ $) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| (|InnerPrimeField| |#1|))) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|init| (($) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)) CONST)) (|index| (($ (|PositiveInteger|)) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|inGroundField?| (((|Boolean|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|generator| (($) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|factor| (((|Factored| $) $) NIL)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) NIL) (((|PositiveInteger|)) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|enumerate| (((|List| $)) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|discreteLog| (((|NonNegativeInteger|) $) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|))) (((|Union| (|NonNegativeInteger|) "failed") $ $) NIL (OR (|has| (|InnerPrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|InnerPrimeField| |#1|) (|Finite|))))) (|dimension| (((|CardinalNumber|)) NIL)) (|differentiate| (($ $) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL) (((|PositiveInteger|) $) NIL)) (|definingPolynomial| (((|SparseUnivariatePolynomial| (|InnerPrimeField| |#1|))) NIL)) (|createPrimitiveElement| (($) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|createNormalElement| (($) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|coordinates| (((|Vector| (|InnerPrimeField| |#1|)) $) NIL) (((|Matrix| (|InnerPrimeField| |#1|)) (|Vector| $)) NIL)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ (|InnerPrimeField| |#1|)) NIL)) (|charthRoot| (($ $) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|))) (((|Union| $ "failed") $) NIL (OR (|has| (|InnerPrimeField| |#1|) (|CharacteristicNonZero|)) (|has| (|InnerPrimeField| |#1|) (|Finite|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|basis| (((|Vector| $)) NIL) (((|Vector| $) (|PositiveInteger|)) NIL)) (|associates?| (((|Boolean|) $ $) NIL)) (|algebraic?| (((|Boolean|) $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (|Frobenius| (($ $) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (D (($ $) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|InnerPrimeField| |#1|) (|Finite|)))) (= (((|Boolean|) $ $) NIL)) (/ (($ $ $) NIL) (($ $ (|InnerPrimeField| |#1|)) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ $ (|InnerPrimeField| |#1|)) NIL) (($ (|InnerPrimeField| |#1|) $) NIL))) 
(((|InnerFiniteField| |#1| |#2|) (|FiniteAlgebraicExtensionField| (|InnerPrimeField| |#1|)) (|PositiveInteger|) (|PositiveInteger|)) (T |InnerFiniteField|)) 
NIL 
(|FiniteAlgebraicExtensionField| (|InnerPrimeField| |#1|)) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) 33)) (|setRow!| (($ $ (|Integer|) |#4|) NIL)) (|setColumn!| (($ $ (|Integer|) |#5|) NIL)) (|sample| (($) NIL T CONST)) (|row| ((|#4| $ (|Integer|)) NIL)) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) 32)) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) 30)) (|parts| (((|List| |#1|) $) NIL)) (|nrows| (((|NonNegativeInteger|) $) 26)) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) 23)) (|ncols| (((|NonNegativeInteger|) $) 28)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minRowIndex| (((|Integer|) $) 24)) (|minColIndex| (((|Integer|) $) 25)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|maxRowIndex| (((|Integer|) $) 27)) (|maxColIndex| (((|Integer|) $) 29)) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) 36 (|has| |#1| (|SetCategory|)))) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|fill!| (($ $ |#1|) NIL)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) 14)) (|empty| (($) 15)) (|elt| ((|#1| $ (|Integer|) (|Integer|)) 31) ((|#1| $ (|Integer|) (|Integer|) |#1|) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) NIL)) (|column| ((|#5| $ (|Integer|)) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|InnerIndexedTwoDimensionalArray| |#1| |#2| |#3| |#4| |#5|) (|TwoDimensionalArrayCategory| |#1| |#4| |#5|) (|Type|) (|Integer|) (|Integer|) (|FiniteLinearAggregate| |#1|) (|FiniteLinearAggregate| |#1|)) (T |InnerIndexedTwoDimensionalArray|)) 
NIL 
(|TwoDimensionalArrayCategory| |#1| |#4| |#5|) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) NIL)) (|third| ((|#1| $) NIL)) (|tail| (($ $) NIL)) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|split!| (($ $ (|Integer|)) 57 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) $) NIL (|has| |#1| (|OrderedSet|))) (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) NIL)) (|sort!| (($ $) NIL (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|has| |#1| (|OrderedSet|)))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $) 55 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sort| (($ $) NIL (|has| |#1| (|OrderedSet|))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setvalue!| ((|#1| $ |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setrest!| (($ $ $) 23 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setlast!| ((|#1| $ |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setfirst!| ((|#1| $ |#1|) 21 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ "first" |#1|) 22 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "rest" $) 24 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ "last" |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|Integer|) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) NIL)) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|second| ((|#1| $) NIL)) (|sample| (($) NIL T CONST)) (|reverse!| (($ $) 28 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) 29)) (|rest| (($ $) 18) (($ $ (|NonNegativeInteger|)) 32)) (|removeDuplicates!| (($ $) 53 (|has| |#1| (|SetCategory|)))) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|remove!| (($ |#1| $) NIL (|has| |#1| (|SetCategory|))) (($ (|Mapping| (|Boolean|) |#1|) $) NIL)) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|qsetelt!| ((|#1| $ (|Integer|) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#1| $ (|Integer|)) NIL)) (|possiblyInfinite?| (((|Boolean|) $) NIL)) (|position| (((|Integer|) |#1| $ (|Integer|)) NIL (|has| |#1| (|SetCategory|))) (((|Integer|) |#1| $) NIL (|has| |#1| (|SetCategory|))) (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) NIL)) (|parts| (((|List| |#1|) $) 27 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) NIL)) (|node?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|new| (($ (|NonNegativeInteger|) |#1|) NIL)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) 31 (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|merge!| (($ $ $) NIL (|has| |#1| (|OrderedSet|))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) 56)) (|merge| (($ $ $) NIL (|has| |#1| (|OrderedSet|))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 51 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|maxIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL)) (|list| (($ |#1|) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|leaves| (((|List| |#1|) $) NIL)) (|leaf?| (((|Boolean|) $) NIL)) (|latex| (((|String|) $) 50 (|has| |#1| (|SetCategory|)))) (|last| ((|#1| $) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|insert!| (($ $ $ (|Integer|)) NIL) (($ |#1| $ (|Integer|)) NIL)) (|insert| (($ $ $ (|Integer|)) NIL) (($ |#1| $ (|Integer|)) NIL)) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|first| ((|#1| $) 13) (($ $ (|NonNegativeInteger|)) NIL)) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) NIL)) (|fill!| (($ $ |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|explicitlyFinite?| (((|Boolean|) $) NIL)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 12)) (|entry?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|entries| (((|List| |#1|) $) NIL)) (|empty?| (((|Boolean|) $) 17)) (|empty| (($) 16)) (|elt| ((|#1| $ "value") NIL) ((|#1| $ "first") 15) (($ $ "rest") 20) ((|#1| $ "last") NIL) (($ $ (|UniversalSegment| (|Integer|))) NIL) ((|#1| $ (|Integer|)) NIL) ((|#1| $ (|Integer|) |#1|) NIL)) (|distance| (((|Integer|) $ $) NIL)) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) NIL) (($ $ (|Integer|)) NIL)) (|delete| (($ $ (|UniversalSegment| (|Integer|))) NIL) (($ $ (|Integer|)) NIL)) (|cyclic?| (((|Boolean|) $) 33)) (|cycleTail| (($ $) NIL)) (|cycleSplit!| (($ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|cycleLength| (((|NonNegativeInteger|) $) NIL)) (|cycleEntry| (($ $) 35)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copyInto!| (($ $ $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) 34)) (|convert| (((|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 26)) (|concat!| (($ $ $) 52) (($ $ |#1|) NIL)) (|concat| (($ $ $) NIL) (($ |#1| $) 10) (($ (|List| $)) NIL) (($ $ |#1|) NIL)) (|coerce| (((|OutputForm|) $) 45 (|has| |#1| (|SetCategory|)))) (|children| (((|List| $) $) NIL)) (|child?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) 47 (|has| |#1| (|SetCategory|)))) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (|#| (((|NonNegativeInteger|) $) 9 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|IndexedList| |#1| |#2|) (|ListAggregate| |#1|) (|Type|) (|Integer|)) (T |IndexedList|)) 
NIL 
(|ListAggregate| |#1|) 
((|rowEchelon| ((|#4| |#4|) 26)) (|rank| (((|NonNegativeInteger|) |#4|) 31)) (|nullity| (((|NonNegativeInteger|) |#4|) 32)) (|nullSpace| (((|List| |#3|) |#4|) 37 (|has| |#3| (ATTRIBUTE |shallowlyMutable|)))) (|inverse| (((|Union| |#4| "failed") |#4|) 47)) (|generalizedInverse| ((|#4| |#4|) 40)) (|determinant| ((|#1| |#4|) 39))) 
(((|InnerMatrixLinearAlgebraFunctions| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |rowEchelon| (|#4| |#4|)) (SIGNATURE |rank| ((|NonNegativeInteger|) |#4|)) (SIGNATURE |nullity| ((|NonNegativeInteger|) |#4|)) (IF (|has| |#3| (ATTRIBUTE |shallowlyMutable|)) (SIGNATURE |nullSpace| ((|List| |#3|) |#4|)) |noBranch|) (SIGNATURE |determinant| (|#1| |#4|)) (SIGNATURE |generalizedInverse| (|#4| |#4|)) (SIGNATURE |inverse| ((|Union| |#4| "failed") |#4|))) (|Field|) (|FiniteLinearAggregate| |#1|) (|FiniteLinearAggregate| |#1|) (|MatrixCategory| |#1| |#2| |#3|)) (T |InnerMatrixLinearAlgebraFunctions|)) 
((|inverse| (*1 *2 *2) (|partial| AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *1 (|InnerMatrixLinearAlgebraFunctions| *3 *4 *5 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *4 *5)))) (|generalizedInverse| (*1 *2 *2) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *1 (|InnerMatrixLinearAlgebraFunctions| *3 *4 *5 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *4 *5)))) (|determinant| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteLinearAggregate| *2)) (|ofCategory| *5 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|InnerMatrixLinearAlgebraFunctions| *2 *4 *5 *3)) (|ofCategory| *3 (|MatrixCategory| *2 *4 *5)))) (|nullSpace| (*1 *2 *3) (AND (|has| *6 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *2 (|List| *6)) (|isDomain| *1 (|InnerMatrixLinearAlgebraFunctions| *4 *5 *6 *3)) (|ofCategory| *3 (|MatrixCategory| *4 *5 *6)))) (|nullity| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|InnerMatrixLinearAlgebraFunctions| *4 *5 *6 *3)) (|ofCategory| *3 (|MatrixCategory| *4 *5 *6)))) (|rank| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|InnerMatrixLinearAlgebraFunctions| *4 *5 *6 *3)) (|ofCategory| *3 (|MatrixCategory| *4 *5 *6)))) (|rowEchelon| (*1 *2 *2) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *1 (|InnerMatrixLinearAlgebraFunctions| *3 *4 *5 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *4 *5))))) 
(CATEGORY |package| (SIGNATURE |rowEchelon| (|#4| |#4|)) (SIGNATURE |rank| ((|NonNegativeInteger|) |#4|)) (SIGNATURE |nullity| ((|NonNegativeInteger|) |#4|)) (IF (|has| |#3| (ATTRIBUTE |shallowlyMutable|)) (SIGNATURE |nullSpace| ((|List| |#3|) |#4|)) |noBranch|) (SIGNATURE |determinant| (|#1| |#4|)) (SIGNATURE |generalizedInverse| (|#4| |#4|)) (SIGNATURE |inverse| ((|Union| |#4| "failed") |#4|))) 
((|rowEchelon| ((|#8| |#4|) 20)) (|nullSpace| (((|List| |#3|) |#4|) 29 (|has| |#7| (ATTRIBUTE |shallowlyMutable|)))) (|inverse| (((|Union| |#8| "failed") |#4|) 23))) 
(((|InnerMatrixQuotientFieldFunctions| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (CATEGORY |package| (SIGNATURE |rowEchelon| (|#8| |#4|)) (SIGNATURE |inverse| ((|Union| |#8| "failed") |#4|)) (IF (|has| |#7| (ATTRIBUTE |shallowlyMutable|)) (SIGNATURE |nullSpace| ((|List| |#3|) |#4|)) |noBranch|)) (|IntegralDomain|) (|FiniteLinearAggregate| |#1|) (|FiniteLinearAggregate| |#1|) (|MatrixCategory| |#1| |#2| |#3|) (|QuotientFieldCategory| |#1|) (|FiniteLinearAggregate| |#5|) (|FiniteLinearAggregate| |#5|) (|MatrixCategory| |#5| |#6| |#7|)) (T |InnerMatrixQuotientFieldFunctions|)) 
((|nullSpace| (*1 *2 *3) (AND (|has| *9 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|ofCategory| *7 (|QuotientFieldCategory| *4)) (|ofCategory| *8 (|FiniteLinearAggregate| *7)) (|ofCategory| *9 (|FiniteLinearAggregate| *7)) (|isDomain| *2 (|List| *6)) (|isDomain| *1 (|InnerMatrixQuotientFieldFunctions| *4 *5 *6 *3 *7 *8 *9 *10)) (|ofCategory| *3 (|MatrixCategory| *4 *5 *6)) (|ofCategory| *10 (|MatrixCategory| *7 *8 *9)))) (|inverse| (*1 *2 *3) (|partial| AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|ofCategory| *7 (|QuotientFieldCategory| *4)) (|ofCategory| *2 (|MatrixCategory| *7 *8 *9)) (|isDomain| *1 (|InnerMatrixQuotientFieldFunctions| *4 *5 *6 *3 *7 *8 *9 *2)) (|ofCategory| *3 (|MatrixCategory| *4 *5 *6)) (|ofCategory| *8 (|FiniteLinearAggregate| *7)) (|ofCategory| *9 (|FiniteLinearAggregate| *7)))) (|rowEchelon| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|ofCategory| *7 (|QuotientFieldCategory| *4)) (|ofCategory| *2 (|MatrixCategory| *7 *8 *9)) (|isDomain| *1 (|InnerMatrixQuotientFieldFunctions| *4 *5 *6 *3 *7 *8 *9 *2)) (|ofCategory| *3 (|MatrixCategory| *4 *5 *6)) (|ofCategory| *8 (|FiniteLinearAggregate| *7)) (|ofCategory| *9 (|FiniteLinearAggregate| *7))))) 
(CATEGORY |package| (SIGNATURE |rowEchelon| (|#8| |#4|)) (SIGNATURE |inverse| ((|Union| |#8| "failed") |#4|)) (IF (|has| |#7| (ATTRIBUTE |shallowlyMutable|)) (SIGNATURE |nullSpace| ((|List| |#3|) |#4|)) |noBranch|)) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|zero?| (((|Boolean|) $) NIL)) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) NIL)) (|vertConcat| (($ $ $) NIL)) (|transpose| (($ (|IndexedVector| |#1| |#3|)) NIL) (($ $) NIL)) (|symmetric?| (((|Boolean|) $) NIL)) (|swapRows!| (($ $ (|Integer|) (|Integer|)) 12)) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) NIL)) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) NIL)) (|squareTop| (($ $) NIL)) (|square?| (((|Boolean|) $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) NIL)) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) NIL) (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) NIL)) (|setRow!| (($ $ (|Integer|) (|IndexedVector| |#1| |#3|)) NIL)) (|setColumn!| (($ $ (|Integer|) (|IndexedVector| |#1| |#2|)) NIL)) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) NIL)) (|sample| (($) NIL T CONST)) (|rowEchelon| (($ $) 19 (|has| |#1| (|EuclideanDomain|)))) (|row| (((|IndexedVector| |#1| |#3|) $ (|Integer|)) NIL)) (|rank| (((|NonNegativeInteger|) $) 22 (|has| |#1| (|IntegralDomain|)))) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) NIL)) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) NIL)) (|pfaffian| ((|#1| $) NIL (|has| |#1| (|CommutativeRing|)))) (|parts| (((|List| |#1|) $) NIL)) (|nullity| (((|NonNegativeInteger|) $) 24 (|has| |#1| (|IntegralDomain|)))) (|nullSpace| (((|List| (|IndexedVector| |#1| |#2|)) $) 27 (|has| |#1| (|IntegralDomain|)))) (|nrows| (((|NonNegativeInteger|) $) NIL)) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) NIL)) (|ncols| (((|NonNegativeInteger|) $) NIL)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minordet| ((|#1| $) 17 (|has| |#1| (ATTRIBUTE (|commutative| "*"))))) (|minRowIndex| (((|Integer|) $) 10)) (|minColIndex| (((|Integer|) $) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|maxRowIndex| (((|Integer|) $) 11)) (|maxColIndex| (((|Integer|) $) NIL)) (|matrix| (($ (|List| (|List| |#1|))) NIL) (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) NIL)) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) NIL)) (|listOfLists| (((|List| (|List| |#1|)) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|inverse| (((|Union| $ "failed") $) 31 (|has| |#1| (|Field|)))) (|horizConcat| (($ $ $) NIL)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|fill!| (($ $ |#1|) NIL)) (|exquo| (((|Union| $ "failed") $ |#1|) NIL (|has| |#1| (|IntegralDomain|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#1| $ (|Integer|) (|Integer|)) NIL) ((|#1| $ (|Integer|) (|Integer|) |#1|) NIL) (($ $ (|List| (|Integer|)) (|List| (|Integer|))) NIL)) (|diagonalMatrix| (($ (|List| |#1|)) NIL) (($ (|List| $)) NIL)) (|diagonal?| (((|Boolean|) $) NIL)) (|determinant| ((|#1| $) 15 (|has| |#1| (ATTRIBUTE (|commutative| "*"))))) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) NIL)) (|columnSpace| (((|List| (|IndexedVector| |#1| |#2|)) $) NIL (|has| |#1| (|EuclideanDomain|)))) (|column| (((|IndexedVector| |#1| |#2|) $ (|Integer|)) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|))) (($ (|IndexedVector| |#1| |#2|)) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|antisymmetric?| (((|Boolean|) $) NIL)) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (/ (($ $ |#1|) NIL (|has| |#1| (|Field|)))) (- (($ $ $) NIL) (($ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| |#1| (|Field|)))) (* (($ $ $) NIL) (($ |#1| $) NIL) (($ $ |#1|) NIL) (($ (|Integer|) $) NIL) (((|IndexedVector| |#1| |#2|) $ (|IndexedVector| |#1| |#2|)) NIL) (((|IndexedVector| |#1| |#3|) (|IndexedVector| |#1| |#3|) $) NIL)) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|IndexedMatrix| |#1| |#2| |#3|) (|MatrixCategory| |#1| (|IndexedVector| |#1| |#3|) (|IndexedVector| |#1| |#2|)) (|Ring|) (|Integer|) (|Integer|)) (T |IndexedMatrix|)) 
NIL 
(|MatrixCategory| |#1| (|IndexedVector| |#1| |#3|) (|IndexedVector| |#1| |#2|)) 
((|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) 74)) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) 67)) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) 82)) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) 36)) (|random| (((|Vector| |#1|) (|PositiveInteger|)) 69)) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) 24)) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) 75)) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) 93)) (|normal?| (((|Boolean|) (|Vector| |#1|)) 78)) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) 59)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) 87)) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) 56)) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) 30)) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) 95)) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) 23)) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) 37)) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) 92)) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) 79)) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) 43)) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) 25))) 
(((|InnerNormalBasisFieldFunctions| |#1|) (CATEGORY |package| (SIGNATURE |setFieldInfo| ((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|)) (SIGNATURE |random| ((|Vector| |#1|) (|PositiveInteger|))) (SIGNATURE |index| ((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |pol| ((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|))) (SIGNATURE |xn| ((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|))) (SIGNATURE |dAndcExp| ((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|))) (SIGNATURE |repSq| ((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|))) (SIGNATURE |expPot| ((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|))) (SIGNATURE |qPot| ((|Vector| |#1|) (|Vector| |#1|) (|Integer|))) (SIGNATURE ** ((|Vector| |#1|) (|Vector| |#1|) (|Integer|))) (SIGNATURE * ((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE / ((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |norm| ((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|))) (SIGNATURE |trace| ((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|))) (SIGNATURE |inv| ((|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |lookup| ((|PositiveInteger|) (|Vector| |#1|))) (SIGNATURE |normal?| ((|Boolean|) (|Vector| |#1|))) (SIGNATURE |basis| ((|Vector| (|Vector| |#1|)) (|PositiveInteger|))) (SIGNATURE |normalElement| ((|Vector| |#1|) (|PositiveInteger|))) (SIGNATURE |minimalPolynomial| ((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)))) (|FiniteFieldCategory|)) (T |InnerNormalBasisFieldFunctions|)) 
((|minimalPolynomial| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4)))) (|normalElement| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Vector| *4)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))) (|basis| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Vector| (|Vector| *4))) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))) (|normal?| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4)))) (|lookup| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4)))) (|inv| (*1 *2 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *3)))) (|trace| (*1 *2 *2 *3) (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4)))) (|norm| (*1 *2 *2 *3) (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4)))) (/ (*1 *2 *2 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *3)))) (* (*1 *2 *2 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *3)))) (** (*1 *2 *2 *3) (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4)))) (|qPot| (*1 *2 *2 *3) (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4)))) (|expPot| (*1 *2 *2 *3 *3) (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|SingleInteger|)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4)))) (|repSq| (*1 *2 *2 *3) (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4)))) (|dAndcExp| (*1 *2 *2 *3 *4) (AND (|isDomain| *2 (|Vector| *5)) (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|SingleInteger|)) (|ofCategory| *5 (|FiniteFieldCategory|)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *5)))) (|xn| (*1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))) (|pol| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4)))) (|index| (*1 *2 *3 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Vector| *4)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))) (|random| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Vector| *4)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)))) (|setFieldInfo| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Vector| (|List| (|Record| (|:| |value| *4) (|:| |index| (|SingleInteger|)))))) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4))))) 
(CATEGORY |package| (SIGNATURE |setFieldInfo| ((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|)) (SIGNATURE |random| ((|Vector| |#1|) (|PositiveInteger|))) (SIGNATURE |index| ((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |pol| ((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|))) (SIGNATURE |xn| ((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|))) (SIGNATURE |dAndcExp| ((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|))) (SIGNATURE |repSq| ((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|))) (SIGNATURE |expPot| ((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|))) (SIGNATURE |qPot| ((|Vector| |#1|) (|Vector| |#1|) (|Integer|))) (SIGNATURE ** ((|Vector| |#1|) (|Vector| |#1|) (|Integer|))) (SIGNATURE * ((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE / ((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |norm| ((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|))) (SIGNATURE |trace| ((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|))) (SIGNATURE |inv| ((|Vector| |#1|) (|Vector| |#1|))) (SIGNATURE |lookup| ((|PositiveInteger|) (|Vector| |#1|))) (SIGNATURE |normal?| ((|Boolean|) (|Vector| |#1|))) (SIGNATURE |basis| ((|Vector| (|Vector| |#1|)) (|PositiveInteger|))) (SIGNATURE |normalElement| ((|Vector| |#1|) (|PositiveInteger|))) (SIGNATURE |minimalPolynomial| ((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)))) 
((|incrementBy| (((|Mapping| |#1| |#1|) |#1|) 11)) (|increment| (((|Mapping| |#1| |#1|)) 10))) 
(((|IncrementingMaps| |#1|) (CATEGORY |package| (SIGNATURE |increment| ((|Mapping| |#1| |#1|))) (SIGNATURE |incrementBy| ((|Mapping| |#1| |#1|) |#1|))) (|Join| (|Monoid|) (|AbelianSemiGroup|))) (T |IncrementingMaps|)) 
((|incrementBy| (*1 *2 *3) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|isDomain| *1 (|IncrementingMaps| *3)) (|ofCategory| *3 (|Join| (|Monoid|) (|AbelianSemiGroup|))))) (|increment| (*1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|isDomain| *1 (|IncrementingMaps| *3)) (|ofCategory| *3 (|Join| (|Monoid|) (|AbelianSemiGroup|)))))) 
(CATEGORY |package| (SIGNATURE |increment| ((|Mapping| |#1| |#1|))) (SIGNATURE |incrementBy| ((|Mapping| |#1| |#1|) |#1|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|sup| (($ $ $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|reductum| (($ $) NIL)) (|monomial| (($ (|NonNegativeInteger|) |#1|) NIL)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|map| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) NIL)) (|leadingSupport| ((|#1| $) NIL)) (|leadingCoefficient| (((|NonNegativeInteger|) $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 20)) (|Zero| (($) NIL T CONST)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) NIL)) (+ (($ $ $) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL))) 
(((|IndexedExponents| |#1|) (|Join| (|OrderedAbelianMonoidSup|) (|IndexedDirectProductCategory| (|NonNegativeInteger|) |#1|)) (|OrderedSet|)) (T |IndexedExponents|)) 
NIL 
(|Join| (|OrderedAbelianMonoidSup|) (|IndexedDirectProductCategory| (|NonNegativeInteger|) |#1|)) 
((|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) 83)) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) 99)) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) 95))) 
(((|InnerNumericEigenPackage| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |charpol| ((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|))) (SIGNATURE |solve1| ((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|)) (SIGNATURE |innerEigenvectors| ((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))))) (|Field|) (|Field|) (|Join| (|Field|) (|OrderedRing|))) (T |InnerNumericEigenPackage|)) 
((|innerEigenvectors| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Matrix| *6)) (|isDomain| *5 (|Mapping| (|Factored| (|SparseUnivariatePolynomial| *6)) (|SparseUnivariatePolynomial| *6))) (|ofCategory| *6 (|Field|)) (|isDomain| *2 (|List| (|Record| (|:| |outval| *7) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| *7)))))) (|isDomain| *1 (|InnerNumericEigenPackage| *6 *7 *4)) (|ofCategory| *7 (|Field|)) (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|))))) (|solve1| (*1 *2 *3 *4) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|List| *6)) (|isDomain| *1 (|InnerNumericEigenPackage| *5 *6 *4)) (|ofCategory| *6 (|Field|)) (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|))))) (|charpol| (*1 *2 *3) (AND (|isDomain| *3 (|Matrix| *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|isDomain| *1 (|InnerNumericEigenPackage| *4 *5 *6)) (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|Join| (|Field|) (|OrderedRing|)))))) 
(CATEGORY |package| (SIGNATURE |charpol| ((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|))) (SIGNATURE |solve1| ((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|)) (SIGNATURE |innerEigenvectors| ((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))))) 
((~= (((|Boolean|) $ $) 7)) (|symbNameV| (((|Symbol|) $) 20)) (|subMultV| (((|NonNegativeInteger|) $) 22)) (|setsymbName!| (((|Symbol|) $ (|Symbol|)) 23)) (|setsubmult!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) 28)) (|setpoint!| ((|#5| $ |#5|) 31)) (|setmult!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) 27)) (|setlocalPoint!| (((|AffinePlane| |#1|) $ (|AffinePlane| |#1|)) 29)) (|setlocalParam!| (((|List| |#6|) $ (|List| |#6|)) 24)) (|setexcpDiv!| ((|#8| $ |#8|) 25)) (|setcurve!| (((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) $ (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|)) 30)) (|setchart!| ((|#9| $ |#9|) 26)) (|pointV| ((|#5| $) 19)) (|multV| (((|NonNegativeInteger|) $) 16)) (|localPointV| (((|AffinePlane| |#1|) $) 17)) (|localParamV| (((|List| |#6|) $) 21)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|excpDivV| ((|#8| $) 14)) (|degree| (((|PositiveInteger|) $) 12)) (|curveV| (((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) $) 18)) (|create| (($ |#5| (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) (|AffinePlane| |#1|) (|NonNegativeInteger|) |#9| (|NonNegativeInteger|) |#8| |#1| (|Symbol|)) 33) (($ |#5| |#3|) 32)) (|coerce| (((|OutputForm|) $) 11)) (|chartV| ((|#9| $) 15)) (|actualExtensionV| ((|#1| $) 13)) (= (((|Boolean|) $ $) 6))) 
(((|InfinitlyClosePointCategory| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8| |#9|) (|Category|) (|Field|) (|List| (|Symbol|)) (|PolynomialCategory| |t#1| |t#4| (|OrderedVariableList| |t#2|)) (|DirectProductCategory| (|#| |t#2|) (|NonNegativeInteger|)) (|ProjectiveSpaceCategory| |t#1|) (|LocalPowerSeriesCategory| |t#1|) (|PlacesCategory| |t#1| |t#6|) (|DivisorCategory| |t#7|) (|BlowUpMethodCategory|)) (T |InfinitlyClosePointCategory|)) 
((|create| (*1 *1 *2 *3 *4 *5 *6 *5 *7 *8 *9) (AND (|isDomain| *3 (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) *8)) (|isDomain| *4 (|AffinePlane| *8)) (|isDomain| *9 (|Symbol|)) (|ofCategory| *8 (|Field|)) (|isDomain| *5 (|NonNegativeInteger|)) (|ofCategory| *12 (|DirectProductCategory| (|#| *10) *5)) (|ofCategory| *13 (|LocalPowerSeriesCategory| *8)) (|ofCategory| *14 (|PlacesCategory| *8 *13)) (|ofCategory| *1 (|InfinitlyClosePointCategory| *8 *10 *11 *12 *2 *13 *14 *7 *6)) (|ofCategory| *11 (|PolynomialCategory| *8 *12 (|OrderedVariableList| *10))) (|ofCategory| *2 (|ProjectiveSpaceCategory| *8)) (|ofCategory| *7 (|DivisorCategory| *14)) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|create| (*1 *1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofCategory| *6 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *7 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *8 (|PlacesCategory| *4 *7)) (|ofCategory| *1 (|InfinitlyClosePointCategory| *4 *5 *3 *6 *2 *7 *8 *9 *10)) (|ofCategory| *3 (|PolynomialCategory| *4 *6 (|OrderedVariableList| *5))) (|ofCategory| *2 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *9 (|DivisorCategory| *8)) (|ofCategory| *10 (|BlowUpMethodCategory|)))) (|setpoint!| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *2 *7 *8 *9 *10)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *2 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *7 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *8 (|PlacesCategory| *3 *7)) (|ofCategory| *9 (|DivisorCategory| *8)) (|ofCategory| *10 (|BlowUpMethodCategory|)))) (|setcurve!| (*1 *2 *1 *2) (AND (|isDomain| *2 (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) *3)) (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *11)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|BlowUpMethodCategory|)))) (|setlocalPoint!| (*1 *2 *1 *2) (AND (|isDomain| *2 (|AffinePlane| *3)) (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *11)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|BlowUpMethodCategory|)))) (|setsubmult!| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *11)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) *2)) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|BlowUpMethodCategory|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|setmult!| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *11)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) *2)) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|BlowUpMethodCategory|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|setchart!| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *2)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *2 (|BlowUpMethodCategory|)))) (|setexcpDiv!| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *2 *10)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *2 (|DivisorCategory| *9)) (|ofCategory| *10 (|BlowUpMethodCategory|)))) (|setlocalParam!| (*1 *2 *1 *2) (AND (|isDomain| *2 (|List| *8)) (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *11)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|BlowUpMethodCategory|)))) (|setsymbName!| (*1 *2 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *11)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|BlowUpMethodCategory|)))) (|subMultV| (*1 *2 *1) (AND (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *11)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) *2)) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|BlowUpMethodCategory|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|localParamV| (*1 *2 *1) (AND (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *11)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|BlowUpMethodCategory|)) (|isDomain| *2 (|List| *8)))) (|symbNameV| (*1 *2 *1) (AND (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *11)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Symbol|)))) (|pointV| (*1 *2 *1) (AND (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *2 *7 *8 *9 *10)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *8 (|PlacesCategory| *3 *7)) (|ofCategory| *9 (|DivisorCategory| *8)) (|ofCategory| *10 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|ProjectiveSpaceCategory| *3)))) (|curveV| (*1 *2 *1) (AND (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *11)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|BlowUpMethodCategory|)) (|isDomain| *2 (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) *3)))) (|localPointV| (*1 *2 *1) (AND (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *11)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|BlowUpMethodCategory|)) (|isDomain| *2 (|AffinePlane| *3)))) (|multV| (*1 *2 *1) (AND (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *11)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) *2)) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|BlowUpMethodCategory|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|chartV| (*1 *2 *1) (AND (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *10 *2)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *2 (|BlowUpMethodCategory|)))) (|excpDivV| (*1 *2 *1) (AND (|ofCategory| *1 (|InfinitlyClosePointCategory| *3 *4 *5 *6 *7 *8 *9 *2 *10)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|ofCategory| *10 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|DivisorCategory| *9)))) (|actualExtensionV| (*1 *2 *1) (AND (|ofCategory| *1 (|InfinitlyClosePointCategory| *2 *3 *4 *5 *6 *7 *8 *9 *10)) (|ofCategory| *4 (|PolynomialCategory| *2 *5 (|OrderedVariableList| *3))) (|ofCategory| *5 (|DirectProductCategory| (|#| *3) (|NonNegativeInteger|))) (|ofCategory| *6 (|ProjectiveSpaceCategory| *2)) (|ofCategory| *7 (|LocalPowerSeriesCategory| *2)) (|ofCategory| *8 (|PlacesCategory| *2 *7)) (|ofCategory| *9 (|DivisorCategory| *8)) (|ofCategory| *10 (|BlowUpMethodCategory|)) (|ofCategory| *2 (|Field|))))) 
(|Join| (|SetCategoryWithDegree|) (CATEGORY |domain| (SIGNATURE |create| ($ |t#5| (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |t#1|) (|AffinePlane| |t#1|) (|NonNegativeInteger|) |t#9| (|NonNegativeInteger|) |t#8| |t#1| (|Symbol|))) (SIGNATURE |create| ($ |t#5| |t#3|)) (SIGNATURE |setpoint!| (|t#5| $ |t#5|)) (SIGNATURE |setcurve!| ((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |t#1|) $ (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |t#1|))) (SIGNATURE |setlocalPoint!| ((|AffinePlane| |t#1|) $ (|AffinePlane| |t#1|))) (SIGNATURE |setsubmult!| ((|NonNegativeInteger|) $ (|NonNegativeInteger|))) (SIGNATURE |setmult!| ((|NonNegativeInteger|) $ (|NonNegativeInteger|))) (SIGNATURE |setchart!| (|t#9| $ |t#9|)) (SIGNATURE |setexcpDiv!| (|t#8| $ |t#8|)) (SIGNATURE |setlocalParam!| ((|List| |t#6|) $ (|List| |t#6|))) (SIGNATURE |setsymbName!| ((|Symbol|) $ (|Symbol|))) (SIGNATURE |subMultV| ((|NonNegativeInteger|) $)) (SIGNATURE |localParamV| ((|List| |t#6|) $)) (SIGNATURE |symbNameV| ((|Symbol|) $)) (SIGNATURE |pointV| (|t#5| $)) (SIGNATURE |curveV| ((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |t#1|) $)) (SIGNATURE |localPointV| ((|AffinePlane| |t#1|) $)) (SIGNATURE |multV| ((|NonNegativeInteger|) $)) (SIGNATURE |chartV| (|t#9| $)) (SIGNATURE |excpDivV| (|t#8| $)) (SIGNATURE |actualExtensionV| (|t#1| $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|SetCategoryWithDegree|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|symbNameV| (((|Symbol|) $) NIL)) (|subMultV| (((|NonNegativeInteger|) $) NIL)) (|setsymbName!| (((|Symbol|) $ (|Symbol|)) NIL)) (|setsubmult!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) NIL)) (|setpoint!| (((|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|) $ (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|)) NIL)) (|setmult!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) NIL)) (|setlocalPoint!| (((|AffinePlane| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) $ (|AffinePlane| (|PseudoAlgebraicClosureOfFiniteField| |#1|))) NIL)) (|setlocalParam!| (((|List| (|NeitherSparseOrDensePowerSeries| (|PseudoAlgebraicClosureOfFiniteField| |#1|))) $ (|List| (|NeitherSparseOrDensePowerSeries| (|PseudoAlgebraicClosureOfFiniteField| |#1|)))) NIL)) (|setexcpDiv!| (((|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) $ (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) NIL)) (|setcurve!| (((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) (|PseudoAlgebraicClosureOfFiniteField| |#1|)) $ (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) (|PseudoAlgebraicClosureOfFiniteField| |#1|))) NIL)) (|setchart!| ((|#3| $ |#3|) NIL)) (|pointV| (((|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|) $) NIL)) (|multV| (((|NonNegativeInteger|) $) NIL)) (|localPointV| (((|AffinePlane| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) $) NIL)) (|localParamV| (((|List| (|NeitherSparseOrDensePowerSeries| (|PseudoAlgebraicClosureOfFiniteField| |#1|))) $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|fullOutput| (((|Boolean|) (|Boolean|)) NIL) (((|Boolean|)) NIL)) (|fullOut| (((|OutputForm|) $) NIL)) (|excpDivV| (((|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) $) NIL)) (|degree| (((|PositiveInteger|) $) NIL)) (|curveV| (((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) (|PseudoAlgebraicClosureOfFiniteField| |#1|)) $) NIL)) (|create| (($ (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|) (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) (|PseudoAlgebraicClosureOfFiniteField| |#1|)) (|AffinePlane| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) (|NonNegativeInteger|) |#3| (|NonNegativeInteger|) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|PseudoAlgebraicClosureOfFiniteField| |#1|) (|Symbol|)) NIL) (($ (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|) (|DistributedMultivariatePolynomial| |#2| (|PseudoAlgebraicClosureOfFiniteField| |#1|))) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (|chartV| ((|#3| $) NIL)) (|actualExtensionV| (((|PseudoAlgebraicClosureOfFiniteField| |#1|) $) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |#1| |#2| |#3|) (|Join| (|InfinitlyClosePointCategory| (|PseudoAlgebraicClosureOfFiniteField| |#1|) |#2| (|DistributedMultivariatePolynomial| |#2| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) (|DirectProduct| (|#| |#2|) (|NonNegativeInteger|)) (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|) (|NeitherSparseOrDensePowerSeries| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) |#3|) (CATEGORY |domain| (SIGNATURE |fullOut| ((|OutputForm|) $)) (SIGNATURE |fullOutput| ((|Boolean|) (|Boolean|))) (SIGNATURE |fullOutput| ((|Boolean|))))) (|FiniteFieldCategory|) (|List| (|Symbol|)) (|BlowUpMethodCategory|)) (T |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField|)) 
((|fullOut| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| *3 *4 *5)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|fullOutput| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| *3 *4 *5)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|fullOutput| (*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| *3 *4 *5)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|))))) 
(|Join| (|InfinitlyClosePointCategory| (|PseudoAlgebraicClosureOfFiniteField| |#1|) |#2| (|DistributedMultivariatePolynomial| |#2| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) (|DirectProduct| (|#| |#2|) (|NonNegativeInteger|)) (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|) (|NeitherSparseOrDensePowerSeries| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) |#3|) (CATEGORY |domain| (SIGNATURE |fullOut| ((|OutputForm|) $)) (SIGNATURE |fullOutput| ((|Boolean|) (|Boolean|))) (SIGNATURE |fullOutput| ((|Boolean|))))) 
((~= (((|Boolean|) $ $) NIL)) (|symbNameV| (((|Symbol|) $) 42)) (|subMultV| (((|NonNegativeInteger|) $) 48)) (|setsymbName!| (((|Symbol|) $ (|Symbol|)) 81)) (|setsubmult!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) 71)) (|setpoint!| ((|#5| $ |#5|) 74)) (|setmult!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) 77)) (|setlocalPoint!| (((|AffinePlane| |#1|) $ (|AffinePlane| |#1|)) 76)) (|setlocalParam!| (((|List| |#6|) $ (|List| |#6|)) 79)) (|setexcpDiv!| ((|#8| $ |#8|) 80)) (|setcurve!| (((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) $ (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|)) 75)) (|setchart!| ((|#9| $ |#9|) 78)) (|pointV| ((|#5| $) 40)) (|multV| (((|NonNegativeInteger|) $) 43)) (|localPointV| (((|AffinePlane| |#1|) $) 45)) (|localParamV| (((|List| |#6|) $) 73)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|fullOutput| (((|Boolean|) (|Boolean|)) 52) (((|Boolean|)) 53)) (|fullOut| (((|OutputForm|) $) 50)) (|excpDivV| ((|#8| $) 47)) (|degree| (((|PositiveInteger|) $) 58)) (|curveV| (((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) $) 44)) (|create| (($ |#5| (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) (|AffinePlane| |#1|) (|NonNegativeInteger|) |#9| (|NonNegativeInteger|) |#8| |#1| (|Symbol|)) 59) (($ |#5| |#3|) 70)) (|coerce| (((|OutputForm|) $) 54)) (|chartV| ((|#9| $) 46)) (|actualExtensionV| ((|#1| $) 55)) (= (((|Boolean|) $ $) NIL))) 
(((|InfinitlyClosePoint| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8| |#9|) (|Join| (|InfinitlyClosePointCategory| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8| |#9|) (CATEGORY |domain| (SIGNATURE |fullOut| ((|OutputForm|) $)) (SIGNATURE |fullOutput| ((|Boolean|) (|Boolean|))) (SIGNATURE |fullOutput| ((|Boolean|))))) (|Field|) (|List| (|Symbol|)) (|PolynomialCategory| |#1| |#4| (|OrderedVariableList| |#2|)) (|DirectProductCategory| (|#| |#2|) (|NonNegativeInteger|)) (|ProjectiveSpaceCategory| |#1|) (|LocalPowerSeriesCategory| |#1|) (|PlacesCategory| |#1| |#6|) (|DivisorCategory| |#7|) (|BlowUpMethodCategory|)) (T |InfinitlyClosePoint|)) 
((|fullOut| (*1 *2 *1) (AND (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|InfinitlyClosePoint| *3 *4 *5 *6 *7 *8 *9 *10 *11)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|BlowUpMethodCategory|)))) (|fullOutput| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|isDomain| *1 (|InfinitlyClosePoint| *3 *4 *5 *6 *7 *8 *9 *10 *11)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|BlowUpMethodCategory|)))) (|fullOutput| (*1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|InfinitlyClosePoint| *3 *4 *5 *6 *7 *8 *9 *10 *11)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *10 (|DivisorCategory| *9)) (|ofCategory| *11 (|BlowUpMethodCategory|))))) 
(|Join| (|InfinitlyClosePointCategory| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8| |#9|) (CATEGORY |domain| (SIGNATURE |fullOut| ((|OutputForm|) $)) (SIGNATURE |fullOutput| ((|Boolean|) (|Boolean|))) (SIGNATURE |fullOutput| ((|Boolean|))))) 
((|plusInfinity| (((|OrderedCompletion| (|Integer|))) 11)) (|minusInfinity| (((|OrderedCompletion| (|Integer|))) 13)) (|infinity| (((|OnePointCompletion| (|Integer|))) 8))) 
(((|Infinity|) (CATEGORY |package| (SIGNATURE |infinity| ((|OnePointCompletion| (|Integer|)))) (SIGNATURE |plusInfinity| ((|OrderedCompletion| (|Integer|)))) (SIGNATURE |minusInfinity| ((|OrderedCompletion| (|Integer|)))))) (T |Infinity|)) 
((|minusInfinity| (*1 *2) (AND (|isDomain| *2 (|OrderedCompletion| (|Integer|))) (|isDomain| *1 (|Infinity|)))) (|plusInfinity| (*1 *2) (AND (|isDomain| *2 (|OrderedCompletion| (|Integer|))) (|isDomain| *1 (|Infinity|)))) (|infinity| (*1 *2) (AND (|isDomain| *2 (|OnePointCompletion| (|Integer|))) (|isDomain| *1 (|Infinity|))))) 
(CATEGORY |package| (SIGNATURE |infinity| ((|OnePointCompletion| (|Integer|)))) (SIGNATURE |plusInfinity| ((|OrderedCompletion| (|Integer|)))) (SIGNATURE |minusInfinity| ((|OrderedCompletion| (|Integer|))))) 
((|packageCall| (((|InputForm|) (|Symbol|)) 15)) (|interpret| ((|#1| (|InputForm|)) 20))) 
(((|InputFormFunctions1| |#1|) (CATEGORY |package| (SIGNATURE |packageCall| ((|InputForm|) (|Symbol|))) (SIGNATURE |interpret| (|#1| (|InputForm|)))) (|Type|)) (T |InputFormFunctions1|)) 
((|interpret| (*1 *2 *3) (AND (|isDomain| *3 (|InputForm|)) (|isDomain| *1 (|InputFormFunctions1| *2)) (|ofCategory| *2 (|Type|)))) (|packageCall| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|InputForm|)) (|isDomain| *1 (|InputFormFunctions1| *4)) (|ofCategory| *4 (|Type|))))) 
(CATEGORY |package| (SIGNATURE |packageCall| ((|InputForm|) (|Symbol|))) (SIGNATURE |interpret| (|#1| (|InputForm|)))) 
((~= (((|Boolean|) $ $) NIL)) (|unparse| (((|String|) $) 46)) (|symbol?| (((|Boolean|) $) 43)) (|symbol| (((|Symbol|) $) 44)) (|string?| (((|Boolean|) $) 41)) (|string| (((|String|) $) 42)) (|parse| (($ (|String|)) 47)) (|pair?| (((|Boolean|) $) NIL)) (|null?| (((|Boolean|) $) NIL)) (|list?| (((|Boolean|) $) NIL)) (|latex| (((|String|) $) NIL)) (|lambda| (($ $ (|List| (|Symbol|))) 20)) (|interpret| (((|Any|) $) 22)) (|integer?| (((|Boolean|) $) NIL)) (|integer| (((|Integer|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) 59)) (|float?| (((|Boolean|) $) NIL)) (|float| (((|DoubleFloat|) $) NIL)) (|flatten| (($ $) 38)) (|expr| (((|OutputForm|) $) NIL)) (|eq| (((|Boolean|) $ $) NIL)) (|elt| (($ $ (|Integer|)) NIL) (($ $ (|List| (|Integer|))) NIL)) (|destruct| (((|List| $) $) 28)) (|declare| (((|Symbol|) (|List| $)) 48)) (|convert| (($ (|List| $)) 52) (($ (|String|)) NIL) (($ (|Symbol|)) 18) (($ (|Integer|)) 8) (($ (|DoubleFloat|)) 25) (($ (|OutputForm|)) NIL) (((|SExpression|) $) 11) (($ (|SExpression|)) 12)) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) 51)) (|coerce| (((|OutputForm|) $) NIL)) (|cdr| (($ $) 50)) (|car| (($ $) 49)) (|binary| (($ $ (|List| $)) 56)) (|atom?| (((|Boolean|) $) 27)) (|Zero| (($) 9 T CONST)) (|One| (($) 10 T CONST)) (= (((|Boolean|) $ $) 60)) (/ (($ $ $) 65)) (+ (($ $ $) 61)) (** (($ $ (|NonNegativeInteger|)) 64) (($ $ (|Integer|)) 63)) (* (($ $ $) 62)) (|#| (((|Integer|) $) NIL))) 
(((|InputForm|) (|Join| (|SExpressionCategory| (|String|) (|Symbol|) (|Integer|) (|DoubleFloat|) (|OutputForm|)) (|ConvertibleTo| (|SExpression|)) (CATEGORY |domain| (SIGNATURE |interpret| ((|Any|) $)) (SIGNATURE |convert| ($ (|SExpression|))) (SIGNATURE |binary| ($ $ (|List| $))) (SIGNATURE |function| ($ $ (|List| (|Symbol|)) (|Symbol|))) (SIGNATURE |lambda| ($ $ (|List| (|Symbol|)))) (SIGNATURE + ($ $ $)) (SIGNATURE * ($ $ $)) (SIGNATURE / ($ $ $)) (SIGNATURE ** ($ $ (|NonNegativeInteger|))) (SIGNATURE ** ($ $ (|Integer|))) (SIGNATURE 0 ($) |constant|) (SIGNATURE 1 ($) |constant|) (SIGNATURE |flatten| ($ $)) (SIGNATURE |unparse| ((|String|) $)) (SIGNATURE |parse| ($ (|String|))) (SIGNATURE |declare| ((|Symbol|) (|List| $))) (SIGNATURE |compile| ((|Symbol|) (|Symbol|) (|List| $)))))) (T |InputForm|)) 
((|interpret| (*1 *2 *1) (AND (|isDomain| *2 (|Any|)) (|isDomain| *1 (|InputForm|)))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|SExpression|)) (|isDomain| *1 (|InputForm|)))) (|binary| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|InputForm|))) (|isDomain| *1 (|InputForm|)))) (|function| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *3 (|Symbol|)) (|isDomain| *1 (|InputForm|)))) (|lambda| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *1 (|InputForm|)))) (+ (*1 *1 *1 *1) (|isDomain| *1 (|InputForm|))) (* (*1 *1 *1 *1) (|isDomain| *1 (|InputForm|))) (/ (*1 *1 *1 *1) (|isDomain| *1 (|InputForm|))) (** (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|InputForm|)))) (** (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|InputForm|)))) (|Zero| (*1 *1) (|isDomain| *1 (|InputForm|))) (|One| (*1 *1) (|isDomain| *1 (|InputForm|))) (|flatten| (*1 *1 *1) (|isDomain| *1 (|InputForm|))) (|unparse| (*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|InputForm|)))) (|parse| (*1 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|InputForm|)))) (|declare| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|InputForm|))) (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|InputForm|)))) (|compile| (*1 *2 *2 *3) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|List| (|InputForm|))) (|isDomain| *1 (|InputForm|))))) 
(|Join| (|SExpressionCategory| (|String|) (|Symbol|) (|Integer|) (|DoubleFloat|) (|OutputForm|)) (|ConvertibleTo| (|SExpression|)) (CATEGORY |domain| (SIGNATURE |interpret| ((|Any|) $)) (SIGNATURE |convert| ($ (|SExpression|))) (SIGNATURE |binary| ($ $ (|List| $))) (SIGNATURE |function| ($ $ (|List| (|Symbol|)) (|Symbol|))) (SIGNATURE |lambda| ($ $ (|List| (|Symbol|)))) (SIGNATURE + ($ $ $)) (SIGNATURE * ($ $ $)) (SIGNATURE / ($ $ $)) (SIGNATURE ** ($ $ (|NonNegativeInteger|))) (SIGNATURE ** ($ $ (|Integer|))) (SIGNATURE (|Zero|) ($) |constant|) (SIGNATURE (|One|) ($) |constant|) (SIGNATURE |flatten| ($ $)) (SIGNATURE |unparse| ((|String|) $)) (SIGNATURE |parse| ($ (|String|))) (SIGNATURE |declare| ((|Symbol|) (|List| $))) (SIGNATURE |compile| ((|Symbol|) (|Symbol|) (|List| $))))) 
((|oddInfiniteProduct| ((|#2| |#2|) 17)) (|infiniteProduct| ((|#2| |#2|) 13)) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) 20)) (|evenInfiniteProduct| ((|#2| |#2|) 15))) 
(((|InfiniteProductCharacteristicZero| |#1| |#2|) (CATEGORY |package| (SIGNATURE |infiniteProduct| (|#2| |#2|)) (SIGNATURE |evenInfiniteProduct| (|#2| |#2|)) (SIGNATURE |oddInfiniteProduct| (|#2| |#2|)) (SIGNATURE |generalInfiniteProduct| (|#2| |#2| (|Integer|) (|Integer|)))) (|Join| (|IntegralDomain|) (|CharacteristicZero|)) (|UnivariateTaylorSeriesCategory| |#1|)) (T |InfiniteProductCharacteristicZero|)) 
((|generalInfiniteProduct| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *1 (|InfiniteProductCharacteristicZero| *4 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *4)))) (|oddInfiniteProduct| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *1 (|InfiniteProductCharacteristicZero| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|evenInfiniteProduct| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *1 (|InfiniteProductCharacteristicZero| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|infiniteProduct| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *1 (|InfiniteProductCharacteristicZero| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))) 
(CATEGORY |package| (SIGNATURE |infiniteProduct| (|#2| |#2|)) (SIGNATURE |evenInfiniteProduct| (|#2| |#2|)) (SIGNATURE |oddInfiniteProduct| (|#2| |#2|)) (SIGNATURE |generalInfiniteProduct| (|#2| |#2| (|Integer|) (|Integer|)))) 
((|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) 32)) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) 53) (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) 52)) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) 87))) 
(((|InnerNumericFloatSolvePackage| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |innerSolve1| ((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|)) (SIGNATURE |innerSolve1| ((|List| |#2|) (|Polynomial| |#1|) |#3|)) (SIGNATURE |innerSolve| ((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|)) (SIGNATURE |makeEq| ((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))))) (|GcdDomain|) (|Field|) (|Join| (|Field|) (|OrderedRing|))) (T |InnerNumericFloatSolvePackage|)) 
((|makeEq| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *6 (|Field|)) (|isDomain| *2 (|List| (|Equation| (|Polynomial| *6)))) (|isDomain| *1 (|InnerNumericFloatSolvePackage| *5 *6 *7)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *7 (|Join| (|Field|) (|OrderedRing|))))) (|innerSolve| (*1 *2 *3 *3 *4 *5) (AND (|isDomain| *3 (|List| (|Polynomial| *6))) (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *6 (|GcdDomain|)) (|isDomain| *2 (|List| (|List| *7))) (|isDomain| *1 (|InnerNumericFloatSolvePackage| *6 *7 *5)) (|ofCategory| *7 (|Field|)) (|ofCategory| *5 (|Join| (|Field|) (|OrderedRing|))))) (|innerSolve1| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Polynomial| *5)) (|ofCategory| *5 (|GcdDomain|)) (|isDomain| *2 (|List| *6)) (|isDomain| *1 (|InnerNumericFloatSolvePackage| *5 *6 *4)) (|ofCategory| *6 (|Field|)) (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|))))) (|innerSolve1| (*1 *2 *3 *4) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *5)) (|ofCategory| *5 (|GcdDomain|)) (|isDomain| *2 (|List| *6)) (|isDomain| *1 (|InnerNumericFloatSolvePackage| *5 *6 *4)) (|ofCategory| *6 (|Field|)) (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))) 
(CATEGORY |package| (SIGNATURE |innerSolve1| ((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|)) (SIGNATURE |innerSolve1| ((|List| |#2|) (|Polynomial| |#1|) |#3|)) (SIGNATURE |innerSolve| ((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|)) (SIGNATURE |makeEq| ((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))))) 
((|reduction| ((|#2| |#2| |#1|) 17)) (|modularGcdPrimitive| ((|#2| (|List| |#2|)) 26)) (|modularGcd| ((|#2| (|List| |#2|)) 45))) 
(((|InnerModularGcd| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |modularGcdPrimitive| (|#2| (|List| |#2|))) (SIGNATURE |modularGcd| (|#2| (|List| |#2|))) (SIGNATURE |reduction| (|#2| |#2| |#1|))) (|EuclideanDomain|) (|UnivariatePolynomialCategory| |#1|) |#1| (|Mapping| |#1| |#1| (|NonNegativeInteger|))) (T |InnerModularGcd|)) 
((|reduction| (*1 *2 *2 *3) (AND (|ofCategory| *3 (|EuclideanDomain|)) (|ofType| *4 *3) (|ofType| *5 (|Mapping| *3 *3 (|NonNegativeInteger|))) (|isDomain| *1 (|InnerModularGcd| *3 *2 *4 *5)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|modularGcd| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|InnerModularGcd| *4 *2 *5 *6)) (|ofCategory| *4 (|EuclideanDomain|)) (|ofType| *5 *4) (|ofType| *6 (|Mapping| *4 *4 (|NonNegativeInteger|))))) (|modularGcdPrimitive| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|InnerModularGcd| *4 *2 *5 *6)) (|ofCategory| *4 (|EuclideanDomain|)) (|ofType| *5 *4) (|ofType| *6 (|Mapping| *4 *4 (|NonNegativeInteger|)))))) 
(CATEGORY |package| (SIGNATURE |modularGcdPrimitive| (|#2| (|List| |#2|))) (SIGNATURE |modularGcd| (|#2| (|List| |#2|))) (SIGNATURE |reduction| (|#2| |#2| |#1|))) 
((|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) 79) (((|Factored| |#4|) |#4| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) 164))) 
(((|InnerMultFact| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|)))) (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))))) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|Join| (|EuclideanDomain|) (|CharacteristicZero|)) (|PolynomialCategory| |#3| |#2| |#1|)) (T |InnerMultFact|)) 
((|factor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| (|Factored| (|SparseUnivariatePolynomial| *7)) (|SparseUnivariatePolynomial| *7))) (|ofCategory| *7 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|PolynomialCategory| *7 *6 *5)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *8))) (|isDomain| *1 (|InnerMultFact| *5 *6 *7 *8)) (|isDomain| *3 (|SparseUnivariatePolynomial| *8)))) (|factor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| (|Factored| (|SparseUnivariatePolynomial| *7)) (|SparseUnivariatePolynomial| *7))) (|ofCategory| *7 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|InnerMultFact| *5 *6 *7 *3)) (|ofCategory| *3 (|PolynomialCategory| *7 *6 *5))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|)))) (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))))) 
((|oddInfiniteProduct| ((|#4| |#4|) 73)) (|infiniteProduct| ((|#4| |#4|) 69)) (|generalInfiniteProduct| ((|#4| |#4| (|Integer|) (|Integer|)) 75)) (|evenInfiniteProduct| ((|#4| |#4|) 71))) 
(((|InfiniteProductFiniteField| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |infiniteProduct| (|#4| |#4|)) (SIGNATURE |evenInfiniteProduct| (|#4| |#4|)) (SIGNATURE |oddInfiniteProduct| (|#4| |#4|)) (SIGNATURE |generalInfiniteProduct| (|#4| |#4| (|Integer|) (|Integer|)))) (|Join| (|Field|) (|Finite|) (|ConvertibleTo| (|Integer|))) (|UnivariatePolynomialCategory| |#1|) (|MonogenicAlgebra| |#1| |#2|) (|UnivariateTaylorSeriesCategory| |#3|)) (T |InfiniteProductFiniteField|)) 
((|generalInfiniteProduct| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|Join| (|Field|) (|Finite|) (|ConvertibleTo| *3))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *6 (|MonogenicAlgebra| *4 *5)) (|isDomain| *1 (|InfiniteProductFiniteField| *4 *5 *6 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *6)))) (|oddInfiniteProduct| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|Field|) (|Finite|) (|ConvertibleTo| (|Integer|)))) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|MonogenicAlgebra| *3 *4)) (|isDomain| *1 (|InfiniteProductFiniteField| *3 *4 *5 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *5)))) (|evenInfiniteProduct| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|Field|) (|Finite|) (|ConvertibleTo| (|Integer|)))) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|MonogenicAlgebra| *3 *4)) (|isDomain| *1 (|InfiniteProductFiniteField| *3 *4 *5 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *5)))) (|infiniteProduct| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|Field|) (|Finite|) (|ConvertibleTo| (|Integer|)))) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|MonogenicAlgebra| *3 *4)) (|isDomain| *1 (|InfiniteProductFiniteField| *3 *4 *5 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |infiniteProduct| (|#4| |#4|)) (SIGNATURE |evenInfiniteProduct| (|#4| |#4|)) (SIGNATURE |oddInfiniteProduct| (|#4| |#4|)) (SIGNATURE |generalInfiniteProduct| (|#4| |#4| (|Integer|) (|Integer|)))) 
((|oddInfiniteProduct| ((|#2| |#2|) 27)) (|infiniteProduct| ((|#2| |#2|) 23)) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) 29)) (|evenInfiniteProduct| ((|#2| |#2|) 25))) 
(((|InfiniteProductPrimeField| |#1| |#2|) (CATEGORY |package| (SIGNATURE |infiniteProduct| (|#2| |#2|)) (SIGNATURE |evenInfiniteProduct| (|#2| |#2|)) (SIGNATURE |oddInfiniteProduct| (|#2| |#2|)) (SIGNATURE |generalInfiniteProduct| (|#2| |#2| (|Integer|) (|Integer|)))) (|Join| (|Field|) (|Finite|) (|ConvertibleTo| (|Integer|))) (|UnivariateTaylorSeriesCategory| |#1|)) (T |InfiniteProductPrimeField|)) 
((|generalInfiniteProduct| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|Join| (|Field|) (|Finite|) (|ConvertibleTo| *3))) (|isDomain| *1 (|InfiniteProductPrimeField| *4 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *4)))) (|oddInfiniteProduct| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|Field|) (|Finite|) (|ConvertibleTo| (|Integer|)))) (|isDomain| *1 (|InfiniteProductPrimeField| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|evenInfiniteProduct| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|Field|) (|Finite|) (|ConvertibleTo| (|Integer|)))) (|isDomain| *1 (|InfiniteProductPrimeField| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|infiniteProduct| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|Field|) (|Finite|) (|ConvertibleTo| (|Integer|)))) (|isDomain| *1 (|InfiniteProductPrimeField| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))) 
(CATEGORY |package| (SIGNATURE |infiniteProduct| (|#2| |#2|)) (SIGNATURE |evenInfiniteProduct| (|#2| |#2|)) (SIGNATURE |oddInfiniteProduct| (|#2| |#2|)) (SIGNATURE |generalInfiniteProduct| (|#2| |#2| (|Integer|) (|Integer|)))) 
((|signAround| (((|Union| (|Integer|) "failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) "failed") |#1|)) 14) (((|Union| (|Integer|) "failed") |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) 13) (((|Union| (|Integer|) "failed") |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) 26))) 
(((|InnerPolySign| |#1| |#2|) (CATEGORY |package| (SIGNATURE |signAround| ((|Union| (|Integer|) "failed") |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|))) (SIGNATURE |signAround| ((|Union| (|Integer|) "failed") |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|))) (SIGNATURE |signAround| ((|Union| (|Integer|) "failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) "failed") |#1|)))) (|Ring|) (|UnivariatePolynomialCategory| |#1|)) (T |InnerPolySign|)) 
((|signAround| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *5 (|Mapping| (|Union| (|Integer|) "failed") *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|InnerPolySign| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|signAround| (*1 *2 *3 *4 *2 *5) (|partial| AND (|isDomain| *5 (|Mapping| (|Union| (|Integer|) "failed") *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|InnerPolySign| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|signAround| (*1 *2 *3 *2 *4) (|partial| AND (|isDomain| *4 (|Mapping| (|Union| (|Integer|) "failed") *5)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|InnerPolySign| *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |signAround| ((|Union| (|Integer|) "failed") |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|))) (SIGNATURE |signAround| ((|Union| (|Integer|) "failed") |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|))) (SIGNATURE |signAround| ((|Union| (|Integer|) "failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) "failed") |#1|)))) 
((|symmetricRemainder| (($ $ $) 78)) (|squareFree| (((|Factored| $) $) 46)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 58)) (|retract| (((|Integer|) $) 36)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 73)) (|rational?| (((|Boolean|) $) 23)) (|rational| (((|Fraction| (|Integer|)) $) 71)) (|prime?| (((|Boolean|) $) 49)) (|powmod| (($ $ $ $) 85)) (|positive?| (((|Boolean|) $) 15)) (|permutation| (($ $ $) 56)) (|patternMatch| (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) 68)) (|nextItem| (((|Union| $ "failed") $) 63)) (|mask| (($ $) 22)) (|invmod| (($ $ $) 83)) (|init| (($) 59)) (|factorial| (($ $) 52)) (|factor| (((|Factored| $) $) 44)) (|even?| (((|Boolean|) $) 13)) (|euclideanSize| (((|NonNegativeInteger|) $) 27)) (|differentiate| (($ $ (|NonNegativeInteger|)) NIL) (($ $) 10)) (|copy| (($ $) 16)) (|convert| (((|Integer|) $) NIL) (((|InputForm|) $) 35) (((|Pattern| (|Integer|)) $) 39) (((|Float|) $) 30) (((|DoubleFloat|) $) 32)) (|characteristic| (((|NonNegativeInteger|)) 8)) (|bit?| (((|Boolean|) $ $) 19)) (|binomial| (($ $ $) 54))) 
(((|IntegerNumberSystem&| |#1|) (CATEGORY |domain| (SIGNATURE |invmod| (|#1| |#1| |#1|)) (SIGNATURE |powmod| (|#1| |#1| |#1| |#1|)) (SIGNATURE |mask| (|#1| |#1|)) (SIGNATURE |copy| (|#1| |#1|)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |rational?| ((|Boolean|) |#1|)) (SIGNATURE |symmetricRemainder| (|#1| |#1| |#1|)) (SIGNATURE |bit?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |even?| ((|Boolean|) |#1|)) (SIGNATURE |init| (|#1|)) (SIGNATURE |nextItem| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |convert| ((|DoubleFloat|) |#1|)) (SIGNATURE |convert| ((|Float|) |#1|)) (SIGNATURE |permutation| (|#1| |#1| |#1|)) (SIGNATURE |factorial| (|#1| |#1|)) (SIGNATURE |binomial| (|#1| |#1| |#1|)) (SIGNATURE |patternMatch| ((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|))) (SIGNATURE |convert| ((|Pattern| (|Integer|)) |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |convert| ((|Integer|) |#1|)) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |positive?| ((|Boolean|) |#1|)) (SIGNATURE |euclideanSize| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) (SIGNATURE |squareFree| ((|Factored| |#1|) |#1|)) (SIGNATURE |prime?| ((|Boolean|) |#1|)) (SIGNATURE |characteristic| ((|NonNegativeInteger|)))) (|IntegerNumberSystem|)) (T |IntegerNumberSystem&|)) 
((|characteristic| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|IntegerNumberSystem&| *3)) (|ofCategory| *3 (|IntegerNumberSystem|))))) 
(CATEGORY |domain| (SIGNATURE |invmod| (|#1| |#1| |#1|)) (SIGNATURE |powmod| (|#1| |#1| |#1| |#1|)) (SIGNATURE |mask| (|#1| |#1|)) (SIGNATURE |copy| (|#1| |#1|)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |rational?| ((|Boolean|) |#1|)) (SIGNATURE |symmetricRemainder| (|#1| |#1| |#1|)) (SIGNATURE |bit?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |even?| ((|Boolean|) |#1|)) (SIGNATURE |init| (|#1|)) (SIGNATURE |nextItem| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |convert| ((|DoubleFloat|) |#1|)) (SIGNATURE |convert| ((|Float|) |#1|)) (SIGNATURE |permutation| (|#1| |#1| |#1|)) (SIGNATURE |factorial| (|#1| |#1|)) (SIGNATURE |binomial| (|#1| |#1| |#1|)) (SIGNATURE |patternMatch| ((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|))) (SIGNATURE |convert| ((|Pattern| (|Integer|)) |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |convert| ((|Integer|) |#1|)) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |positive?| ((|Boolean|) |#1|)) (SIGNATURE |euclideanSize| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) (SIGNATURE |squareFree| ((|Factored| |#1|) |#1|)) (SIGNATURE |prime?| ((|Boolean|) |#1|)) (SIGNATURE |characteristic| ((|NonNegativeInteger|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|symmetricRemainder| (($ $ $) 83)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|submod| (($ $ $ $) 71)) (|squareFreePart| (($ $) 50)) (|squareFree| (((|Factored| $) $) 51)) (|sizeLess?| (((|Boolean|) $ $) 123)) (|sign| (((|Integer|) $) 112)) (|shift| (($ $ $) 86)) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 104)) (|retract| (((|Integer|) $) 103)) (|rem| (($ $ $) 127)) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) 102) (((|Matrix| (|Integer|)) (|Matrix| $)) 101)) (|recip| (((|Union| $ "failed") $) 33)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 80)) (|rational?| (((|Boolean|) $) 82)) (|rational| (((|Fraction| (|Integer|)) $) 81)) (|random| (($) 79) (($ $) 78)) (|quo| (($ $ $) 126)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 121)) (|prime?| (((|Boolean|) $) 52)) (|powmod| (($ $ $ $) 69)) (|positiveRemainder| (($ $ $) 84)) (|positive?| (((|Boolean|) $) 114)) (|permutation| (($ $ $) 95)) (|patternMatch| (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) 98)) (|one?| (((|Boolean|) $) 30)) (|odd?| (((|Boolean|) $) 90)) (|nextItem| (((|Union| $ "failed") $) 92)) (|negative?| (((|Boolean|) $) 113)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 130)) (|mulmod| (($ $ $ $) 70)) (|min| (($ $ $) 115)) (|max| (($ $ $) 116)) (|mask| (($ $) 73)) (|length| (($ $) 87)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|invmod| (($ $ $) 68)) (|init| (($) 91 T CONST)) (|inc| (($ $) 75)) (|hash| (((|SingleInteger|) $) 10) (($ $) 77)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|factorial| (($ $) 96)) (|factor| (((|Factored| $) $) 49)) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 129) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 128)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 122)) (|even?| (((|Boolean|) $) 89)) (|euclideanSize| (((|NonNegativeInteger|) $) 124)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 125)) (|differentiate| (($ $ (|NonNegativeInteger|)) 109) (($ $) 107)) (|dec| (($ $) 74)) (|copy| (($ $) 76)) (|convert| (((|Integer|) $) 106) (((|InputForm|) $) 100) (((|Pattern| (|Integer|)) $) 99) (((|Float|) $) 94) (((|DoubleFloat|) $) 93)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42) (($ (|Integer|)) 105)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|bit?| (((|Boolean|) $ $) 85)) (|binomial| (($ $ $) 97)) (|base| (($) 88)) (|associates?| (((|Boolean|) $ $) 38)) (|addmod| (($ $ $ $) 72)) (|abs| (($ $) 111)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $ (|NonNegativeInteger|)) 110) (($ $) 108)) (>= (((|Boolean|) $ $) 118)) (> (((|Boolean|) $ $) 119)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 117)) (< (((|Boolean|) $ $) 120)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|IntegerNumberSystem|) (|Category|)) (T |IntegerNumberSystem|)) 
((|odd?| (*1 *2 *1) (AND (|ofCategory| *1 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|)))) (|even?| (*1 *2 *1) (AND (|ofCategory| *1 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|)))) (|base| (*1 *1) (|ofCategory| *1 (|IntegerNumberSystem|))) (|length| (*1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|))) (|shift| (*1 *1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|))) (|bit?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|)))) (|positiveRemainder| (*1 *1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|))) (|symmetricRemainder| (*1 *1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|))) (|rational?| (*1 *2 *1) (AND (|ofCategory| *1 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|)))) (|rational| (*1 *2 *1) (AND (|ofCategory| *1 (|IntegerNumberSystem|)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|rationalIfCan| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|IntegerNumberSystem|)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|random| (*1 *1) (|ofCategory| *1 (|IntegerNumberSystem|))) (|random| (*1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|))) (|hash| (*1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|))) (|copy| (*1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|))) (|inc| (*1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|))) (|dec| (*1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|))) (|mask| (*1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|))) (|addmod| (*1 *1 *1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|))) (|submod| (*1 *1 *1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|))) (|mulmod| (*1 *1 *1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|))) (|powmod| (*1 *1 *1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|))) (|invmod| (*1 *1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|)))) 
(|Join| (|UniqueFactorizationDomain|) (|EuclideanDomain|) (|OrderedIntegralDomain|) (|DifferentialRing|) (|ConvertibleTo| (|Integer|)) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|ConvertibleTo| (|InputForm|)) (|ConvertibleTo| (|Pattern| (|Integer|))) (|PatternMatchable| (|Integer|)) (|CombinatorialFunctionCategory|) (|RealConstant|) (|CharacteristicZero|) (|StepThrough|) (CATEGORY |domain| (SIGNATURE |odd?| ((|Boolean|) $)) (SIGNATURE |even?| ((|Boolean|) $)) (ATTRIBUTE |multiplicativeValuation|) (SIGNATURE |base| ($)) (SIGNATURE |length| ($ $)) (SIGNATURE |shift| ($ $ $)) (SIGNATURE |bit?| ((|Boolean|) $ $)) (SIGNATURE |positiveRemainder| ($ $ $)) (SIGNATURE |symmetricRemainder| ($ $ $)) (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") $)) (SIGNATURE |random| ($)) (SIGNATURE |random| ($ $)) (SIGNATURE |hash| ($ $)) (SIGNATURE |copy| ($ $)) (SIGNATURE |inc| ($ $)) (SIGNATURE |dec| ($ $)) (SIGNATURE |mask| ($ $)) (SIGNATURE |addmod| ($ $ $ $)) (SIGNATURE |submod| ($ $ $ $)) (SIGNATURE |mulmod| ($ $ $ $)) (SIGNATURE |powmod| ($ $ $ $)) (SIGNATURE |invmod| ($ $ $)) (ATTRIBUTE |canonicalUnitNormal|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CombinatorialFunctionCategory|) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|DoubleFloat|)) . T) ((|ConvertibleTo| (|Float|)) . T) ((|ConvertibleTo| (|InputForm|)) . T) ((|ConvertibleTo| (|Integer|)) . T) ((|ConvertibleTo| (|Pattern| (|Integer|))) . T) ((|DifferentialRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|LinearlyExplicitRingOver| (|Integer|)) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedIntegralDomain|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|PatternMatchable| (|Integer|)) . T) ((|PrincipalIdealDomain|) . T) ((|RealConstant|) . T) ((|RetractableTo| (|Integer|)) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|StepThrough|) . T) ((|UniqueFactorizationDomain|) . T)) 
((~= (((|Boolean|) $ $) NIL (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))))) (|table| (($) NIL) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL)) (|swap!| (((|Void|) $ |#1| |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setelt| ((|#2| $ |#1| |#2|) NIL)) (|select!| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|select| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|search| (((|Union| |#2| "failed") |#1| $) NIL)) (|sample| (($) NIL T CONST)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))))) (|remove!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| |#2| "failed") |#1| $) NIL)) (|remove| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| ((|#2| $ |#1| |#2|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#2| $ |#1|) NIL)) (|parts| (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|List| |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| ((|#1| $) NIL (|has| |#1| (|OrderedSet|)))) (|members| (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|List| |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (((|Boolean|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|maxIndex| ((|#1| $) NIL (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ (|Mapping| |#2| |#2|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL) (($ (|Mapping| |#2| |#2|) $) NIL) (($ (|Mapping| |#2| |#2| |#2|) $ $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))))) (|keys| (((|List| |#1|) $) NIL)) (|key?| (((|Boolean|) |#1| $) NIL)) (|inspect| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL)) (|insert!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL)) (|indices| (((|List| |#1|) $) NIL)) (|index?| (((|Boolean|) |#1| $) NIL)) (|hash| (((|SingleInteger|) $) NIL (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))))) (|first| ((|#2| $) NIL (|has| |#1| (|OrderedSet|)))) (|find| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL)) (|fill!| (($ $ |#2|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|extract!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) NIL (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ $ (|Equation| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) NIL (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ $ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ $ (|List| |#2|) (|List| |#2|)) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ |#2| |#2|) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|Equation| |#2|)) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|List| (|Equation| |#2|))) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|entry?| (((|Boolean|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|entries| (((|List| |#2|) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#2| $ |#1|) NIL) ((|#2| $ |#1| |#2|) NIL)) (|dictionary| (($) NIL) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (((|NonNegativeInteger|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) NIL (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL)) (|coerce| (((|OutputForm|) $) NIL (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))))) (|bag| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) NIL (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|InnerTable| |#1| |#2| |#3|) (|Join| (|TableAggregate| |#1| |#2|) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|))) (|SetCategory|) (|SetCategory|) (|Join| (|TableAggregate| |#1| |#2|) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|)))) (T |InnerTable|)) 
NIL 
(|Join| (|TableAggregate| |#1| |#2|) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|))) 
((|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) 49))) 
(((|AlgebraicIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |algint| ((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))))) (|Join| (|OrderedSet|) (|IntegralDomain|)) (|Join| (|AlgebraicallyClosedField|) (|FunctionSpace| |#1|))) (T |AlgebraicIntegration|)) 
((|algint| (*1 *2 *3 *4 *4 *5) (AND (|isDomain| *4 (|Kernel| *3)) (|isDomain| *5 (|Mapping| (|SparseUnivariatePolynomial| *3) (|SparseUnivariatePolynomial| *3))) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|FunctionSpace| *6))) (|ofCategory| *6 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *2 (|IntegrationResult| *3)) (|isDomain| *1 (|AlgebraicIntegration| *6 *3))))) 
(CATEGORY |package| (SIGNATURE |algint| ((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))))) 
((|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) 195)) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) 191)) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) 198))) 
(((|AlgebraicIntegrate| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |algintegrate| ((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|))) (SIGNATURE |palgintegrate| ((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|))) (SIGNATURE |palginfieldint| ((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)))) (|Join| (|OrderedSet|) (|IntegralDomain|) (|RetractableTo| (|Integer|))) (|Join| (|AlgebraicallyClosedField|) (|FunctionSpace| |#1|)) (|UnivariatePolynomialCategory| |#2|) (|UnivariatePolynomialCategory| (|Fraction| |#3|)) (|FunctionFieldCategory| |#2| |#3| |#4|)) (T |AlgebraicIntegrate|)) 
((|palginfieldint| (*1 *2 *2 *3) (|partial| AND (|isDomain| *3 (|Mapping| *6 *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Join| (|AlgebraicallyClosedField|) (|FunctionSpace| *4))) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|) (|RetractableTo| (|Integer|)))) (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|isDomain| *1 (|AlgebraicIntegrate| *4 *5 *6 *7 *2)) (|ofCategory| *2 (|FunctionFieldCategory| *5 *6 *7)))) (|palgintegrate| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| *7 *7)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|ofCategory| *6 (|Join| (|AlgebraicallyClosedField|) (|FunctionSpace| *5))) (|ofCategory| *5 (|Join| (|OrderedSet|) (|IntegralDomain|) (|RetractableTo| (|Integer|)))) (|ofCategory| *8 (|UnivariatePolynomialCategory| (|Fraction| *7))) (|isDomain| *2 (|IntegrationResult| *3)) (|isDomain| *1 (|AlgebraicIntegrate| *5 *6 *7 *8 *3)) (|ofCategory| *3 (|FunctionFieldCategory| *6 *7 *8)))) (|algintegrate| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| *7 *7)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|ofCategory| *6 (|Join| (|AlgebraicallyClosedField|) (|FunctionSpace| *5))) (|ofCategory| *5 (|Join| (|OrderedSet|) (|IntegralDomain|) (|RetractableTo| (|Integer|)))) (|ofCategory| *8 (|UnivariatePolynomialCategory| (|Fraction| *7))) (|isDomain| *2 (|IntegrationResult| *3)) (|isDomain| *1 (|AlgebraicIntegrate| *5 *6 *7 *8 *3)) (|ofCategory| *3 (|FunctionFieldCategory| *6 *7 *8))))) 
(CATEGORY |package| (SIGNATURE |algintegrate| ((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|))) (SIGNATURE |palgintegrate| ((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|))) (SIGNATURE |palginfieldint| ((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)))) 
((|bitTruth| (((|Boolean|) (|Integer|) (|Integer|)) 10)) (|bitLength| (((|Integer|) (|Integer|)) 7)) (|bitCoef| (((|Integer|) (|Integer|) (|Integer|)) 8))) 
(((|IntegerBits|) (CATEGORY |package| (SIGNATURE |bitLength| ((|Integer|) (|Integer|))) (SIGNATURE |bitCoef| ((|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |bitTruth| ((|Boolean|) (|Integer|) (|Integer|))))) (T |IntegerBits|)) 
((|bitTruth| (*1 *2 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|IntegerBits|)))) (|bitCoef| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerBits|)))) (|bitLength| (*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerBits|))))) 
(CATEGORY |package| (SIGNATURE |bitLength| ((|Integer|) (|Integer|))) (SIGNATURE |bitCoef| ((|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |bitTruth| ((|Boolean|) (|Integer|) (|Integer|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|width| ((|#1| $) 60)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|tanh| (($ $) 90)) (|tan| (($ $) 73)) (|sup| ((|#1| $) 61)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sqrt| (($ $) 72)) (|sinh| (($ $) 89)) (|sin| (($ $) 74)) (|sech| (($ $) 88)) (|sec| (($ $) 75)) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 68)) (|retract| (((|Integer|) $) 67)) (|recip| (((|Union| $ "failed") $) 33)) (|qinterval| (($ |#1| |#1|) 65)) (|positive?| (((|Boolean|) $) 59)) (|pi| (($) 100)) (|one?| (((|Boolean|) $) 30)) (|nthRoot| (($ $ (|Integer|)) 71)) (|negative?| (((|Boolean|) $) 58)) (|min| (($ $ $) 106)) (|max| (($ $ $) 105)) (|log| (($ $) 97)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|interval| (($ |#1| |#1|) 66) (($ |#1|) 64) (($ (|Fraction| (|Integer|))) 63)) (|inf| ((|#1| $) 62)) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|exp| (($ $) 98)) (|csch| (($ $) 87)) (|csc| (($ $) 76)) (|coth| (($ $) 86)) (|cot| (($ $) 77)) (|cosh| (($ $) 85)) (|cos| (($ $) 78)) (|contains?| (((|Boolean|) $ |#1|) 57)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42) (($ (|Integer|)) 69)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|atanh| (($ $) 96)) (|atan| (($ $) 84)) (|associates?| (((|Boolean|) $ $) 38)) (|asinh| (($ $) 95)) (|asin| (($ $) 83)) (|asech| (($ $) 94)) (|asec| (($ $) 82)) (|acsch| (($ $) 93)) (|acsc| (($ $) 81)) (|acoth| (($ $) 92)) (|acot| (($ $) 80)) (|acosh| (($ $) 91)) (|acos| (($ $) 79)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (>= (((|Boolean|) $ $) 103)) (> (((|Boolean|) $ $) 102)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 104)) (< (((|Boolean|) $ $) 101)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ $) 99) (($ $ (|Fraction| (|Integer|))) 70)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|IntervalCategory| |#1|) (|Category|) (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))) (T |IntervalCategory|)) 
((|interval| (*1 *1 *2 *2) (AND (|ofCategory| *1 (|IntervalCategory| *2)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))))) (|qinterval| (*1 *1 *2 *2) (AND (|ofCategory| *1 (|IntervalCategory| *2)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))))) (|interval| (*1 *1 *2) (AND (|ofCategory| *1 (|IntervalCategory| *2)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))))) (|interval| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|ofCategory| *1 (|IntervalCategory| *3)) (|ofCategory| *3 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))))) (|inf| (*1 *2 *1) (AND (|ofCategory| *1 (|IntervalCategory| *2)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))))) (|sup| (*1 *2 *1) (AND (|ofCategory| *1 (|IntervalCategory| *2)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))))) (|width| (*1 *2 *1) (AND (|ofCategory| *1 (|IntervalCategory| *2)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))))) (|positive?| (*1 *2 *1) (AND (|ofCategory| *1 (|IntervalCategory| *3)) (|ofCategory| *3 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))) (|isDomain| *2 (|Boolean|)))) (|negative?| (*1 *2 *1) (AND (|ofCategory| *1 (|IntervalCategory| *3)) (|ofCategory| *3 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))) (|isDomain| *2 (|Boolean|)))) (|contains?| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|IntervalCategory| *3)) (|ofCategory| *3 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))) (|isDomain| *2 (|Boolean|))))) 
(|Join| (|GcdDomain|) (|OrderedSet|) (|TranscendentalFunctionCategory|) (|RadicalCategory|) (|RetractableTo| (|Integer|)) (CATEGORY |domain| (ATTRIBUTE |approximate|) (SIGNATURE |interval| ($ |t#1| |t#1|)) (SIGNATURE |qinterval| ($ |t#1| |t#1|)) (SIGNATURE |interval| ($ |t#1|)) (SIGNATURE |interval| ($ (|Fraction| (|Integer|)))) (SIGNATURE |inf| (|t#1| $)) (SIGNATURE |sup| (|t#1| $)) (SIGNATURE |width| (|t#1| $)) (SIGNATURE |positive?| ((|Boolean|) $)) (SIGNATURE |negative?| ((|Boolean|) $)) (SIGNATURE |contains?| ((|Boolean|) $ |t#1|)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|ArcHyperbolicFunctionCategory|) . T) ((|ArcTrigonometricFunctionCategory|) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ElementaryFunctionCategory|) . T) ((|EntireRing|) . T) ((|GcdDomain|) . T) ((|HyperbolicFunctionCategory|) . T) ((|IntegralDomain|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedSet|) . T) ((|RadicalCategory|) . T) ((|RetractableTo| (|Integer|)) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) . T) ((|TrigonometricFunctionCategory|) . T)) 
((|placesOfDegree| (((|Void|) (|PositiveInteger|) |#3| (|List| |#5|)) 55)) (|intersectionDivisor| ((|#8| |#3| |#3| (|List| |#10|) (|List| |#5|)) 52))) 
(((|IntersectionDivisorPackage| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8| |#9| |#10| |#11|) (CATEGORY |package| (SIGNATURE |intersectionDivisor| (|#8| |#3| |#3| (|List| |#10|) (|List| |#5|))) (SIGNATURE |placesOfDegree| ((|Void|) (|PositiveInteger|) |#3| (|List| |#5|)))) (|Field|) (|List| (|Symbol|)) (|PolynomialCategory| |#1| |#4| (|OrderedVariableList| |#2|)) (|DirectProductCategory| (|#| |#2|) (|NonNegativeInteger|)) (|ProjectiveSpaceCategory| |#1|) (|LocalPowerSeriesCategory| |#1|) (|PlacesCategory| |#1| |#6|) (|DivisorCategory| |#7|) (|InfinitlyClosePointCategory| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8| |#11|) (|DesingTreeCategory| |#9|) (|BlowUpMethodCategory|)) (T |IntersectionDivisorPackage|)) 
((|placesOfDegree| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *5 (|List| *9)) (|ofCategory| *9 (|ProjectiveSpaceCategory| *6)) (|ofCategory| *6 (|Field|)) (|ofType| *7 (|List| (|Symbol|))) (|ofCategory| *4 (|PolynomialCategory| *6 *8 (|OrderedVariableList| *7))) (|ofCategory| *8 (|DirectProductCategory| (|#| *7) (|NonNegativeInteger|))) (|ofCategory| *10 (|LocalPowerSeriesCategory| *6)) (|ofCategory| *11 (|PlacesCategory| *6 *10)) (|ofCategory| *12 (|DivisorCategory| *11)) (|ofCategory| *13 (|InfinitlyClosePointCategory| *6 *7 *4 *8 *9 *10 *11 *12 *15)) (|ofCategory| *15 (|BlowUpMethodCategory|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|IntersectionDivisorPackage| *6 *7 *4 *8 *9 *10 *11 *12 *13 *14 *15)) (|ofCategory| *14 (|DesingTreeCategory| *13)))) (|intersectionDivisor| (*1 *2 *3 *3 *4 *5) (AND (|isDomain| *4 (|List| *13)) (|isDomain| *5 (|List| *9)) (|ofCategory| *9 (|ProjectiveSpaceCategory| *6)) (|ofCategory| *13 (|DesingTreeCategory| *12)) (|ofCategory| *6 (|Field|)) (|ofCategory| *12 (|InfinitlyClosePointCategory| *6 *7 *3 *8 *9 *10 *11 *2 *14)) (|ofCategory| *14 (|BlowUpMethodCategory|)) (|ofType| *7 (|List| (|Symbol|))) (|ofCategory| *3 (|PolynomialCategory| *6 *8 (|OrderedVariableList| *7))) (|ofCategory| *8 (|DirectProductCategory| (|#| *7) (|NonNegativeInteger|))) (|ofCategory| *10 (|LocalPowerSeriesCategory| *6)) (|ofCategory| *11 (|PlacesCategory| *6 *10)) (|ofCategory| *2 (|DivisorCategory| *11)) (|isDomain| *1 (|IntersectionDivisorPackage| *6 *7 *3 *8 *9 *10 *11 *2 *12 *13 *14))))) 
(CATEGORY |package| (SIGNATURE |intersectionDivisor| (|#8| |#3| |#3| (|List| |#10|) (|List| |#5|))) (SIGNATURE |placesOfDegree| ((|Void|) (|PositiveInteger|) |#3| (|List| |#5|)))) 
((|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 9)) (|unitCanonical| (($ $) 11)) (|unit?| (((|Boolean|) $) 18)) (|recip| (((|Union| $ "failed") $) 16)) (|associates?| (((|Boolean|) $ $) 20))) 
(((|IntegralDomain&| |#1|) (CATEGORY |domain| (SIGNATURE |unit?| ((|Boolean|) |#1|)) (SIGNATURE |associates?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |unitCanonical| (|#1| |#1|)) (SIGNATURE |unitNormal| ((|Record| (|:| |unit| |#1|) (|:| |canonical| |#1|) (|:| |associate| |#1|)) |#1|)) (SIGNATURE |recip| ((|Union| |#1| "failed") |#1|))) (|IntegralDomain|)) (T |IntegralDomain&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |unit?| ((|Boolean|) |#1|)) (SIGNATURE |associates?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |unitCanonical| (|#1| |#1|)) (SIGNATURE |unitNormal| ((|Record| (|:| |unit| |#1|) (|:| |canonical| |#1|) (|:| |associate| |#1|)) |#1|)) (SIGNATURE |recip| ((|Union| |#1| "failed") |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|IntegralDomain|) (|Category|)) (T |IntegralDomain|)) 
((|exquo| (*1 *1 *1 *1) (|partial| |ofCategory| *1 (|IntegralDomain|))) (|unitNormal| (*1 *2 *1) (AND (|isDomain| *2 (|Record| (|:| |unit| *1) (|:| |canonical| *1) (|:| |associate| *1))) (|ofCategory| *1 (|IntegralDomain|)))) (|unitCanonical| (*1 *1 *1) (|ofCategory| *1 (|IntegralDomain|))) (|associates?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|)))) (|unit?| (*1 *2 *1) (AND (|ofCategory| *1 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|))))) 
(|Join| (|CommutativeRing|) (|Algebra| $) (|EntireRing|) (CATEGORY |domain| (SIGNATURE |exquo| ((|Union| $ "failed") $ $)) (SIGNATURE |unitNormal| ((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $)) (SIGNATURE |unitCanonical| ($ $)) (SIGNATURE |associates?| ((|Boolean|) $ $)) (SIGNATURE |unit?| ((|Boolean|) $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|LeftModule| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) 35)) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) 58)) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) 147)) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) 149)) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) 38))) 
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(CATEGORY |package| (SIGNATURE |lfextendedint| ((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|)) (SIGNATURE |lflimitedint| ((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|))) (SIGNATURE |lfinfieldint| ((|Union| |#2| "failed") |#2| (|Symbol|))) (SIGNATURE |lfintegrate| ((|IntegrationResult| |#2|) |#2| (|Symbol|))) (SIGNATURE |lfextlimint| ((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))))) 
((|groebner| (((|List| |#5|) (|List| |#5|)) 41))) 
(((|InterfaceGroebnerPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |groebner| ((|List| |#5|) (|List| |#5|)))) (|Field|) (|List| (|Symbol|)) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#3| |#4|)) (T |InterfaceGroebnerPackage|)) 
((|groebner| (*1 *2 *2) (AND (|isDomain| *2 (|List| *7)) (|ofCategory| *7 (|PolynomialCategory| *3 *5 *6)) (|ofCategory| *3 (|Field|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *1 (|InterfaceGroebnerPackage| *3 *4 *5 *6 *7)) (|ofType| *4 (|List| (|Symbol|)))))) 
(CATEGORY |package| (SIGNATURE |groebner| ((|List| |#5|) (|List| |#5|)))) 
((|squareFree| (((|Factored| |#1|) |#1|) 18)) (|factor| (((|Factored| |#1|) |#1|) 32)) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) 43)) (|BasicMethod| (((|Factored| |#1|) |#1|) 49))) 
(((|IntegerFactorizationPackage| |#1|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) (SIGNATURE |squareFree| ((|Factored| |#1|) |#1|)) (SIGNATURE |BasicMethod| ((|Factored| |#1|) |#1|)) (SIGNATURE |PollardSmallFactor| ((|Union| |#1| "failed") |#1|))) (|IntegerNumberSystem|)) (T |IntegerFactorizationPackage|)) 
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(CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) (SIGNATURE |squareFree| ((|Factored| |#1|) |#1|)) (SIGNATURE |BasicMethod| ((|Factored| |#1|) |#1|)) (SIGNATURE |PollardSmallFactor| ((|Union| |#1| "failed") |#1|))) 
((|interpolateFormsForFact| (((|List| |#3|) |#8| (|List| |#3|)) 45)) (|interpolateForms| (((|List| |#3|) |#8| (|NonNegativeInteger|) |#3| (|List| |#3|)) 44)) (|basisOfInterpolateFormsForFact| (((|List| (|Vector| |#1|)) |#8| (|List| |#3|)) 26)) (|basisOfInterpolateForms| (((|List| (|Vector| |#1|)) |#8| (|List| |#3|)) 27))) 
(((|InterpolateFormsPackage| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (CATEGORY |package| (SIGNATURE |basisOfInterpolateForms| ((|List| (|Vector| |#1|)) |#8| (|List| |#3|))) (SIGNATURE |basisOfInterpolateFormsForFact| ((|List| (|Vector| |#1|)) |#8| (|List| |#3|))) (SIGNATURE |interpolateFormsForFact| ((|List| |#3|) |#8| (|List| |#3|))) (SIGNATURE |interpolateForms| ((|List| |#3|) |#8| (|NonNegativeInteger|) |#3| (|List| |#3|)))) (|Field|) (|List| (|Symbol|)) (|PolynomialCategory| |#1| |#4| (|OrderedVariableList| |#2|)) (|DirectProductCategory| (|#| |#2|) (|NonNegativeInteger|)) (|ProjectiveSpaceCategory| |#1|) (|LocalPowerSeriesCategory| |#1|) (|PlacesCategory| |#1| |#6|) (|DivisorCategory| |#7|)) (T |InterpolateFormsPackage|)) 
((|interpolateForms| (*1 *2 *3 *4 *5 *2) (AND (|isDomain| *2 (|List| *5)) (|ofCategory| *5 (|PolynomialCategory| *6 *8 (|OrderedVariableList| *7))) (|ofCategory| *8 (|DirectProductCategory| (|#| *7) *4)) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *6 (|Field|)) (|ofType| *7 (|List| (|Symbol|))) (|ofCategory| *10 (|LocalPowerSeriesCategory| *6)) (|ofCategory| *11 (|PlacesCategory| *6 *10)) (|isDomain| *1 (|InterpolateFormsPackage| *6 *7 *5 *8 *9 *10 *11 *3)) (|ofCategory| *9 (|ProjectiveSpaceCategory| *6)) (|ofCategory| *3 (|DivisorCategory| *11)))) (|interpolateFormsForFact| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *9 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *10 (|PlacesCategory| *4 *9)) (|isDomain| *1 (|InterpolateFormsPackage| *4 *5 *6 *7 *8 *9 *10 *3)) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *3 (|DivisorCategory| *10)))) (|basisOfInterpolateFormsForFact| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *7)) (|ofCategory| *7 (|PolynomialCategory| *5 *8 (|OrderedVariableList| *6))) (|ofCategory| *8 (|DirectProductCategory| (|#| *6) (|NonNegativeInteger|))) (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *10 (|LocalPowerSeriesCategory| *5)) (|ofCategory| *11 (|PlacesCategory| *5 *10)) (|isDomain| *2 (|List| (|Vector| *5))) (|isDomain| *1 (|InterpolateFormsPackage| *5 *6 *7 *8 *9 *10 *11 *3)) (|ofCategory| *9 (|ProjectiveSpaceCategory| *5)) (|ofCategory| *3 (|DivisorCategory| *11)))) (|basisOfInterpolateForms| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *7)) (|ofCategory| *7 (|PolynomialCategory| *5 *8 (|OrderedVariableList| *6))) (|ofCategory| *8 (|DirectProductCategory| (|#| *6) (|NonNegativeInteger|))) (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *10 (|LocalPowerSeriesCategory| *5)) (|ofCategory| *11 (|PlacesCategory| *5 *10)) (|isDomain| *2 (|List| (|Vector| *5))) (|isDomain| *1 (|InterpolateFormsPackage| *5 *6 *7 *8 *9 *10 *11 *3)) (|ofCategory| *9 (|ProjectiveSpaceCategory| *5)) (|ofCategory| *3 (|DivisorCategory| *11))))) 
(CATEGORY |package| (SIGNATURE |basisOfInterpolateForms| ((|List| (|Vector| |#1|)) |#8| (|List| |#3|))) (SIGNATURE |basisOfInterpolateFormsForFact| ((|List| (|Vector| |#1|)) |#8| (|List| |#3|))) (SIGNATURE |interpolateFormsForFact| ((|List| |#3|) |#8| (|List| |#3|))) (SIGNATURE |interpolateForms| ((|List| |#3|) |#8| (|NonNegativeInteger|) |#3| (|List| |#3|)))) 
((|showTheFTable| (($) 9)) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 29)) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) 26)) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| 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(|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) 21)) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 33)) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point 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(((|IntegrationFunctionsTable|) (CATEGORY |domain| (SIGNATURE |showTheFTable| ($)) (SIGNATURE |clearTheFTable| ((|Void|))) (SIGNATURE |keys| ((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $)) (SIGNATURE |fTable| ($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))))) (SIGNATURE |insert!| ($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| 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|notEvaluated| "Range not yet evaluated"))))) (|isDomain| *1 (|IntegrationFunctionsTable|)))) (|entries| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is 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|singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) (|isDomain| *1 (|IntegrationFunctionsTable|)))) (|fTable| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) (|isDomain| *1 (|IntegrationFunctionsTable|)))) (|keys| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (|isDomain| *1 (|IntegrationFunctionsTable|)))) (|clearTheFTable| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 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|str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))))) (SIGNATURE |insert!| ($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) (SIGNATURE |showAttributes| ((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |entries| ((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $)) (SIGNATURE |entry| ((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) 
((|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) 28)) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) 96) (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) 106)) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) 78) (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) 50)) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) 85) (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) 105)) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) 101) (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) 107)) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) 124 (|has| |#3| (|LinearOrdinaryDifferentialOperatorCategory| |#2|))) (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) 123 (|has| |#3| (|LinearOrdinaryDifferentialOperatorCategory| |#2|)))) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) 48)) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) 27))) 
(((|GenusZeroIntegration| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |palgint0| ((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |palgint0| ((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|)))) (SIGNATURE |palgextint0| ((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |palgextint0| ((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|)))) (SIGNATURE |palglimint0| ((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |palglimint0| ((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|)))) (SIGNATURE |palgRDE0| ((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |palgRDE0| ((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|)))) (SIGNATURE |univariate| ((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |multivariate| (|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|)) (SIGNATURE |lift| ((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|))) (IF (|has| |#3| (|LinearOrdinaryDifferentialOperatorCategory| |#2|)) (PROGN (SIGNATURE |palgLODE0| ((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |palgLODE0| ((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))))) |noBranch|)) (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|CharacteristicZero|) (|LinearlyExplicitRingOver| (|Integer|))) (|Join| (|FunctionSpace| |#1|) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|)) (|SetCategory|)) (T |GenusZeroIntegration|)) 
((|palgLODE0| (*1 *2 *3 *4 *5 *5 *5 *4 *6) (AND (|isDomain| *5 (|Kernel| *4)) (|isDomain| *6 (|Fraction| (|SparseUnivariatePolynomial| *4))) (|ofCategory| *4 (|Join| (|FunctionSpace| *7) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|))) (|ofCategory| *7 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|CharacteristicZero|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |particular| (|Union| *4 "failed")) (|:| |basis| (|List| *4)))) (|isDomain| *1 (|GenusZeroIntegration| *7 *4 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4)) (|ofCategory| *3 (|SetCategory|)))) (|palgLODE0| (*1 *2 *3 *4 *5 *5 *4 *6) (AND (|isDomain| *5 (|Kernel| *4)) (|isDomain| *6 (|SparseUnivariatePolynomial| *4)) (|ofCategory| *4 (|Join| (|FunctionSpace| *7) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|))) (|ofCategory| *7 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|CharacteristicZero|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |particular| (|Union| *4 "failed")) (|:| |basis| (|List| *4)))) (|isDomain| *1 (|GenusZeroIntegration| *7 *4 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4)) (|ofCategory| *3 (|SetCategory|)))) (|lift| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Kernel| *6)) (|ofCategory| *6 (|Join| (|FunctionSpace| *5) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|))) (|ofCategory| *5 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|CharacteristicZero|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| *6)))) (|isDomain| *1 (|GenusZeroIntegration| *5 *6 *7)) (|isDomain| *3 (|SparseUnivariatePolynomial| *6)) (|ofCategory| *7 (|SetCategory|)))) (|multivariate| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| *2)))) (|isDomain| *4 (|Kernel| *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *5) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|))) (|ofCategory| *5 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|CharacteristicZero|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|GenusZeroIntegration| *5 *2 *6)) (|ofCategory| *6 (|SetCategory|)))) (|univariate| (*1 *2 *3 *4 *4 *5) (AND (|isDomain| *4 (|Kernel| *3)) (|ofCategory| *3 (|Join| (|FunctionSpace| *6) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|))) (|ofCategory| *6 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|CharacteristicZero|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| *3)))) (|isDomain| *1 (|GenusZeroIntegration| *6 *3 *7)) (|isDomain| *5 (|SparseUnivariatePolynomial| *3)) (|ofCategory| *7 (|SetCategory|)))) (|palgRDE0| (*1 *2 *2 *2 *3 *3 *4 *3 *2 *5) (|partial| AND (|isDomain| *3 (|Kernel| *2)) (|isDomain| *4 (|Mapping| (|Union| *2 "failed") *2 *2 (|Symbol|))) (|isDomain| *5 (|Fraction| (|SparseUnivariatePolynomial| *2))) (|ofCategory| *2 (|Join| (|FunctionSpace| *6) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|))) (|ofCategory| *6 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|CharacteristicZero|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|GenusZeroIntegration| *6 *2 *7)) (|ofCategory| *7 (|SetCategory|)))) (|palgRDE0| (*1 *2 *2 *2 *3 *3 *4 *2 *5) (|partial| AND (|isDomain| *3 (|Kernel| *2)) (|isDomain| *4 (|Mapping| (|Union| *2 "failed") *2 *2 (|Symbol|))) (|isDomain| *5 (|SparseUnivariatePolynomial| *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *6) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|))) (|ofCategory| *6 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|CharacteristicZero|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|GenusZeroIntegration| *6 *2 *7)) (|ofCategory| *7 (|SetCategory|)))) (|palglimint0| (*1 *2 *3 *4 *4 *5 *4 *3 *6) (|partial| AND (|isDomain| *4 (|Kernel| *3)) (|isDomain| *5 (|List| *3)) (|isDomain| *6 (|Fraction| (|SparseUnivariatePolynomial| *3))) (|ofCategory| *3 (|Join| (|FunctionSpace| *7) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|))) (|ofCategory| *7 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|CharacteristicZero|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |mainpart| *3) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| *3) (|:| |logand| *3)))))) (|isDomain| *1 (|GenusZeroIntegration| *7 *3 *8)) (|ofCategory| *8 (|SetCategory|)))) (|palglimint0| (*1 *2 *3 *4 *4 *5 *3 *6) (|partial| AND (|isDomain| *4 (|Kernel| *3)) (|isDomain| *5 (|List| *3)) (|isDomain| *6 (|SparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|Join| (|FunctionSpace| *7) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|))) (|ofCategory| *7 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|CharacteristicZero|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |mainpart| *3) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| *3) (|:| |logand| *3)))))) (|isDomain| *1 (|GenusZeroIntegration| *7 *3 *8)) (|ofCategory| *8 (|SetCategory|)))) (|palgextint0| (*1 *2 *3 *4 *4 *3 *4 *3 *5) (|partial| AND (|isDomain| *4 (|Kernel| *3)) (|isDomain| *5 (|Fraction| (|SparseUnivariatePolynomial| *3))) (|ofCategory| *3 (|Join| (|FunctionSpace| *6) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|))) (|ofCategory| *6 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|CharacteristicZero|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |ratpart| *3) (|:| |coeff| *3))) (|isDomain| *1 (|GenusZeroIntegration| *6 *3 *7)) (|ofCategory| *7 (|SetCategory|)))) (|palgextint0| (*1 *2 *3 *4 *4 *3 *3 *5) (|partial| AND (|isDomain| *4 (|Kernel| *3)) (|isDomain| *5 (|SparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|Join| (|FunctionSpace| *6) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|))) (|ofCategory| *6 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|CharacteristicZero|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |ratpart| *3) (|:| |coeff| *3))) (|isDomain| *1 (|GenusZeroIntegration| *6 *3 *7)) (|ofCategory| *7 (|SetCategory|)))) (|palgint0| (*1 *2 *3 *4 *4 *4 *3 *5) (AND (|isDomain| *4 (|Kernel| *3)) (|isDomain| *5 (|Fraction| (|SparseUnivariatePolynomial| *3))) (|ofCategory| *3 (|Join| (|FunctionSpace| *6) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|))) (|ofCategory| *6 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|CharacteristicZero|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|IntegrationResult| *3)) (|isDomain| *1 (|GenusZeroIntegration| *6 *3 *7)) (|ofCategory| *7 (|SetCategory|)))) (|palgint0| (*1 *2 *3 *4 *4 *3 *5) (AND (|isDomain| *4 (|Kernel| *3)) (|isDomain| *5 (|SparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|Join| (|FunctionSpace| *6) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|))) (|ofCategory| *6 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|CharacteristicZero|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|IntegrationResult| *3)) (|isDomain| *1 (|GenusZeroIntegration| *6 *3 *7)) (|ofCategory| *7 (|SetCategory|))))) 
(CATEGORY |package| (SIGNATURE |palgint0| ((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |palgint0| ((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|)))) (SIGNATURE |palgextint0| ((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |palgextint0| ((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|)))) (SIGNATURE |palglimint0| ((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |palglimint0| ((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|)))) (SIGNATURE |palgRDE0| ((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |palgRDE0| ((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|)))) (SIGNATURE |univariate| ((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |multivariate| (|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|)) (SIGNATURE |lift| ((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|))) (IF (|has| |#3| (|LinearOrdinaryDifferentialOperatorCategory| |#2|)) (PROGN (SIGNATURE |palgLODE0| ((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |palgLODE0| ((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))))) |noBranch|)) 
((|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) 65)) (|sumOfDivisors| (((|Integer|) (|Integer|)) 64)) (|numberOfDivisors| (((|Integer|) (|Integer|)) 63)) (|moebiusMu| (((|Integer|) (|Integer|)) 68)) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) 48)) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) 45)) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) 20)) (|fibonacci| (((|Integer|) (|Integer|)) 21)) (|eulerPhi| (((|Integer|) (|Integer|)) 57)) (|euler| (((|Integer|) (|Integer|)) 32)) (|divisors| (((|List| (|Integer|)) (|Integer|)) 62)) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) 43)) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) 41))) 
(((|IntegerNumberTheoryFunctions|) (CATEGORY |package| (SIGNATURE |bernoulli| ((|Fraction| (|Integer|)) (|Integer|))) (SIGNATURE |chineseRemainder| ((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |divisors| ((|List| (|Integer|)) (|Integer|))) (SIGNATURE |euler| ((|Integer|) (|Integer|))) (SIGNATURE |eulerPhi| ((|Integer|) (|Integer|))) (SIGNATURE |fibonacci| ((|Integer|) (|Integer|))) (SIGNATURE |harmonic| ((|Fraction| (|Integer|)) (|Integer|))) (SIGNATURE |jacobi| ((|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |legendre| ((|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |moebiusMu| ((|Integer|) (|Integer|))) (SIGNATURE |numberOfDivisors| ((|Integer|) (|Integer|))) (SIGNATURE |sumOfDivisors| ((|Integer|) (|Integer|))) (SIGNATURE |sumOfKthPowerDivisors| ((|Integer|) (|Integer|) (|NonNegativeInteger|))))) (T |IntegerNumberTheoryFunctions|)) 
((|sumOfKthPowerDivisors| (*1 *2 *2 *3) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|IntegerNumberTheoryFunctions|)))) (|sumOfDivisors| (*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerNumberTheoryFunctions|)))) (|numberOfDivisors| (*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerNumberTheoryFunctions|)))) (|moebiusMu| (*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerNumberTheoryFunctions|)))) (|legendre| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerNumberTheoryFunctions|)))) (|jacobi| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerNumberTheoryFunctions|)))) (|harmonic| (*1 *2 *3) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|IntegerNumberTheoryFunctions|)) (|isDomain| *3 (|Integer|)))) (|fibonacci| (*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerNumberTheoryFunctions|)))) (|eulerPhi| (*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerNumberTheoryFunctions|)))) (|euler| (*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerNumberTheoryFunctions|)))) (|divisors| (*1 *2 *3) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|IntegerNumberTheoryFunctions|)) (|isDomain| *3 (|Integer|)))) (|chineseRemainder| (*1 *2 *2 *2 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerNumberTheoryFunctions|)))) (|bernoulli| (*1 *2 *3) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|IntegerNumberTheoryFunctions|)) (|isDomain| *3 (|Integer|))))) 
(CATEGORY |package| (SIGNATURE |bernoulli| ((|Fraction| (|Integer|)) (|Integer|))) (SIGNATURE |chineseRemainder| ((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |divisors| ((|List| (|Integer|)) (|Integer|))) (SIGNATURE |euler| ((|Integer|) (|Integer|))) (SIGNATURE |eulerPhi| ((|Integer|) (|Integer|))) (SIGNATURE |fibonacci| ((|Integer|) (|Integer|))) (SIGNATURE |harmonic| ((|Fraction| (|Integer|)) (|Integer|))) (SIGNATURE |jacobi| ((|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |legendre| ((|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |moebiusMu| ((|Integer|) (|Integer|))) (SIGNATURE |numberOfDivisors| ((|Integer|) (|Integer|))) (SIGNATURE |sumOfDivisors| ((|Integer|) (|Integer|))) (SIGNATURE |sumOfKthPowerDivisors| ((|Integer|) (|Integer|) (|NonNegativeInteger|)))) 
((|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) 52))) 
(((|AlgebraicHermiteIntegration| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |HermiteIntegrate| ((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)))) (|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|)) (T |AlgebraicHermiteIntegration|)) 
((|HermiteIntegrate| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| *6 *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Field|)) (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|isDomain| *2 (|Record| (|:| |answer| *3) (|:| |logpart| *3))) (|isDomain| *1 (|AlgebraicHermiteIntegration| *5 *6 *7 *3)) (|ofCategory| *3 (|FunctionFieldCategory| *5 *6 *7))))) 
(CATEGORY |package| (SIGNATURE |HermiteIntegrate| ((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)))) 
((|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) 18))) 
(((|TranscendentalHermiteIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |HermiteIntegrate| ((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)))) (|Field|) (|UnivariatePolynomialCategory| |#1|)) (T |TranscendentalHermiteIntegration|)) 
((|HermiteIntegrate| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| *6 *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Record| (|:| |answer| (|Fraction| *6)) (|:| |logpart| (|Fraction| *6)) (|:| |specpart| (|Fraction| *6)) (|:| |polypart| *6))) (|isDomain| *1 (|TranscendentalHermiteIntegration| *5 *6)) (|isDomain| *3 (|Fraction| *6))))) 
(CATEGORY |package| (SIGNATURE |HermiteIntegrate| ((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)))) 
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(((|Integer|) (|Join| (|IntegerNumberSystem|) (|ConvertibleTo| (|String|)) (|OpenMath|) (CATEGORY |domain| (SIGNATURE |random| ($ $)) (ATTRIBUTE |canonical|) (ATTRIBUTE |canonicalsClosed|) (ATTRIBUTE |noetherian|) (ATTRIBUTE |infinite|)))) (T |Integer|)) 
((|random| (*1 *1 *1) (|isDomain| *1 (|Integer|)))) 
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((|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) 14)) (|integer?| (((|Boolean|) |#1|) 13)) (|integer| (((|Integer|) |#1|) 9))) 
(((|IntegerRetractions| |#1|) (CATEGORY |package| (SIGNATURE |integer| ((|Integer|) |#1|)) (SIGNATURE |integer?| ((|Boolean|) |#1|)) (SIGNATURE |integerIfCan| ((|Union| (|Integer|) "failed") |#1|))) (|RetractableTo| (|Integer|))) (T |IntegerRetractions|)) 
((|integerIfCan| (*1 *2 *3) (|partial| AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerRetractions| *3)) (|ofCategory| *3 (|RetractableTo| *2)))) (|integer?| (*1 *2 *3) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|IntegerRetractions| *3)) (|ofCategory| *3 (|RetractableTo| (|Integer|))))) (|integer| (*1 *2 *3) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerRetractions| *3)) (|ofCategory| *3 (|RetractableTo| *2))))) 
(CATEGORY |package| (SIGNATURE |integer| ((|Integer|) |#1|)) (SIGNATURE |integer?| ((|Boolean|) |#1|)) (SIGNATURE |integerIfCan| ((|Union| (|Integer|) "failed") |#1|))) 
((|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) 43)) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) 25)) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) 20)) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) 32))) 
(((|RationalFunctionIntegration| |#1|) (CATEGORY |package| (SIGNATURE |internalIntegrate| ((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |infieldIntegrate| ((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |limitedIntegrate| ((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |extendedIntegrate| ((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))))) (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|)) (|CharacteristicZero|))) (T |RationalFunctionIntegration|)) 
((|extendedIntegrate| (*1 *2 *3 *4 *3) (|partial| AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *2 (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| *5))) (|:| |coeff| (|Fraction| (|Polynomial| *5))))) (|isDomain| *1 (|RationalFunctionIntegration| *5)) (|isDomain| *3 (|Fraction| (|Polynomial| *5))))) (|limitedIntegrate| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|List| (|Fraction| (|Polynomial| *6)))) (|isDomain| *3 (|Fraction| (|Polynomial| *6))) (|ofCategory| *6 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *2 (|Record| (|:| |mainpart| *3) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| *3) (|:| |logand| *3)))))) (|isDomain| *1 (|RationalFunctionIntegration| *6)))) (|infieldIntegrate| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|Fraction| (|Polynomial| *4))) (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *1 (|RationalFunctionIntegration| *4)))) (|internalIntegrate| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *2 (|IntegrationResult| (|Fraction| (|Polynomial| *5)))) (|isDomain| *1 (|RationalFunctionIntegration| *5)) (|isDomain| *3 (|Fraction| (|Polynomial| *5)))))) 
(CATEGORY |package| (SIGNATURE |internalIntegrate| ((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |infieldIntegrate| ((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |limitedIntegrate| ((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |extendedIntegrate| ((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))))) 
((~= (((|Boolean|) $ $) 59)) (|zero?| (((|Boolean|) $) 36)) (|width| ((|#1| $) 30)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) 63)) (|tanh| (($ $) 123)) (|tan| (($ $) 103)) (|sup| ((|#1| $) 28)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sqrt| (($ $) NIL)) (|sinh| (($ $) 125)) (|sin| (($ $) 99)) (|sech| (($ $) 127)) (|sec| (($ $) 107)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 78)) (|retract| (((|Integer|) $) 80)) (|recip| (((|Union| $ "failed") $) 62)) (|qinterval| (($ |#1| |#1|) 26)) (|positive?| (((|Boolean|) $) 33)) (|pi| (($) 89)) (|one?| (((|Boolean|) $) 43)) (|nthRoot| (($ $ (|Integer|)) NIL)) (|negative?| (((|Boolean|) $) 34)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|log| (($ $) 91)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|interval| (($ |#1| |#1|) 20) (($ |#1|) 25) (($ (|Fraction| (|Integer|))) 77)) (|inf| ((|#1| $) 27)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) 65) (($ (|List| $)) NIL)) (|exquo| (((|Union| $ "failed") $ $) 64)) (|exp| (($ $) 93)) (|csch| (($ $) 131)) (|csc| (($ $) 105)) (|coth| (($ $) 133)) (|cot| (($ $) 109)) (|cosh| (($ $) 129)) (|cos| (($ $) 101)) (|contains?| (((|Boolean|) $ |#1|) 31)) (|coerce| (((|OutputForm|) $) 85) (($ (|Integer|)) 67) (($ $) NIL) (($ (|Integer|)) 67)) (|characteristic| (((|NonNegativeInteger|)) 87)) (|atanh| (($ $) 145)) (|atan| (($ $) 115)) (|associates?| (((|Boolean|) $ $) NIL)) (|asinh| (($ $) 143)) (|asin| (($ $) 111)) (|asech| (($ $) 141)) (|asec| (($ $) 121)) (|acsch| (($ $) 139)) (|acsc| (($ $) 119)) (|acoth| (($ $) 137)) (|acot| (($ $) 117)) (|acosh| (($ $) 135)) (|acos| (($ $) 113)) (^ (($ $ (|PositiveInteger|)) 55) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 21 T CONST)) (|One| (($) 10 T CONST)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 37)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 35)) (- (($ $) 41) (($ $ $) 42)) (+ (($ $ $) 40)) (** (($ $ (|PositiveInteger|)) 54) (($ $ (|NonNegativeInteger|)) NIL) (($ $ $) 95) (($ $ (|Fraction| (|Integer|))) 147)) (* (($ (|PositiveInteger|) $) 51) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 50) (($ $ $) 48))) 
(((|Interval| |#1|) (|IntervalCategory| |#1|) (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))) (T |Interval|)) 
NIL 
(|IntervalCategory| |#1|) 
((|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) 24))) 
(((|IntegerSolveLinearPolynomialEquation|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquation| ((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|)))))) (T |IntegerSolveLinearPolynomialEquation|)) 
((|solveLinearPolynomialEquation| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| (|Integer|)))) (|isDomain| *3 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *1 (|IntegerSolveLinearPolynomialEquation|))))) 
(CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquation| ((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))))) 
((|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) 18)) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) 23)) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) 10)) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) 51 (|has| |#1| (|IntegralDomain|)))) (|mkPrim| ((|#2| |#2| (|Symbol|)) 76 (AND (|has| |#2| (|ElementaryFunctionCategory|)) (|has| |#1| (|GcdDomain|))))) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) 25)) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) 24)) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) 100 (AND (|has| |#2| (|ElementaryFunctionCategory|)) (|has| |#2| (|LiouvillianFunctionCategory|)) (|has| |#2| (|RetractableTo| (|Symbol|))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|PatternMatchable| (|Integer|))))))) 
(((|IntegrationTools| |#1| |#2|) (CATEGORY |package| (SIGNATURE |varselect| ((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|))) (SIGNATURE |kmax| ((|Kernel| |#2|) (|List| (|Kernel| |#2|)))) (SIGNATURE |ksec| ((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|))) (SIGNATURE |union| ((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)))) (SIGNATURE |vark| ((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|))) (IF (|has| |#1| (|IntegralDomain|)) (SIGNATURE |removeConstantTerm| (|#2| |#2| (|Symbol|))) |noBranch|) (IF (|has| |#1| (|GcdDomain|)) (IF (|has| |#2| (|ElementaryFunctionCategory|)) (PROGN (SIGNATURE |mkPrim| (|#2| |#2| (|Symbol|))) (IF (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (IF (|has| |#1| (|PatternMatchable| (|Integer|))) (IF (|has| |#2| (|LiouvillianFunctionCategory|)) (IF (|has| |#2| (|RetractableTo| (|Symbol|))) (SIGNATURE |intPatternMatch| ((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)))) |noBranch|) |noBranch|) |noBranch|) |noBranch|)) |noBranch|) |noBranch|)) (|OrderedSet|) (|FunctionSpace| |#1|)) (T |IntegrationTools|)) 
((|intPatternMatch| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *5 (|Mapping| (|IntegrationResult| *3) *3 (|Symbol|))) (|isDomain| *6 (|Mapping| (|Union| (|Record| (|:| |special| *3) (|:| |integrand| *3)) "failed") *3 (|Symbol|))) (|ofCategory| *3 (|ElementaryFunctionCategory|)) (|ofCategory| *3 (|LiouvillianFunctionCategory|)) (|ofCategory| *3 (|RetractableTo| *4)) (|ofCategory| *3 (|FunctionSpace| *7)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *7 (|ConvertibleTo| (|Pattern| (|Integer|)))) (|ofCategory| *7 (|GcdDomain|)) (|ofCategory| *7 (|PatternMatchable| (|Integer|))) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|IntegrationResult| *3)) (|isDomain| *1 (|IntegrationTools| *7 *3)))) (|mkPrim| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|IntegrationTools| *4 *2)) (|ofCategory| *2 (|ElementaryFunctionCategory|)) (|ofCategory| *2 (|FunctionSpace| *4)))) (|removeConstantTerm| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|IntegrationTools| *4 *2)) (|ofCategory| *2 (|FunctionSpace| *4)))) (|vark| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *6 (|FunctionSpace| *5)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| (|Kernel| *6))) (|isDomain| *1 (|IntegrationTools| *5 *6)))) (|union| (*1 *2 *2 *2) (AND (|isDomain| *2 (|List| (|Kernel| *4))) (|ofCategory| *4 (|FunctionSpace| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|IntegrationTools| *3 *4)))) (|ksec| (*1 *2 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Kernel| *6))) (|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Kernel| *6)) (|ofCategory| *6 (|FunctionSpace| *5)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|IntegrationTools| *5 *6)))) (|kmax| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Kernel| *5))) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|Kernel| *5)) (|isDomain| *1 (|IntegrationTools| *4 *5)) (|ofCategory| *5 (|FunctionSpace| *4)))) (|varselect| (*1 *2 *2 *3) (AND (|isDomain| *2 (|List| (|Kernel| *5))) (|isDomain| *3 (|Symbol|)) (|ofCategory| *5 (|FunctionSpace| *4)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|IntegrationTools| *4 *5))))) 
(CATEGORY |package| (SIGNATURE |varselect| ((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|))) (SIGNATURE |kmax| ((|Kernel| |#2|) (|List| (|Kernel| |#2|)))) (SIGNATURE |ksec| ((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|))) (SIGNATURE |union| ((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)))) (SIGNATURE |vark| ((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|))) (IF (|has| |#1| (|IntegralDomain|)) (SIGNATURE |removeConstantTerm| (|#2| |#2| (|Symbol|))) |noBranch|) (IF (|has| |#1| (|GcdDomain|)) (IF (|has| |#2| (|ElementaryFunctionCategory|)) (PROGN (SIGNATURE |mkPrim| (|#2| |#2| (|Symbol|))) (IF (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (IF (|has| |#1| (|PatternMatchable| (|Integer|))) (IF (|has| |#2| (|LiouvillianFunctionCategory|)) (IF (|has| |#2| (|RetractableTo| (|Symbol|))) (SIGNATURE |intPatternMatch| ((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)))) |noBranch|) |noBranch|) |noBranch|) |noBranch|)) |noBranch|) |noBranch|)) 
((|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) 167)) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) 143)) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) 140)) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) 129)) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) 153)) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) 170)) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) 173)) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) 81)) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) 88)) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) 147)) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) 133)) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) 157)) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) 178))) 
(((|TranscendentalIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |primintegrate| ((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|))) (SIGNATURE |expintegrate| ((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|))) (SIGNATURE |tanintegrate| ((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|))) (SIGNATURE |primextendedint| ((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|))) (SIGNATURE |expextendedint| ((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|))) (SIGNATURE |primlimitedint| ((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|)))) (SIGNATURE |explimitedint| ((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|)))) (SIGNATURE |primextintfrac| ((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|))) (SIGNATURE |primlimintfrac| ((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|)))) (SIGNATURE |primintfldpoly| ((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|)) (SIGNATURE |expintfldpoly| ((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|))) (SIGNATURE |monomialIntegrate| ((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|))) (SIGNATURE |monomialIntPoly| ((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)))) (|Field|) (|UnivariatePolynomialCategory| |#1|)) (T |TranscendentalIntegration|)) 
((|monomialIntPoly| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| *3 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Record| (|:| |answer| *3) (|:| |polypart| *3))) (|isDomain| *1 (|TranscendentalIntegration| *5 *3)))) (|monomialIntegrate| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| *6 *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Record| (|:| |ir| (|IntegrationResult| (|Fraction| *6))) (|:| |specpart| (|Fraction| *6)) (|:| |polypart| *6))) (|isDomain| *1 (|TranscendentalIntegration| *5 *6)) (|isDomain| *3 (|Fraction| *6)))) (|expintfldpoly| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|LaurentPolynomial| *4 *5)) (|isDomain| *3 (|Mapping| (|Record| (|:| |ans| *4) (|:| |right| *4) (|:| |sol?| (|Boolean|))) (|Integer|) *4)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|TranscendentalIntegration| *4 *5)))) (|primintfldpoly| (*1 *2 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Mapping| (|Union| (|Record| (|:| |ratpart| *4) (|:| |coeff| *4)) "failed") *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *1 (|TranscendentalIntegration| *4 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)))) (|primlimintfrac| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *4 (|Mapping| *7 *7)) (|isDomain| *5 (|List| (|Fraction| *7))) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|isDomain| *3 (|Fraction| *7)) (|ofCategory| *6 (|Field|)) (|isDomain| *2 (|Record| (|:| |mainpart| *3) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| *3) (|:| |logand| *3)))))) (|isDomain| *1 (|TranscendentalIntegration| *6 *7)))) (|primextintfrac| (*1 *2 *3 *4 *3) (|partial| AND (|isDomain| *4 (|Mapping| *6 *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Record| (|:| |ratpart| (|Fraction| *6)) (|:| |coeff| (|Fraction| *6)))) (|isDomain| *1 (|TranscendentalIntegration| *5 *6)) (|isDomain| *3 (|Fraction| *6)))) (|explimitedint| (*1 *2 *3 *4 *5 *6) (|partial| AND (|isDomain| *4 (|Mapping| *8 *8)) (|isDomain| *5 (|Mapping| (|Record| (|:| |ans| *7) (|:| |right| *7) (|:| |sol?| (|Boolean|))) (|Integer|) *7)) (|isDomain| *6 (|List| (|Fraction| *8))) (|ofCategory| *7 (|Field|)) (|ofCategory| *8 (|UnivariatePolynomialCategory| *7)) (|isDomain| *3 (|Fraction| *8)) (|isDomain| *2 (|Record| (|:| |answer| (|Record| (|:| |mainpart| *3) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| *3) (|:| |logand| *3)))))) (|:| |a0| *7))) (|isDomain| *1 (|TranscendentalIntegration| *7 *8)))) (|primlimitedint| (*1 *2 *3 *4 *5 *6) (|partial| AND (|isDomain| *4 (|Mapping| *8 *8)) (|isDomain| *5 (|Mapping| (|Union| (|Record| (|:| |ratpart| *7) (|:| |coeff| *7)) "failed") *7)) (|isDomain| *6 (|List| (|Fraction| *8))) (|ofCategory| *7 (|Field|)) (|ofCategory| *8 (|UnivariatePolynomialCategory| *7)) (|isDomain| *3 (|Fraction| *8)) (|isDomain| *2 (|Record| (|:| |answer| (|Record| (|:| |mainpart| *3) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| *3) (|:| |logand| *3)))))) (|:| |a0| *7))) (|isDomain| *1 (|TranscendentalIntegration| *7 *8)))) (|expextendedint| (*1 *2 *3 *4 *5 *3) (AND (|isDomain| *4 (|Mapping| *7 *7)) (|isDomain| *5 (|Mapping| (|Record| (|:| |ans| *6) (|:| |right| *6) (|:| |sol?| (|Boolean|))) (|Integer|) *6)) (|ofCategory| *6 (|Field|)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|isDomain| *2 (|Union| (|Record| (|:| |answer| (|Fraction| *7)) (|:| |a0| *6)) (|Record| (|:| |ratpart| (|Fraction| *7)) (|:| |coeff| (|Fraction| *7))) "failed")) (|isDomain| *1 (|TranscendentalIntegration| *6 *7)) (|isDomain| *3 (|Fraction| *7)))) (|primextendedint| (*1 *2 *3 *4 *5 *3) (AND (|isDomain| *4 (|Mapping| *7 *7)) (|isDomain| *5 (|Mapping| (|Union| (|Record| (|:| |ratpart| *6) (|:| |coeff| *6)) "failed") *6)) (|ofCategory| *6 (|Field|)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|isDomain| *2 (|Union| (|Record| (|:| |answer| (|Fraction| *7)) (|:| |a0| *6)) (|Record| (|:| |ratpart| (|Fraction| *7)) (|:| |coeff| (|Fraction| *7))) "failed")) (|isDomain| *1 (|TranscendentalIntegration| *6 *7)) (|isDomain| *3 (|Fraction| *7)))) (|tanintegrate| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|Mapping| *7 *7)) (|isDomain| *5 (|Mapping| (|Union| (|List| *6) "failed") (|Integer|) *6 *6)) (|ofCategory| *6 (|Field|)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|isDomain| *2 (|Record| (|:| |answer| (|IntegrationResult| (|Fraction| *7))) (|:| |a0| *6))) (|isDomain| *1 (|TranscendentalIntegration| *6 *7)) (|isDomain| *3 (|Fraction| *7)))) (|expintegrate| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|Mapping| *7 *7)) (|isDomain| *5 (|Mapping| (|Record| (|:| |ans| *6) (|:| |right| *6) (|:| |sol?| (|Boolean|))) (|Integer|) *6)) (|ofCategory| *6 (|Field|)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|isDomain| *2 (|Record| (|:| |answer| (|IntegrationResult| (|Fraction| *7))) (|:| |a0| *6))) (|isDomain| *1 (|TranscendentalIntegration| *6 *7)) (|isDomain| *3 (|Fraction| *7)))) (|primintegrate| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|Mapping| *7 *7)) (|isDomain| *5 (|Mapping| (|Union| (|Record| (|:| |ratpart| *6) (|:| |coeff| *6)) "failed") *6)) (|ofCategory| *6 (|Field|)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|isDomain| *2 (|Record| (|:| |answer| (|IntegrationResult| (|Fraction| *7))) (|:| |a0| *6))) (|isDomain| *1 (|TranscendentalIntegration| *6 *7)) (|isDomain| *3 (|Fraction| *7))))) 
(CATEGORY |package| (SIGNATURE |primintegrate| ((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|))) (SIGNATURE |expintegrate| ((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|))) (SIGNATURE |tanintegrate| ((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|))) (SIGNATURE |primextendedint| ((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|))) (SIGNATURE |expextendedint| ((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|))) (SIGNATURE |primlimitedint| ((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|)))) (SIGNATURE |explimitedint| ((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|)))) (SIGNATURE |primextintfrac| ((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|))) (SIGNATURE |primlimintfrac| ((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|)))) (SIGNATURE |primintfldpoly| ((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|)) (SIGNATURE |expintfldpoly| ((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|))) (SIGNATURE |monomialIntegrate| ((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|))) (SIGNATURE |monomialIntPoly| ((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)))) 
((|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) 10))) 
(((|InverseLaplaceTransform| |#1| |#2|) (CATEGORY |package| (SIGNATURE |inverseLaplace| ((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)))) (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|))) (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|SpecialFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| |#1|))) (T |InverseLaplaceTransform|)) 
((|inverseLaplace| (*1 *2 *2 *3 *3) (|partial| AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|InverseLaplaceTransform| *4 *2)) (|ofCategory| *2 (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|SpecialFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *4)))))) 
(CATEGORY |package| (SIGNATURE |inverseLaplace| ((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sqrt| (($ $ (|Integer|)) 65)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sample| (($) NIL T CONST)) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) 71)) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) 57)) (|quotientByP| (($ $) 33)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|order| (((|NonNegativeInteger|) $) 15)) (|one?| (((|Boolean|) $) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|modulus| (((|Integer|)) 27)) (|moduloP| (((|Integer|) $) 31)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|extend| (($ $ (|Integer|)) 21)) (|exquo| (((|Union| $ "failed") $ $) 58)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) 16)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 60)) (|digits| (((|Stream| (|Integer|)) $) 18)) (|complete| (($ $) 23)) (|coerce| (((|OutputForm|) $) 85) (($ (|Integer|)) 51) (($ $) NIL)) (|characteristic| (((|NonNegativeInteger|)) 14)) (|associates?| (((|Boolean|) $ $) NIL)) (|approximate| (((|Integer|) $ (|Integer|)) 35)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 34 T CONST)) (|One| (($) 19 T CONST)) (= (((|Boolean|) $ $) 38)) (- (($ $) 50) (($ $ $) 36)) (+ (($ $ $) 49)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 53) (($ $ $) 54))) 
(((|InnerPAdicInteger| |#1| |#2|) (|PAdicIntegerCategory| |#1|) (|Integer|) (|Boolean|)) (T |InnerPAdicInteger|)) 
NIL 
(|PAdicIntegerCategory| |#1|) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 18)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|transcendent?| (((|Boolean|) $) NIL)) (|transcendenceDegree| (((|NonNegativeInteger|)) NIL)) (|trace| (($ $ (|PositiveInteger|)) NIL (|has| $ (|Finite|))) (($ $) NIL)) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) 47)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|size| (((|NonNegativeInteger|)) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| $ "failed") $) 75)) (|retract| (($ $) 74)) (|represents| (($ (|Vector| $)) 73)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 42)) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) 30)) (|random| (($) NIL)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|primitiveElement| (($) 49)) (|primitive?| (((|Boolean|) $) NIL)) (|primeFrobenius| (($ $) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL) (((|PositiveInteger|) $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|normalElement| (($) 35 (|has| $ (|Finite|)))) (|normal?| (((|Boolean|) $) NIL (|has| $ (|Finite|)))) (|norm| (($ $ (|PositiveInteger|)) NIL (|has| $ (|Finite|))) (($ $) NIL)) (|nextItem| (((|Union| $ "failed") $) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) NIL (|has| $ (|Finite|))) (((|SparseUnivariatePolynomial| $) $) 83)) (|lookup| (((|PositiveInteger|) $) 55)) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| $) $) NIL (|has| $ (|Finite|)))) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $ $) NIL (|has| $ (|Finite|))) (((|SparseUnivariatePolynomial| $) $) NIL (|has| $ (|Finite|)))) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| $)) NIL (|has| $ (|Finite|)))) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|init| (($) NIL T CONST)) (|index| (($ (|PositiveInteger|)) 48)) (|inGroundField?| (((|Boolean|) $) 67)) (|hash| (((|SingleInteger|) $) NIL)) (|generator| (($) 16 (|has| $ (|Finite|)))) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) 40)) (|factor| (((|Factored| $) $) NIL)) (|extensionDegree| (((|PositiveInteger|)) 66) (((|OnePointCompletion| (|PositiveInteger|))) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|enumerate| (((|List| $)) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) NIL) (((|NonNegativeInteger|) $) NIL)) (|dimension| (((|CardinalNumber|)) NIL)) (|differentiate| (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (|degree| (((|PositiveInteger|) $) 65) (((|OnePointCompletion| (|PositiveInteger|)) $) NIL)) (|definingPolynomial| (((|SparseUnivariatePolynomial| $)) 82)) (|createPrimitiveElement| (($) 54)) (|createNormalElement| (($) 36 (|has| $ (|Finite|)))) (|coordinates| (((|Matrix| $) (|Vector| $)) NIL) (((|Vector| $) $) 71)) (|convert| (((|Integer|) $) 26)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) 28) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL)) (|charthRoot| (((|Union| $ "failed") $) NIL) (($ $) 84)) (|characteristic| (((|NonNegativeInteger|)) 37)) (|basis| (((|Vector| $) (|PositiveInteger|)) 77) (((|Vector| $)) 76)) (|associates?| (((|Boolean|) $ $) NIL)) (|algebraic?| (((|Boolean|) $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) 19 T CONST)) (|One| (($) 15 T CONST)) (|Frobenius| (($ $ (|NonNegativeInteger|)) NIL (|has| $ (|Finite|))) (($ $) NIL (|has| $ (|Finite|)))) (D (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (= (((|Boolean|) $ $) NIL)) (/ (($ $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) 24)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 61) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL))) 
(((|InnerPrimeField| |#1|) (|Join| (|FiniteFieldCategory|) (|FiniteAlgebraicExtensionField| $) (|ConvertibleTo| (|Integer|))) (|PositiveInteger|)) (T |InnerPrimeField|)) 
NIL 
(|Join| (|FiniteFieldCategory|) (|FiniteAlgebraicExtensionField| $) (|ConvertibleTo| (|Integer|))) 
((|iprint| (((|Void|) (|String|)) 10))) 
(((|InternalPrintPackage|) (CATEGORY |package| (SIGNATURE |iprint| ((|Void|) (|String|))))) (T |InternalPrintPackage|)) 
((|iprint| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|InternalPrintPackage|))))) 
(CATEGORY |package| (SIGNATURE |iprint| ((|Void|) (|String|)))) 
((|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) 37)) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) 39)) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) 46))) 
(((|IntegrationResultToFunction| |#1| |#2|) (CATEGORY |package| (SIGNATURE |split| ((|IntegrationResult| |#2|) (|IntegrationResult| |#2|))) (SIGNATURE |expand| ((|List| |#2|) (|IntegrationResult| |#2|))) (SIGNATURE |complexExpand| (|#2| (|IntegrationResult| |#2|)))) (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|LinearlyExplicitRingOver| (|Integer|))) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|))) (T |IntegrationResultToFunction|)) 
((|complexExpand| (*1 *2 *3) (AND (|isDomain| *3 (|IntegrationResult| *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedFunctionSpace| *4) (|TranscendentalFunctionCategory|))) (|isDomain| *1 (|IntegrationResultToFunction| *4 *2)) (|ofCategory| *4 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|LinearlyExplicitRingOver| (|Integer|)))))) (|expand| (*1 *2 *3) (AND (|isDomain| *3 (|IntegrationResult| *5)) (|ofCategory| *5 (|Join| (|AlgebraicallyClosedFunctionSpace| *4) (|TranscendentalFunctionCategory|))) (|ofCategory| *4 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|IntegrationResultToFunction| *4 *5)))) (|split| (*1 *2 *2) (AND (|isDomain| *2 (|IntegrationResult| *4)) (|ofCategory| *4 (|Join| (|AlgebraicallyClosedFunctionSpace| *3) (|TranscendentalFunctionCategory|))) (|ofCategory| *3 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|IntegrationResultToFunction| *3 *4))))) 
(CATEGORY |package| (SIGNATURE |split| ((|IntegrationResult| |#2|) (|IntegrationResult| |#2|))) (SIGNATURE |expand| ((|List| |#2|) (|IntegrationResult| |#2|))) (SIGNATURE |complexExpand| (|#2| (|IntegrationResult| |#2|)))) 
((|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) 38) (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) 11) (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) 31) (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) 26))) 
(((|IntegrationResultFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|))) (SIGNATURE |map| ((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed"))) (SIGNATURE |map| ((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed"))) (SIGNATURE |map| ((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")))) (|Field|) (|Field|)) (T |IntegrationResultFunctions2|)) 
((|map| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Union| (|Record| (|:| |mainpart| *5) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| *5) (|:| |logand| *5))))) "failed")) (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|Field|)) (|isDomain| *2 (|Record| (|:| |mainpart| *6) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| *6) (|:| |logand| *6)))))) (|isDomain| *1 (|IntegrationResultFunctions2| *5 *6)))) (|map| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Mapping| *2 *5)) (|isDomain| *4 (|Union| *5 "failed")) (|ofCategory| *5 (|Field|)) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|IntegrationResultFunctions2| *5 *2)))) (|map| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Union| (|Record| (|:| |ratpart| *5) (|:| |coeff| *5)) "failed")) (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|Field|)) (|isDomain| *2 (|Record| (|:| |ratpart| *6) (|:| |coeff| *6))) (|isDomain| *1 (|IntegrationResultFunctions2| *5 *6)))) (|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|IntegrationResult| *5)) (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|Field|)) (|isDomain| *2 (|IntegrationResult| *6)) (|isDomain| *1 (|IntegrationResultFunctions2| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |map| ((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|))) (SIGNATURE |map| ((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed"))) (SIGNATURE |map| ((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed"))) (SIGNATURE |map| ((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 68)) (|retract| ((|#1| $) NIL)) (|ratpart| ((|#1| $) 24)) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) 26)) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) 22)) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) 25)) (|latex| (((|String|) $) NIL)) (|integral| (($ |#1| |#1|) 32) (($ |#1| (|Symbol|)) 43 (|has| |#1| (|RetractableTo| (|Symbol|))))) (|hash| (((|SingleInteger|) $) NIL)) (|elem?| (((|Boolean|) $) 28)) (|differentiate| ((|#1| $ (|Mapping| |#1| |#1|)) 80) ((|#1| $ (|Symbol|)) 81 (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (|coerce| (((|OutputForm|) $) 95) (($ |#1|) 23)) (|Zero| (($) 16 T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) 15) (($ $ $) NIL)) (+ (($ $ $) 77)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 14) (($ (|Fraction| (|Integer|)) $) 35) (($ $ (|Fraction| (|Integer|))) NIL))) 
(((|IntegrationResult| |#1|) (|Join| (|Module| (|Fraction| (|Integer|))) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |mkAnswer| ($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))))) (SIGNATURE |ratpart| (|#1| $)) (SIGNATURE |logpart| ((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $)) (SIGNATURE |notelem| ((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $)) (SIGNATURE |elem?| ((|Boolean|) $)) (SIGNATURE |integral| ($ |#1| |#1|)) (SIGNATURE |differentiate| (|#1| $ (|Mapping| |#1| |#1|))) (IF (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (SIGNATURE |differentiate| (|#1| $ (|Symbol|))) |noBranch|) (IF (|has| |#1| (|RetractableTo| (|Symbol|))) (SIGNATURE |integral| ($ |#1| (|Symbol|))) |noBranch|))) (|Field|)) (T |IntegrationResult|)) 
((|mkAnswer| (*1 *1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| *2)) (|:| |logand| (|SparseUnivariatePolynomial| *2))))) (|isDomain| *4 (|List| (|Record| (|:| |integrand| *2) (|:| |intvar| *2)))) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|IntegrationResult| *2)))) (|ratpart| (*1 *2 *1) (AND (|isDomain| *1 (|IntegrationResult| *2)) (|ofCategory| *2 (|Field|)))) (|logpart| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| *3)) (|:| |logand| (|SparseUnivariatePolynomial| *3))))) (|isDomain| *1 (|IntegrationResult| *3)) (|ofCategory| *3 (|Field|)))) (|notelem| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |integrand| *3) (|:| |intvar| *3)))) (|isDomain| *1 (|IntegrationResult| *3)) (|ofCategory| *3 (|Field|)))) (|elem?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|IntegrationResult| *3)) (|ofCategory| *3 (|Field|)))) (|integral| (*1 *1 *2 *2) (AND (|isDomain| *1 (|IntegrationResult| *2)) (|ofCategory| *2 (|Field|)))) (|differentiate| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Mapping| *2 *2)) (|isDomain| *1 (|IntegrationResult| *2)) (|ofCategory| *2 (|Field|)))) (|differentiate| (*1 *2 *1 *3) (AND (|ofCategory| *2 (|Field|)) (|ofCategory| *2 (|PartialDifferentialRing| *3)) (|isDomain| *1 (|IntegrationResult| *2)) (|isDomain| *3 (|Symbol|)))) (|integral| (*1 *1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *1 (|IntegrationResult| *2)) (|ofCategory| *2 (|RetractableTo| *3)) (|ofCategory| *2 (|Field|))))) 
(|Join| (|Module| (|Fraction| (|Integer|))) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |mkAnswer| ($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))))) (SIGNATURE |ratpart| (|#1| $)) (SIGNATURE |logpart| ((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $)) (SIGNATURE |notelem| ((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $)) (SIGNATURE |elem?| ((|Boolean|) $)) (SIGNATURE |integral| ($ |#1| |#1|)) (SIGNATURE |differentiate| (|#1| $ (|Mapping| |#1| |#1|))) (IF (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (SIGNATURE |differentiate| (|#1| $ (|Symbol|))) |noBranch|) (IF (|has| |#1| (|RetractableTo| (|Symbol|))) (SIGNATURE |integral| ($ |#1| (|Symbol|))) |noBranch|))) 
((|perfectSquare?| (((|Boolean|) |#1|) 16)) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) 14)) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) 30) (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) 18)) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) 19)) (|approxSqrt| ((|#1| |#1|) 31)) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) 33))) 
(((|IntegerRoots| |#1|) (CATEGORY |package| (SIGNATURE |perfectNthPower?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |perfectNthRoot| ((|Union| |#1| "failed") |#1| (|NonNegativeInteger|))) (SIGNATURE |perfectNthRoot| ((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|)) (SIGNATURE |approxNthRoot| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |perfectSquare?| ((|Boolean|) |#1|)) (SIGNATURE |perfectSqrt| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |approxSqrt| (|#1| |#1|))) (|IntegerNumberSystem|)) (T |IntegerRoots|)) 
((|approxSqrt| (*1 *2 *2) (AND (|isDomain| *1 (|IntegerRoots| *2)) (|ofCategory| *2 (|IntegerNumberSystem|)))) (|perfectSqrt| (*1 *2 *2) (|partial| AND (|isDomain| *1 (|IntegerRoots| *2)) (|ofCategory| *2 (|IntegerNumberSystem|)))) (|perfectSquare?| (*1 *2 *3) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|IntegerRoots| *3)) (|ofCategory| *3 (|IntegerNumberSystem|)))) (|approxNthRoot| (*1 *2 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|IntegerRoots| *2)) (|ofCategory| *2 (|IntegerNumberSystem|)))) (|perfectNthRoot| (*1 *2 *3) (AND (|isDomain| *2 (|Record| (|:| |base| *3) (|:| |exponent| (|NonNegativeInteger|)))) (|isDomain| *1 (|IntegerRoots| *3)) (|ofCategory| *3 (|IntegerNumberSystem|)))) (|perfectNthRoot| (*1 *2 *2 *3) (|partial| AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|IntegerRoots| *2)) (|ofCategory| *2 (|IntegerNumberSystem|)))) (|perfectNthPower?| (*1 *2 *3 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|IntegerRoots| *3)) (|ofCategory| *3 (|IntegerNumberSystem|))))) 
(CATEGORY |package| (SIGNATURE |perfectNthPower?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |perfectNthRoot| ((|Union| |#1| "failed") |#1| (|NonNegativeInteger|))) (SIGNATURE |perfectNthRoot| ((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|)) (SIGNATURE |approxNthRoot| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |perfectSquare?| ((|Boolean|) |#1|)) (SIGNATURE |perfectSqrt| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |approxSqrt| (|#1| |#1|))) 
((|generateIrredPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) 26))) 
(((|IrredPolyOverFiniteField| |#1|) (CATEGORY |package| (SIGNATURE |generateIrredPoly| ((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)))) (|FiniteFieldCategory|)) (T |IrredPolyOverFiniteField|)) 
((|generateIrredPoly| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|isDomain| *1 (|IrredPolyOverFiniteField| *4)) (|ofCategory| *4 (|FiniteFieldCategory|))))) 
(CATEGORY |package| (SIGNATURE |generateIrredPoly| ((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)))) 
((|split| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) 26)) (|integrate| (((|Union| (|Expression| |#1|) (|List| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) 32 (|has| |#1| (|CharacteristicZero|)))) (|expand| (((|List| (|Expression| |#1|)) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) 18)) (|complexIntegrate| (((|Expression| |#1|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) 30 (|has| |#1| (|CharacteristicZero|)))) (|complexExpand| (((|Expression| |#1|) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) 20))) 
(((|IntegrationResultRFToFunction| |#1|) (CATEGORY |package| (SIGNATURE |split| ((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |expand| ((|List| (|Expression| |#1|)) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |complexExpand| ((|Expression| |#1|) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|))))) (IF (|has| |#1| (|CharacteristicZero|)) (PROGN (SIGNATURE |integrate| ((|Union| (|Expression| |#1|) (|List| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |complexIntegrate| ((|Expression| |#1|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)))) |noBranch|)) (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|LinearlyExplicitRingOver| (|Integer|)))) (T |IntegrationResultRFToFunction|)) 
((|complexIntegrate| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5))) (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|CharacteristicZero|)) (|ofCategory| *5 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Expression| *5)) (|isDomain| *1 (|IntegrationResultRFToFunction| *5)))) (|integrate| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5))) (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|CharacteristicZero|)) (|ofCategory| *5 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Union| (|Expression| *5) (|List| (|Expression| *5)))) (|isDomain| *1 (|IntegrationResultRFToFunction| *5)))) (|complexExpand| (*1 *2 *3) (AND (|isDomain| *3 (|IntegrationResult| (|Fraction| (|Polynomial| *4)))) (|ofCategory| *4 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Expression| *4)) (|isDomain| *1 (|IntegrationResultRFToFunction| *4)))) (|expand| (*1 *2 *3) (AND (|isDomain| *3 (|IntegrationResult| (|Fraction| (|Polynomial| *4)))) (|ofCategory| *4 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|List| (|Expression| *4))) (|isDomain| *1 (|IntegrationResultRFToFunction| *4)))) (|split| (*1 *2 *2) (AND (|isDomain| *2 (|IntegrationResult| (|Fraction| (|Polynomial| *3)))) (|ofCategory| *3 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)) (|OrderedSet|) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|IntegrationResultRFToFunction| *3))))) 
(CATEGORY |package| (SIGNATURE |split| ((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |expand| ((|List| (|Expression| |#1|)) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |complexExpand| ((|Expression| |#1|) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|))))) (IF (|has| |#1| (|CharacteristicZero|)) (PROGN (SIGNATURE |integrate| ((|Union| (|Expression| |#1|) (|List| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |complexIntegrate| ((|Expression| |#1|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)))) |noBranch|)) 
((|irreducibleRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|)) (|List| (|Permutation| (|Integer|)))) 45) (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) 46) (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|Permutation| (|Integer|))) 41)) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|Integer|))) 39))) 
(((|IrrRepSymNatPackage|) (CATEGORY |package| (SIGNATURE |dimensionOfIrreducibleRepresentation| ((|NonNegativeInteger|) (|List| (|Integer|)))) (SIGNATURE |irreducibleRepresentation| ((|Matrix| (|Integer|)) (|List| (|Integer|)) (|Permutation| (|Integer|)))) (SIGNATURE |irreducibleRepresentation| ((|List| (|Matrix| (|Integer|))) (|List| (|Integer|)))) (SIGNATURE |irreducibleRepresentation| ((|List| (|Matrix| (|Integer|))) (|List| (|Integer|)) (|List| (|Permutation| (|Integer|))))))) (T |IrrRepSymNatPackage|)) 
((|irreducibleRepresentation| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *4 (|List| (|Permutation| (|Integer|)))) (|isDomain| *2 (|List| (|Matrix| (|Integer|)))) (|isDomain| *1 (|IrrRepSymNatPackage|)))) (|irreducibleRepresentation| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|List| (|Matrix| (|Integer|)))) (|isDomain| *1 (|IrrRepSymNatPackage|)))) (|irreducibleRepresentation| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *4 (|Permutation| (|Integer|))) (|isDomain| *2 (|Matrix| (|Integer|))) (|isDomain| *1 (|IrrRepSymNatPackage|)))) (|dimensionOfIrreducibleRepresentation| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|IrrRepSymNatPackage|))))) 
(CATEGORY |package| (SIGNATURE |dimensionOfIrreducibleRepresentation| ((|NonNegativeInteger|) (|List| (|Integer|)))) (SIGNATURE |irreducibleRepresentation| ((|Matrix| (|Integer|)) (|List| (|Integer|)) (|Permutation| (|Integer|)))) (SIGNATURE |irreducibleRepresentation| ((|List| (|Matrix| (|Integer|))) (|List| (|Integer|)))) (SIGNATURE |irreducibleRepresentation| ((|List| (|Matrix| (|Integer|))) (|List| (|Integer|)) (|List| (|Permutation| (|Integer|)))))) 
((|rur| (((|List| |#5|) |#5| (|Boolean|)) 72)) (|checkRur| (((|Boolean|) |#5| (|List| |#5|)) 30))) 
(((|InternalRationalUnivariateRepresentationPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |rur| ((|List| |#5|) |#5| (|Boolean|))) (SIGNATURE |checkRur| ((|Boolean|) |#5| (|List| |#5|)))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|)) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|SquareFreeRegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |InternalRationalUnivariateRepresentationPackage|)) 
((|checkRur| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *3)) (|ofCategory| *3 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|InternalRationalUnivariateRepresentationPackage| *5 *6 *7 *8 *3)))) (|rur| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|InternalRationalUnivariateRepresentationPackage| *5 *6 *7 *8 *3)) (|ofCategory| *3 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8))))) 
(CATEGORY |package| (SIGNATURE |rur| ((|List| |#5|) |#5| (|Boolean|))) (SIGNATURE |checkRur| ((|Boolean|) |#5| (|List| |#5|)))) 
((~= (((|Boolean|) $ $) NIL (|has| (|Character|) (|SetCategory|)))) (|upperCase!| (($ $) 34)) (|upperCase| (($ $) NIL)) (|trim| (($ $ (|Character|)) NIL) (($ $ (|CharacterClass|)) NIL)) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|suffix?| (((|Boolean|) $ $) 51)) (|substring?| (((|Boolean|) $ $ (|Integer|)) 46)) (|split| (((|List| $) $ (|Character|)) 59) (((|List| $) $ (|CharacterClass|)) 60)) (|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) (|Character|) (|Character|)) $) NIL) (((|Boolean|) $) NIL (|has| (|Character|) (|OrderedSet|)))) (|sort!| (($ (|Mapping| (|Boolean|) (|Character|) (|Character|)) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $) NIL (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|has| (|Character|) (|OrderedSet|))))) (|sort| (($ (|Mapping| (|Boolean|) (|Character|) (|Character|)) $) NIL) (($ $) NIL (|has| (|Character|) (|OrderedSet|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setelt| (((|Character|) $ (|Integer|) (|Character|)) 45 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Character|) $ (|UniversalSegment| (|Integer|)) (|Character|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select| (($ (|Mapping| (|Boolean|) (|Character|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) NIL T CONST)) (|rightTrim| (($ $ (|Character|)) 63) (($ $ (|CharacterClass|)) 64)) (|reverse!| (($ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) NIL)) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) 44)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Character|) (|SetCategory|))))) (|remove| (($ (|Character|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Character|) (|SetCategory|)))) (($ (|Mapping| (|Boolean|) (|Character|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| (((|Character|) (|Mapping| (|Character|) (|Character|) (|Character|)) $ (|Character|) (|Character|)) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Character|) (|SetCategory|)))) (((|Character|) (|Mapping| (|Character|) (|Character|) (|Character|)) $ (|Character|)) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Character|) (|Mapping| (|Character|) (|Character|) (|Character|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| (((|Character|) $ (|Integer|) (|Character|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| (((|Character|) $ (|Integer|)) NIL)) (|prefix?| (((|Boolean|) $ $) 70)) (|position| (((|Integer|) (|Mapping| (|Boolean|) (|Character|)) $) NIL) (((|Integer|) (|Character|) $) NIL (|has| (|Character|) (|SetCategory|))) (((|Integer|) (|Character|) $ (|Integer|)) 48 (|has| (|Character|) (|SetCategory|))) (((|Integer|) $ $ (|Integer|)) 47) (((|Integer|) (|CharacterClass|) $ (|Integer|)) 50)) (|parts| (((|List| (|Character|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|new| (($ (|NonNegativeInteger|) (|Character|)) 9)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) 28 (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL (|has| (|Character|) (|OrderedSet|)))) (|merge| (($ (|Mapping| (|Boolean|) (|Character|) (|Character|)) $ $) NIL) (($ $ $) NIL (|has| (|Character|) (|OrderedSet|)))) (|members| (((|List| (|Character|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|Character|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Character|) (|SetCategory|))))) (|maxIndex| (((|Integer|) $) 42 (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| (|Character|) (|OrderedSet|)))) (|match?| (((|Boolean|) $ $ (|Character|)) 71)) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) 69)) (|map!| (($ (|Mapping| (|Character|) (|Character|)) $) 33 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| (|Character|) (|Character|)) $) NIL) (($ (|Mapping| (|Character|) (|Character|) (|Character|)) $ $) NIL)) (|lowerCase!| (($ $) 37)) (|lowerCase| (($ $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|leftTrim| (($ $ (|Character|)) 61) (($ $ (|CharacterClass|)) 62)) (|latex| (((|String|) $) 38 (|has| (|Character|) (|SetCategory|)))) (|insert| (($ (|Character|) $ (|Integer|)) NIL) (($ $ $ (|Integer|)) 23)) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|hash| (((|Integer|) $) 68) (((|SingleInteger|) $) NIL (|has| (|Character|) (|SetCategory|)))) (|first| (((|Character|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|find| (((|Union| (|Character|) "failed") (|Mapping| (|Boolean|) (|Character|)) $) NIL)) (|fill!| (($ $ (|Character|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) (|Character|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| (|Character|)))) NIL (AND (|has| (|Character|) (|Evalable| (|Character|))) (|has| (|Character|) (|SetCategory|)))) (($ $ (|Equation| (|Character|))) NIL (AND (|has| (|Character|) (|Evalable| (|Character|))) (|has| (|Character|) (|SetCategory|)))) (($ $ (|Character|) (|Character|)) NIL (AND (|has| (|Character|) (|Evalable| (|Character|))) (|has| (|Character|) (|SetCategory|)))) (($ $ (|List| (|Character|)) (|List| (|Character|))) NIL (AND (|has| (|Character|) (|Evalable| (|Character|))) (|has| (|Character|) (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|entry?| (((|Boolean|) (|Character|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Character|) (|SetCategory|))))) (|entries| (((|List| (|Character|)) $) NIL)) (|empty?| (((|Boolean|) $) 12)) (|empty| (($) 10)) (|elt| (((|Character|) $ (|Integer|) (|Character|)) NIL) (((|Character|) $ (|Integer|)) 52) (($ $ (|UniversalSegment| (|Integer|))) 21) (($ $ $) NIL)) (|delete| (($ $ (|Integer|)) NIL) (($ $ (|UniversalSegment| (|Integer|))) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|Character|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) (|Character|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Character|) (|SetCategory|))))) (|copyInto!| (($ $ $ (|Integer|)) 65 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) 17)) (|convert| (((|InputForm|) $) NIL (|has| (|Character|) (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| (|Character|))) NIL)) (|concat| (($ $ (|Character|)) NIL) (($ (|Character|) $) NIL) (($ $ $) 16) (($ (|List| $)) 66)) (|coerce| (($ (|Character|)) NIL) (((|OutputForm|) $) 27 (|has| (|Character|) (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|Character|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (>= (((|Boolean|) $ $) NIL (|has| (|Character|) (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| (|Character|) (|OrderedSet|)))) (= (((|Boolean|) $ $) 14 (|has| (|Character|) (|SetCategory|)))) (<= (((|Boolean|) $ $) NIL (|has| (|Character|) (|OrderedSet|)))) (< (((|Boolean|) $ $) 15 (|has| (|Character|) (|OrderedSet|)))) (|#| (((|NonNegativeInteger|) $) 13 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|IndexedString| |#1|) (|Join| (|StringAggregate|) (CATEGORY |domain| (SIGNATURE |hash| ((|Integer|) $)))) (|Integer|)) (T |IndexedString|)) 
((|hash| (*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IndexedString| *3)) (|ofType| *3 *2)))) 
(|Join| (|StringAggregate|) (CATEGORY |domain| (SIGNATURE |hash| ((|Integer|) $)))) 
((|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) 23) (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) 32))) 
(((|InnerPolySum| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |sum| ((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|))) (SIGNATURE |sum| ((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|IntegralDomain|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |InnerPolySum|)) 
((|sum| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *6 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| (|Integer|)))) (|isDomain| *1 (|InnerPolySum| *5 *4 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *6 *5 *4)))) (|sum| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|Segment| *3)) (|ofCategory| *3 (|PolynomialCategory| *7 *6 *4)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *7 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| (|Integer|)))) (|isDomain| *1 (|InnerPolySum| *6 *4 *7 *3))))) 
(CATEGORY |package| (SIGNATURE |sum| ((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|))) (SIGNATURE |sum| ((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 64)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) NIL)) (|variable| (((|Symbol|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|truncate| (($ $ (|Integer|)) 54) (($ $ (|Integer|) (|Integer|)) 55)) (|terms| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) 61)) (|taylorQuoByVar| (($ $) 100)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) 215)) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) 34)) (|sample| (($) NIL T CONST)) (|reductum| (($ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|pole?| (((|Boolean|) $) NIL)) (|order| (((|Integer|) $) 59) (((|Integer|) $ (|Integer|)) 60)) (|one?| (((|Boolean|) $) NIL)) (|multiplyExponents| (($ $ (|PositiveInteger|)) 77)) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) 74)) (|monomial?| (((|Boolean|) $) 25)) (|monomial| (($ |#1| (|Integer|)) 22) (($ $ (|SingletonAsOrderedSet|) (|Integer|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|Integer|))) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) 68)) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) 11)) (|leadingMonomial| (($ $) NIL)) (|leadingCoefficient| ((|#1| $) NIL)) (|latex| (((|String|) $) NIL)) (|integrate| (($ $) 112 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) 99)) (|iCompose| (($ $ $) 108)) (|hash| (((|SingleInteger|) $) NIL)) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) 13)) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) 12)) (|extend| (($ $ (|Integer|)) 45)) (|exquo| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|eval| (((|Stream| |#1|) $ |#1|) NIL (|has| |#1| (SIGNATURE ** (|#1| |#1| (|Integer|)))))) (|elt| ((|#1| $ (|Integer|)) 57) (($ $ $) NIL (|has| (|Integer|) (|SemiGroup|)))) (|differentiate| (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) (($ $) 71 (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) (|degree| (((|Integer|) $) NIL)) (|complete| (($ $) 46)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) 28) (($ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $) NIL (|has| |#1| (|IntegralDomain|))) (($ |#1|) 27 (|has| |#1| (|CommutativeRing|)))) (|coefficient| ((|#1| $ (|Integer|)) 56)) (|charthRoot| (((|Union| $ "failed") $) NIL (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) 37)) (|center| ((|#1| $) NIL)) (|cTanh| (($ $) 180 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cTan| (($ $) 156 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cSinh| (($ $) 177 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cSin| (($ $) 153 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cSech| (($ $) 182 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cSec| (($ $) 159 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) 146 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cPower| (($ $ |#1|) 121 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cLog| (($ $) 150 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cExp| (($ $) 148 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cCsch| (($ $) 183 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cCsc| (($ $) 160 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cCoth| (($ $) 181 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cCot| (($ $) 158 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cCosh| (($ $) 178 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cCos| (($ $) 154 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cAtanh| (($ $) 188 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cAtan| (($ $) 168 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cAsinh| (($ $) 185 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cAsin| (($ $) 163 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cAsech| (($ $) 192 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cAsec| (($ $) 172 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cAcsch| (($ $) 194 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cAcsc| (($ $) 174 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cAcoth| (($ $) 190 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cAcot| (($ $) 170 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cAcosh| (($ $) 187 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cAcos| (($ $) 166 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|associates?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|approximate| ((|#1| $ (|Integer|)) NIL (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| (|Integer|)))) (|has| |#1| (SIGNATURE |coerce| (|#1| (|Symbol|))))))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 29 T CONST)) (|One| (($) 38 T CONST)) (D (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) (($ $) NIL (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) (= (((|Boolean|) $ $) 66)) (/ (($ $ |#1|) NIL (|has| |#1| (|Field|)))) (- (($ $) 85) (($ $ $) 65)) (+ (($ $ $) 82)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 103)) (* (($ (|PositiveInteger|) $) 90) (($ (|NonNegativeInteger|) $) 88) (($ (|Integer|) $) 86) (($ $ $) 96) (($ $ |#1|) NIL) (($ |#1| $) 115) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) 
(((|InnerSparseUnivariatePowerSeries| |#1|) (|Join| (|UnivariatePowerSeriesCategory| |#1| (|Integer|)) (CATEGORY |domain| (SIGNATURE |makeSeries| ($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))))) (SIGNATURE |getRef| ((|Reference| (|OrderedCompletion| (|Integer|))) $)) (SIGNATURE |getStream| ((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $)) (SIGNATURE |series| ($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))))) (SIGNATURE |monomial?| ((|Boolean|) $)) (SIGNATURE |multiplyCoefficients| ($ (|Mapping| |#1| (|Integer|)) $)) (SIGNATURE |iExquo| ((|Union| $ "failed") $ $ (|Boolean|))) (SIGNATURE |taylorQuoByVar| ($ $)) (SIGNATURE |iCompose| ($ $ $)) (SIGNATURE |seriesToOutputForm| ((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|)))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |integrate| ($ $)) (SIGNATURE |cPower| ($ $ |#1|)) (SIGNATURE |cRationalPower| ($ $ (|Fraction| (|Integer|)))) (SIGNATURE |cExp| ($ $)) (SIGNATURE |cLog| ($ $)) (SIGNATURE |cSin| ($ $)) (SIGNATURE |cCos| ($ $)) (SIGNATURE |cTan| ($ $)) (SIGNATURE |cCot| ($ $)) (SIGNATURE |cSec| ($ $)) (SIGNATURE |cCsc| ($ $)) (SIGNATURE |cAsin| ($ $)) (SIGNATURE |cAcos| ($ $)) (SIGNATURE |cAtan| ($ $)) (SIGNATURE |cAcot| ($ $)) (SIGNATURE |cAsec| ($ $)) (SIGNATURE |cAcsc| ($ $)) (SIGNATURE |cSinh| ($ $)) (SIGNATURE |cCosh| ($ $)) (SIGNATURE |cTanh| ($ $)) (SIGNATURE |cCoth| ($ $)) (SIGNATURE |cSech| ($ $)) (SIGNATURE |cCsch| ($ $)) (SIGNATURE |cAsinh| ($ $)) (SIGNATURE |cAcosh| ($ $)) (SIGNATURE |cAtanh| ($ $)) (SIGNATURE |cAcoth| ($ $)) (SIGNATURE |cAsech| ($ $)) (SIGNATURE |cAcsch| ($ $))) |noBranch|))) (|Ring|)) (T |InnerSparseUnivariatePowerSeries|)) 
((|monomial?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *3)) (|ofCategory| *3 (|Ring|)))) (|makeSeries| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Reference| (|OrderedCompletion| (|Integer|)))) (|isDomain| *3 (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| *4)))) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *4)))) (|getRef| (*1 *2 *1) (AND (|isDomain| *2 (|Reference| (|OrderedCompletion| (|Integer|)))) (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *3)) (|ofCategory| *3 (|Ring|)))) (|getStream| (*1 *2 *1) (AND (|isDomain| *2 (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| *3)))) (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *3)) (|ofCategory| *3 (|Ring|)))) (|series| (*1 *1 *2) (AND (|isDomain| *2 (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| *3)))) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *3)))) (|multiplyCoefficients| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 (|Integer|))) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *3)))) (|iExquo| (*1 *1 *1 *1 *2) (|partial| AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *3)) (|ofCategory| *3 (|Ring|)))) (|taylorQuoByVar| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Ring|)))) (|iCompose| (*1 *1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Ring|)))) (|seriesToOutputForm| (*1 *2 *3 *4 *5 *6 *7) (AND (|isDomain| *3 (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| *6)))) (|isDomain| *4 (|Reference| (|OrderedCompletion| (|Integer|)))) (|isDomain| *5 (|Symbol|)) (|isDomain| *7 (|Fraction| (|Integer|))) (|ofCategory| *6 (|Ring|)) (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *6)))) (|integrate| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cPower| (*1 *1 *1 *2) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cRationalPower| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *3)) (|ofCategory| *3 (|Algebra| *2)) (|ofCategory| *3 (|Ring|)))) (|cExp| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cLog| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cSin| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cCos| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cTan| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cCot| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cSec| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cCsc| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cAsin| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cAcos| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cAtan| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cAcot| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cAsec| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cAcsc| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cSinh| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cCosh| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cTanh| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cCoth| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cSech| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cCsch| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cAsinh| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cAcosh| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cAtanh| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cAcoth| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cAsech| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|)))) (|cAcsch| (*1 *1 *1) (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|))))) 
(|Join| (|UnivariatePowerSeriesCategory| |#1| (|Integer|)) (CATEGORY |domain| (SIGNATURE |makeSeries| ($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))))) (SIGNATURE |getRef| ((|Reference| (|OrderedCompletion| (|Integer|))) $)) (SIGNATURE |getStream| ((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $)) (SIGNATURE |series| ($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))))) (SIGNATURE |monomial?| ((|Boolean|) $)) (SIGNATURE |multiplyCoefficients| ($ (|Mapping| |#1| (|Integer|)) $)) (SIGNATURE |iExquo| ((|Union| $ "failed") $ $ (|Boolean|))) (SIGNATURE |taylorQuoByVar| ($ $)) (SIGNATURE |iCompose| ($ $ $)) (SIGNATURE |seriesToOutputForm| ((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|)))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |integrate| ($ $)) (SIGNATURE |cPower| ($ $ |#1|)) (SIGNATURE |cRationalPower| ($ $ (|Fraction| (|Integer|)))) (SIGNATURE |cExp| ($ $)) (SIGNATURE |cLog| ($ $)) (SIGNATURE |cSin| ($ $)) (SIGNATURE |cCos| ($ $)) (SIGNATURE |cTan| ($ $)) (SIGNATURE |cCot| ($ $)) (SIGNATURE |cSec| ($ $)) (SIGNATURE |cCsc| ($ $)) (SIGNATURE |cAsin| ($ $)) (SIGNATURE |cAcos| ($ $)) (SIGNATURE |cAtan| ($ $)) (SIGNATURE |cAcot| ($ $)) (SIGNATURE |cAsec| ($ $)) (SIGNATURE |cAcsc| ($ $)) (SIGNATURE |cSinh| ($ $)) (SIGNATURE |cCosh| ($ $)) (SIGNATURE |cTanh| ($ $)) (SIGNATURE |cCoth| ($ $)) (SIGNATURE |cSech| ($ $)) (SIGNATURE |cCsch| ($ $)) (SIGNATURE |cAsinh| ($ $)) (SIGNATURE |cAcosh| ($ $)) (SIGNATURE |cAtanh| ($ $)) (SIGNATURE |cAcoth| ($ $)) (SIGNATURE |cAsech| ($ $)) (SIGNATURE |cAcsch| ($ $))) |noBranch|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|series| (($ (|Stream| |#1|)) 9)) (|sample| (($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) 42)) (|pole?| (((|Boolean|) $) 52)) (|order| (((|NonNegativeInteger|) $) 55) (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) 54)) (|one?| (((|Boolean|) $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|exquo| (((|Union| $ "failed") $ $) 44 (|has| |#1| (|IntegralDomain|)))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|coefficients| (((|Stream| |#1|) $) 23)) (|characteristic| (((|NonNegativeInteger|)) 51)) (|associates?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 10 T CONST)) (|One| (($) 14 T CONST)) (= (((|Boolean|) $ $) 22)) (- (($ $) 30) (($ $ $) 16)) (+ (($ $ $) 25)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 49)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 34) (($ $ $) 28) (($ |#1| $) 37) (($ $ |#1|) 38) (($ $ (|Integer|)) 36))) 
(((|InnerTaylorSeries| |#1|) (|Join| (|Ring|) (CATEGORY |domain| (SIGNATURE |coefficients| ((|Stream| |#1|) $)) (SIGNATURE |series| ($ (|Stream| |#1|))) (SIGNATURE |pole?| ((|Boolean|) $)) (SIGNATURE |order| ((|NonNegativeInteger|) $)) (SIGNATURE |order| ((|NonNegativeInteger|) $ (|NonNegativeInteger|))) (SIGNATURE * ($ |#1| $)) (SIGNATURE * ($ $ |#1|)) (SIGNATURE * ($ $ (|Integer|))) (IF (|has| |#1| (|IntegralDomain|)) (ATTRIBUTE (|IntegralDomain|)) |noBranch|))) (|Ring|)) (T |InnerTaylorSeries|)) 
((|coefficients| (*1 *2 *1) (AND (|isDomain| *2 (|Stream| *3)) (|isDomain| *1 (|InnerTaylorSeries| *3)) (|ofCategory| *3 (|Ring|)))) (|series| (*1 *1 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|InnerTaylorSeries| *3)))) (|pole?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|InnerTaylorSeries| *3)) (|ofCategory| *3 (|Ring|)))) (|order| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|InnerTaylorSeries| *3)) (|ofCategory| *3 (|Ring|)))) (|order| (*1 *2 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|InnerTaylorSeries| *3)) (|ofCategory| *3 (|Ring|)))) (* (*1 *1 *2 *1) (AND (|isDomain| *1 (|InnerTaylorSeries| *2)) (|ofCategory| *2 (|Ring|)))) (* (*1 *1 *1 *2) (AND (|isDomain| *1 (|InnerTaylorSeries| *2)) (|ofCategory| *2 (|Ring|)))) (* (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|InnerTaylorSeries| *3)) (|ofCategory| *3 (|Ring|))))) 
(|Join| (|Ring|) (CATEGORY |domain| (SIGNATURE |coefficients| ((|Stream| |#1|) $)) (SIGNATURE |series| ($ (|Stream| |#1|))) (SIGNATURE |pole?| ((|Boolean|) $)) (SIGNATURE |order| ((|NonNegativeInteger|) $)) (SIGNATURE |order| ((|NonNegativeInteger|) $ (|NonNegativeInteger|))) (SIGNATURE * ($ |#1| $)) (SIGNATURE * ($ $ |#1|)) (SIGNATURE * ($ $ (|Integer|))) (IF (|has| |#1| (|IntegralDomain|)) (ATTRIBUTE (|IntegralDomain|)) |noBranch|))) 
((|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) 15))) 
(((|InfiniteTupleFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)))) (|Type|) (|Type|)) (T |InfiniteTupleFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|InfiniteTuple| *5)) (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|InfiniteTuple| *6)) (|isDomain| *1 (|InfiniteTupleFunctions2| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |map| ((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)))) 
((|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) 20) (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) 19) (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) 18))) 
(((|InfiniteTupleFunctions3| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |map| ((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|))) (SIGNATURE |map| ((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|))) (SIGNATURE |map| ((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)))) (|Type|) (|Type|) (|Type|)) (T |InfiniteTupleFunctions3|)) 
((|map| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *8 *6 *7)) (|isDomain| *4 (|InfiniteTuple| *6)) (|isDomain| *5 (|Stream| *7)) (|ofCategory| *6 (|Type|)) (|ofCategory| *7 (|Type|)) (|ofCategory| *8 (|Type|)) (|isDomain| *2 (|Stream| *8)) (|isDomain| *1 (|InfiniteTupleFunctions3| *6 *7 *8)))) (|map| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *8 *6 *7)) (|isDomain| *4 (|Stream| *6)) (|isDomain| *5 (|InfiniteTuple| *7)) (|ofCategory| *6 (|Type|)) (|ofCategory| *7 (|Type|)) (|ofCategory| *8 (|Type|)) (|isDomain| *2 (|Stream| *8)) (|isDomain| *1 (|InfiniteTupleFunctions3| *6 *7 *8)))) (|map| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *8 *6 *7)) (|isDomain| *4 (|InfiniteTuple| *6)) (|isDomain| *5 (|InfiniteTuple| *7)) (|ofCategory| *6 (|Type|)) (|ofCategory| *7 (|Type|)) (|ofCategory| *8 (|Type|)) (|isDomain| *2 (|InfiniteTuple| *8)) (|isDomain| *1 (|InfiniteTupleFunctions3| *6 *7 *8))))) 
(CATEGORY |package| (SIGNATURE |map| ((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|))) (SIGNATURE |map| ((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|))) (SIGNATURE |map| ((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)))) 
((|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) 55)) (|explogs2trigs| (((|Complex| |#2|) |#3|) 116)) (GF2FG ((|#3| (|Complex| |#2|)) 43)) (FG2F ((|#2| |#3|) 19)) (F2FG ((|#3| |#2|) 32))) 
(((|InnerTrigonometricManipulations| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE GF2FG (|#3| (|Complex| |#2|))) (SIGNATURE FG2F (|#2| |#3|)) (SIGNATURE F2FG (|#3| |#2|)) (SIGNATURE |explogs2trigs| ((|Complex| |#2|) |#3|)) (SIGNATURE |trigs2explogs| (|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))))) (|Join| (|IntegralDomain|) (|OrderedSet|)) (|Join| (|FunctionSpace| |#1|) (|RadicalCategory|) (|TranscendentalFunctionCategory|)) (|Join| (|FunctionSpace| (|Complex| |#1|)) (|RadicalCategory|) (|TranscendentalFunctionCategory|))) (T |InnerTrigonometricManipulations|)) 
((|trigs2explogs| (*1 *2 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Kernel| *2))) (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *2 (|Join| (|FunctionSpace| (|Complex| *5)) (|RadicalCategory|) (|TranscendentalFunctionCategory|))) (|ofCategory| *5 (|Join| (|IntegralDomain|) (|OrderedSet|))) (|isDomain| *1 (|InnerTrigonometricManipulations| *5 *6 *2)) (|ofCategory| *6 (|Join| (|FunctionSpace| *5) (|RadicalCategory|) (|TranscendentalFunctionCategory|))))) (|explogs2trigs| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|))) (|isDomain| *2 (|Complex| *5)) (|isDomain| *1 (|InnerTrigonometricManipulations| *4 *5 *3)) (|ofCategory| *5 (|Join| (|FunctionSpace| *4) (|RadicalCategory|) (|TranscendentalFunctionCategory|))) (|ofCategory| *3 (|Join| (|FunctionSpace| (|Complex| *4)) (|RadicalCategory|) (|TranscendentalFunctionCategory|))))) (F2FG (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|))) (|ofCategory| *2 (|Join| (|FunctionSpace| (|Complex| *4)) (|RadicalCategory|) (|TranscendentalFunctionCategory|))) (|isDomain| *1 (|InnerTrigonometricManipulations| *4 *3 *2)) (|ofCategory| *3 (|Join| (|FunctionSpace| *4) (|RadicalCategory|) (|TranscendentalFunctionCategory|))))) (FG2F (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|))) (|ofCategory| *2 (|Join| (|FunctionSpace| *4) (|RadicalCategory|) (|TranscendentalFunctionCategory|))) (|isDomain| *1 (|InnerTrigonometricManipulations| *4 *2 *3)) (|ofCategory| *3 (|Join| (|FunctionSpace| (|Complex| *4)) (|RadicalCategory|) (|TranscendentalFunctionCategory|))))) (GF2FG (*1 *2 *3) (AND (|isDomain| *3 (|Complex| *5)) (|ofCategory| *5 (|Join| (|FunctionSpace| *4) (|RadicalCategory|) (|TranscendentalFunctionCategory|))) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|))) (|ofCategory| *2 (|Join| (|FunctionSpace| (|Complex| *4)) (|RadicalCategory|) (|TranscendentalFunctionCategory|))) (|isDomain| *1 (|InnerTrigonometricManipulations| *4 *5 *2))))) 
(CATEGORY |package| (SIGNATURE GF2FG (|#3| (|Complex| |#2|))) (SIGNATURE FG2F (|#2| |#3|)) (SIGNATURE F2FG (|#3| |#2|)) (SIGNATURE |explogs2trigs| ((|Complex| |#2|) |#3|)) (SIGNATURE |trigs2explogs| (|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))))) 
((|select| (($ (|Mapping| (|Boolean|) |#1|) $) 16)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) 9)) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) 12)) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) 14)) (|construct| (((|Stream| |#1|) $) 17)) (|coerce| (((|OutputForm|) $) NIL))) 
(((|InfiniteTuple| |#1|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (SIGNATURE |filterWhile| ($ (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |filterUntil| ($ (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |select| ($ (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |generate| ($ (|Mapping| |#1| |#1|) |#1|)) (SIGNATURE |construct| ((|Stream| |#1|) $)))) (|Type|)) (T |InfiniteTuple|)) 
((|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|InfiniteTuple| *3)))) (|filterWhile| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|InfiniteTuple| *3)))) (|filterUntil| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|InfiniteTuple| *3)))) (|select| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|InfiniteTuple| *3)))) (|generate| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|InfiniteTuple| *3)))) (|construct| (*1 *2 *1) (AND (|isDomain| *2 (|Stream| *3)) (|isDomain| *1 (|InfiniteTuple| *3)) (|ofCategory| *3 (|Type|))))) 
(|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (SIGNATURE |filterWhile| ($ (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |filterUntil| ($ (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |select| ($ (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |generate| ($ (|Mapping| |#1| |#1|) |#1|)) (SIGNATURE |construct| ((|Stream| |#1|) $)))) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|zero| (($ (|NonNegativeInteger|)) NIL (|has| |#1| (|AbelianMonoid|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) NIL) (((|Boolean|) $) NIL (|has| |#1| (|OrderedSet|)))) (|sort!| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $) NIL (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|has| |#1| (|OrderedSet|))))) (|sort| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) NIL) (($ $) NIL (|has| |#1| (|OrderedSet|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setelt| ((|#1| $ (|Integer|) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) NIL T CONST)) (|reverse!| (($ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) NIL)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|remove| (($ |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| ((|#1| $ (|Integer|) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#1| $ (|Integer|)) NIL)) (|position| (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) NIL) (((|Integer|) |#1| $) NIL (|has| |#1| (|SetCategory|))) (((|Integer|) |#1| $ (|Integer|)) NIL (|has| |#1| (|SetCategory|)))) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|outerProduct| (((|Matrix| |#1|) $ $) NIL (|has| |#1| (|Ring|)))) (|new| (($ (|NonNegativeInteger|) |#1|) NIL)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|merge| (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) NIL) (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|maxIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL)) (|magnitude| ((|#1| $) NIL (AND (|has| |#1| (|RadicalCategory|)) (|has| |#1| (|Ring|))))) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|length| ((|#1| $) NIL (AND (|has| |#1| (|RadicalCategory|)) (|has| |#1| (|Ring|))))) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|insert| (($ |#1| $ (|Integer|)) NIL) (($ $ $ (|Integer|)) NIL)) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|first| ((|#1| $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) NIL)) (|fill!| (($ $ |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|entry?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|entries| (((|List| |#1|) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#1| $ (|Integer|) |#1|) NIL) ((|#1| $ (|Integer|)) NIL) (($ $ (|UniversalSegment| (|Integer|))) NIL)) (|dot| ((|#1| $ $) NIL (|has| |#1| (|Ring|)))) (|delete| (($ $ (|Integer|)) NIL) (($ $ (|UniversalSegment| (|Integer|))) NIL)) (|cross| (($ $ $) NIL (|has| |#1| (|Ring|)))) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copyInto!| (($ $ $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) NIL)) (|concat| (($ $ |#1|) NIL) (($ |#1| $) NIL) (($ $ $) NIL) (($ (|List| $)) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (- (($ $) NIL (|has| |#1| (|AbelianGroup|))) (($ $ $) NIL (|has| |#1| (|AbelianGroup|)))) (+ (($ $ $) NIL (|has| |#1| (|AbelianSemiGroup|)))) (* (($ (|Integer|) $) NIL (|has| |#1| (|AbelianGroup|))) (($ |#1| $) NIL (|has| |#1| (|Monoid|))) (($ $ |#1|) NIL (|has| |#1| (|Monoid|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|IndexedVector| |#1| |#2|) (|VectorCategory| |#1|) (|Type|) (|Integer|)) (T |IndexedVector|)) 
NIL 
(|VectorCategory| |#1|) 
((|swap!| (((|Void|) $ |#2| |#2|) 36)) (|minIndex| ((|#2| $) 23)) (|maxIndex| ((|#2| $) 21)) (|map!| (($ (|Mapping| |#3| |#3|) $) 32)) (|map| (($ (|Mapping| |#3| |#3|) $) 30)) (|first| ((|#3| $) 26)) (|fill!| (($ $ |#3|) 33)) (|entry?| (((|Boolean|) |#3| $) 17)) (|entries| (((|List| |#3|) $) 15)) (|elt| ((|#3| $ |#2| |#3|) 12) ((|#3| $ |#2|) NIL))) 
(((|IndexedAggregate&| |#1| |#2| |#3|) (CATEGORY |domain| (SIGNATURE |swap!| ((|Void|) |#1| |#2| |#2|)) (SIGNATURE |fill!| (|#1| |#1| |#3|)) (SIGNATURE |first| (|#3| |#1|)) (SIGNATURE |minIndex| (|#2| |#1|)) (SIGNATURE |maxIndex| (|#2| |#1|)) (SIGNATURE |entry?| ((|Boolean|) |#3| |#1|)) (SIGNATURE |entries| ((|List| |#3|) |#1|)) (SIGNATURE |elt| (|#3| |#1| |#2|)) (SIGNATURE |elt| (|#3| |#1| |#2| |#3|)) (SIGNATURE |map!| (|#1| (|Mapping| |#3| |#3|) |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#3| |#3|) |#1|))) (|IndexedAggregate| |#2| |#3|) (|SetCategory|) (|Type|)) (T |IndexedAggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |swap!| ((|Void|) |#1| |#2| |#2|)) (SIGNATURE |fill!| (|#1| |#1| |#3|)) (SIGNATURE |first| (|#3| |#1|)) (SIGNATURE |minIndex| (|#2| |#1|)) (SIGNATURE |maxIndex| (|#2| |#1|)) (SIGNATURE |entry?| ((|Boolean|) |#3| |#1|)) (SIGNATURE |entries| ((|List| |#3|) |#1|)) (SIGNATURE |elt| (|#3| |#1| |#2|)) (SIGNATURE |elt| (|#3| |#1| |#2| |#3|)) (SIGNATURE |map!| (|#1| (|Mapping| |#3| |#3|) |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#3| |#3|) |#1|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#2| (|SetCategory|)))) (|swap!| (((|Void|) $ |#1| |#1|) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setelt| ((|#2| $ |#1| |#2|) 49 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) 7 T CONST)) (|qsetelt!| ((|#2| $ |#1| |#2|) 50 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#2| $ |#1|) 48)) (|parts| (((|List| |#2|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|minIndex| ((|#1| $) 40 (|has| |#1| (|OrderedSet|)))) (|members| (((|List| |#2|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#2| $) 27 (AND (|has| |#2| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|maxIndex| ((|#1| $) 41 (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| |#2| |#2|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#2| |#2|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (|has| |#2| (|SetCategory|)))) (|indices| (((|List| |#1|) $) 43)) (|index?| (((|Boolean|) |#1| $) 44)) (|hash| (((|SingleInteger|) $) 21 (|has| |#2| (|SetCategory|)))) (|first| ((|#2| $) 39 (|has| |#1| (|OrderedSet|)))) (|fill!| (($ $ |#2|) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#2|))) 26 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|Equation| |#2|)) 25 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ |#2| |#2|) 24 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|List| |#2|) (|List| |#2|)) 23 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|entry?| (((|Boolean|) |#2| $) 42 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|entries| (((|List| |#2|) $) 45)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| ((|#2| $ |#1| |#2|) 47) ((|#2| $ |#1|) 46)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#2| $) 28 (AND (|has| |#2| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|coerce| (((|OutputForm|) $) 20 (|has| |#2| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#2| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|IndexedAggregate| |#1| |#2|) (|Category|) (|SetCategory|) (|Type|)) (T |IndexedAggregate|)) 
((|entries| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|List| *4)))) (|index?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|indices| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|List| *3)))) (|entry?| (*1 *2 *3 *1) (AND (|has| *1 (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *1 (|IndexedAggregate| *4 *3)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|maxIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *2 *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|OrderedSet|)))) (|minIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *2 *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|OrderedSet|)))) (|first| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *2 (|Type|)))) (|fill!| (*1 *1 *1 *2) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|IndexedAggregate| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|Type|)))) (|swap!| (*1 *2 *1 *3 *3) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|IndexedAggregate| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Void|))))) 
(|Join| (|HomogeneousAggregate| |t#2|) (|EltableAggregate| |t#1| |t#2|) (CATEGORY |domain| (SIGNATURE |entries| ((|List| |t#2|) $)) (SIGNATURE |index?| ((|Boolean|) |t#1| $)) (SIGNATURE |indices| ((|List| |t#1|) $)) (IF (|has| |t#2| (|SetCategory|)) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (SIGNATURE |entry?| ((|Boolean|) |t#2| $)) |noBranch|) |noBranch|) (IF (|has| |t#1| (|OrderedSet|)) (PROGN (SIGNATURE |maxIndex| (|t#1| $)) (SIGNATURE |minIndex| (|t#1| $)) (SIGNATURE |first| (|t#2| $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |shallowlyMutable|)) (PROGN (SIGNATURE |fill!| ($ $ |t#2|)) (SIGNATURE |swap!| ((|Void|) $ |t#1| |t#1|))) |noBranch|))) 
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|#1|)))) NIL (AND (|has| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)) (|Evalable| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)))) (|has| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)) (|SetCategory|)))) (($ $ (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)) (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|))) NIL (AND (|has| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)) (|Evalable| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)))) (|has| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)) (|SetCategory|)))) (($ $ (|Equation| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)))) NIL (AND (|has| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)) (|Evalable| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)))) (|has| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)) (|SetCategory|)))) (($ $ (|List| (|Equation| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|))))) NIL (AND (|has| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)) (|Evalable| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)))) (|has| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)) (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|entry?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|entries| (((|List| |#1|) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) 37)) (|elt| ((|#1| $ (|String|) |#1|) NIL) ((|#1| $ (|String|)) 42)) (|dictionary| (($ (|List| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)))) NIL) (($) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) (((|NonNegativeInteger|) (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)) (|SetCategory|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) NIL (|has| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)) (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)))) NIL)) (|coerce| (((|OutputForm|) $) 21)) (|close!| (($ $) 26)) (|bag| (($ (|List| (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|)))) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 20)) (|#| (((|NonNegativeInteger|) $) 41 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|KeyedAccessFile| |#1|) (|Join| (|FileCategory| (|FileName|) (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|))) (|TableAggregate| (|String|) |#1|) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (SIGNATURE |pack!| ($ $)))) (|SetCategory|)) (T |KeyedAccessFile|)) 
((|pack!| (*1 *1 *1) (AND (|isDomain| *1 (|KeyedAccessFile| *2)) (|ofCategory| *2 (|SetCategory|))))) 
(|Join| (|FileCategory| (|FileName|) (|Record| (|:| |key| (|String|)) (|:| |entry| |#1|))) (|TableAggregate| (|String|) |#1|) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (SIGNATURE |pack!| ($ $)))) 
((|member?| (((|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) $) 15)) (|keys| (((|List| |#2|) $) 19)) (|key?| (((|Boolean|) |#2| $) 12))) 
(((|KeyedDictionary&| |#1| |#2| |#3|) (CATEGORY |domain| (SIGNATURE |keys| ((|List| |#2|) |#1|)) (SIGNATURE |key?| ((|Boolean|) |#2| |#1|)) (SIGNATURE |member?| ((|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) |#1|))) (|KeyedDictionary| |#2| |#3|) (|SetCategory|) (|SetCategory|)) (T |KeyedDictionary&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |keys| ((|List| |#2|) |#1|)) (SIGNATURE |key?| ((|Boolean|) |#2| |#1|)) (SIGNATURE |member?| ((|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) |#1|))) 
((~= (((|Boolean|) $ $) 18 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|select!| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 42 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|select| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 52 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|search| (((|Union| |#2| "failed") |#1| $) 57)) (|sample| (($) 7 T CONST)) (|removeDuplicates| (($ $) 55 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 44 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 43 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| |#2| "failed") |#1| $) 58)) (|remove| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 54 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 51 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 53 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 50 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 49 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|parts| (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|members| (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 27 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (|keys| (((|List| |#1|) $) 59)) (|key?| (((|Boolean|) |#1| $) 60)) (|inspect| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 36)) (|insert!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 37)) (|hash| (((|SingleInteger|) $) 21 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (|find| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 48)) (|extract!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 38)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) 26 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ $ (|Equation| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 25 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 24 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ $ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 23 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|dictionary| (($) 46) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 45)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 28 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|convert| (((|InputForm|) $) 56 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 47)) (|coerce| (((|OutputForm|) $) 20 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (|bag| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 39)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|KeyedDictionary| |#1| |#2|) (|Category|) (|SetCategory|) (|SetCategory|)) (T |KeyedDictionary|)) 
((|key?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|KeyedDictionary| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|keys| (*1 *2 *1) (AND (|ofCategory| *1 (|KeyedDictionary| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|List| *3)))) (|remove!| (*1 *2 *3 *1) (|partial| AND (|ofCategory| *1 (|KeyedDictionary| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)))) (|search| (*1 *2 *3 *1) (|partial| AND (|ofCategory| *1 (|KeyedDictionary| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|))))) 
(|Join| (|Dictionary| (|Record| (|:| |key| |t#1|) (|:| |entry| |t#2|))) (CATEGORY |domain| (SIGNATURE |key?| ((|Boolean|) |t#1| $)) (SIGNATURE |keys| ((|List| |t#1|) $)) (SIGNATURE |remove!| ((|Union| |t#2| "failed") |t#1| $)) (SIGNATURE |search| ((|Union| |t#2| "failed") |t#1| $)))) 
(((|Aggregate|) . T) ((|BagAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|BasicType|) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) ((|Collection| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|ConvertibleTo| (|InputForm|)) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|ConvertibleTo| (|InputForm|))) ((|Dictionary| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|DictionaryOperations| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))) ((|HomogeneousAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|InnerEvalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))) ((|SetCategory|) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) ((|Type|) . T)) 
((|constantKernel| (((|Kernel| |#2|) |#1|) 15)) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) 19))) 
(((|KernelFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |constantKernel| ((|Kernel| |#2|) |#1|)) (SIGNATURE |constantIfCan| ((|Union| |#1| "failed") (|Kernel| |#2|)))) (|OrderedSet|) (|OrderedSet|)) (T |KernelFunctions2|)) 
((|constantIfCan| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|Kernel| *4)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|OrderedSet|)) (|isDomain| *1 (|KernelFunctions2| *2 *4)))) (|constantKernel| (*1 *2 *3) (AND (|isDomain| *2 (|Kernel| *4)) (|isDomain| *1 (|KernelFunctions2| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|OrderedSet|))))) 
(CATEGORY |package| (SIGNATURE |constantKernel| ((|Kernel| |#2|) |#1|)) (SIGNATURE |constantIfCan| ((|Union| |#1| "failed") (|Kernel| |#2|)))) 
((~= (((|Boolean|) $ $) NIL)) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) 36)) (|setPosition| (((|Void|) $ (|NonNegativeInteger|)) 26)) (|position| (((|NonNegativeInteger|) $) 25)) (|operator| (((|BasicOperator|) $) 12)) (|name| (((|Symbol|) $) 20)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|latex| (((|String|) $) NIL)) (|kernel| (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) 30) (($ (|Symbol|)) 31)) (|is?| (((|Boolean|) $ (|BasicOperator|)) 18) (((|Boolean|) $ (|Symbol|)) 16)) (|height| (((|NonNegativeInteger|) $) 22)) (|hash| (((|SingleInteger|) $) NIL)) (|convert| (((|Pattern| (|Integer|)) $) 69 (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|))))) (((|Pattern| (|Float|)) $) 75 (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|))))) (((|InputForm|) $) 62 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|coerce| (((|OutputForm|) $) 51)) (|argument| (((|List| |#1|) $) 24)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 39)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 40))) 
(((|Kernel| |#1|) (|Join| (|CachableSet|) (|Patternable| |#1|) (CATEGORY |domain| (SIGNATURE |name| ((|Symbol|) $)) (SIGNATURE |operator| ((|BasicOperator|) $)) (SIGNATURE |argument| ((|List| |#1|) $)) (SIGNATURE |height| ((|NonNegativeInteger|) $)) (SIGNATURE |kernel| ($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|))) (SIGNATURE |kernel| ($ (|Symbol|))) (SIGNATURE |symbolIfCan| ((|Union| (|Symbol|) "failed") $)) (SIGNATURE |is?| ((|Boolean|) $ (|BasicOperator|))) (SIGNATURE |is?| ((|Boolean|) $ (|Symbol|))) (IF (|has| |#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |noBranch|))) (|OrderedSet|)) (T |Kernel|)) 
((|name| (*1 *2 *1) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|Kernel| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|operator| (*1 *2 *1) (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *1 (|Kernel| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|argument| (*1 *2 *1) (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|Kernel| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|height| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Kernel| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|kernel| (*1 *1 *2 *3 *4) (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|Kernel| *5)))) (|kernel| (*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|Kernel| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|symbolIfCan| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|Kernel| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|is?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Kernel| *4)) (|ofCategory| *4 (|OrderedSet|)))) (|is?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Kernel| *4)) (|ofCategory| *4 (|OrderedSet|))))) 
(|Join| (|CachableSet|) (|Patternable| |#1|) (CATEGORY |domain| (SIGNATURE |name| ((|Symbol|) $)) (SIGNATURE |operator| ((|BasicOperator|) $)) (SIGNATURE |argument| ((|List| |#1|) $)) (SIGNATURE |height| ((|NonNegativeInteger|) $)) (SIGNATURE |kernel| ($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|))) (SIGNATURE |kernel| ($ (|Symbol|))) (SIGNATURE |symbolIfCan| ((|Union| (|Symbol|) "failed") $)) (SIGNATURE |is?| ((|Boolean|) $ (|BasicOperator|))) (SIGNATURE |is?| ((|Boolean|) $ (|Symbol|))) (IF (|has| |#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |noBranch|))) 
((|coerce| ((|#1| $) 6))) 
(((|CoercibleTo| |#1|) (|Category|) (|Type|)) (T |CoercibleTo|)) 
((|coerce| (*1 *2 *1) (AND (|ofCategory| *1 (|CoercibleTo| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (CATEGORY |domain| (SIGNATURE |coerce| (|t#1| $)))) 
((|convert| ((|#1| $) 6))) 
(((|ConvertibleTo| |#1|) (|Category|) (|Type|)) (T |ConvertibleTo|)) 
((|convert| (*1 *2 *1) (AND (|ofCategory| *1 (|ConvertibleTo| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (CATEGORY |domain| (SIGNATURE |convert| (|t#1| $)))) 
((|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) 13) (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) 14))) 
(((|Kovacic| |#1| |#2|) (CATEGORY |package| (SIGNATURE |kovacic| ((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|))) (SIGNATURE |kovacic| ((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)))) (|Join| (|CharacteristicZero|) (|AlgebraicallyClosedField|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|)))) (|UnivariatePolynomialCategory| |#1|)) (T |Kovacic|)) 
((|kovacic| (*1 *2 *3 *3 *3 *4) (|partial| AND (|isDomain| *4 (|Mapping| (|Factored| *6) *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Join| (|CharacteristicZero|) (|AlgebraicallyClosedField|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|isDomain| *2 (|SparseUnivariatePolynomial| (|Fraction| *6))) (|isDomain| *1 (|Kovacic| *5 *6)) (|isDomain| *3 (|Fraction| *6)))) (|kovacic| (*1 *2 *3 *3 *3) (|partial| AND (|ofCategory| *4 (|Join| (|CharacteristicZero|) (|AlgebraicallyClosedField|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|SparseUnivariatePolynomial| (|Fraction| *5))) (|isDomain| *1 (|Kovacic| *4 *5)) (|isDomain| *3 (|Fraction| *5))))) 
(CATEGORY |package| (SIGNATURE |kovacic| ((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|))) (SIGNATURE |kovacic| ((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)))) 
((|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ |#2|) 10))) 
(((|LeftAlgebra&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|LeftAlgebra| |#2|) (|Ring|)) (T |LeftAlgebra&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ |#1|) 35)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ |#1| $) 36))) 
(((|LeftAlgebra| |#1|) (|Category|) (|Ring|)) (T |LeftAlgebra|)) 
((|coerce| (*1 *1 *2) (AND (|ofCategory| *1 (|LeftAlgebra| *2)) (|ofCategory| *2 (|Ring|))))) 
(|Join| (|Ring|) (|LeftModule| |t#1|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |t#1|)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sign| (((|Integer|) $) NIL (|has| |#1| (|OrderedRing|)))) (|sample| (($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL)) (|positive?| (((|Boolean|) $) NIL (|has| |#1| (|OrderedRing|)))) (|one?| (((|Boolean|) $) NIL)) (|numer| ((|#1| $) 13)) (|negative?| (((|Boolean|) $) NIL (|has| |#1| (|OrderedRing|)))) (|min| (($ $ $) NIL (|has| |#1| (|OrderedRing|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedRing|)))) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|denom| ((|#3| $) 15)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ |#2|) NIL)) (|characteristic| (((|NonNegativeInteger|)) 20)) (|abs| (($ $) NIL (|has| |#1| (|OrderedRing|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) 12 T CONST)) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedRing|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedRing|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedRing|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedRing|)))) (/ (($ $ |#3|) NIL) (($ |#1| |#3|) 11)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 17) (($ $ |#2|) NIL) (($ |#2| $) NIL))) 
(((|LocalAlgebra| |#1| |#2| |#3|) (|Join| (|Algebra| |#2|) (CATEGORY |domain| (IF (|has| |#1| (|OrderedRing|)) (ATTRIBUTE (|OrderedRing|)) |noBranch|) (SIGNATURE / ($ $ |#3|)) (SIGNATURE / ($ |#1| |#3|)) (SIGNATURE |numer| (|#1| $)) (SIGNATURE |denom| (|#3| $)))) (|Algebra| |#2|) (|CommutativeRing|) (|SubsetCategory| (|Monoid|) |#2|)) (T |LocalAlgebra|)) 
((/ (*1 *1 *1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *1 (|LocalAlgebra| *3 *4 *2)) (|ofCategory| *3 (|Algebra| *4)) (|ofCategory| *2 (|SubsetCategory| (|Monoid|) *4)))) (/ (*1 *1 *2 *3) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *1 (|LocalAlgebra| *2 *4 *3)) (|ofCategory| *2 (|Algebra| *4)) (|ofCategory| *3 (|SubsetCategory| (|Monoid|) *4)))) (|numer| (*1 *2 *1) (AND (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *2 (|Algebra| *3)) (|isDomain| *1 (|LocalAlgebra| *2 *3 *4)) (|ofCategory| *4 (|SubsetCategory| (|Monoid|) *3)))) (|denom| (*1 *2 *1) (AND (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *2 (|SubsetCategory| (|Monoid|) *4)) (|isDomain| *1 (|LocalAlgebra| *3 *4 *2)) (|ofCategory| *3 (|Algebra| *4))))) 
(|Join| (|Algebra| |#2|) (CATEGORY |domain| (IF (|has| |#1| (|OrderedRing|)) (ATTRIBUTE (|OrderedRing|)) |noBranch|) (SIGNATURE / ($ $ |#3|)) (SIGNATURE / ($ |#1| |#3|)) (SIGNATURE |numer| (|#1| $)) (SIGNATURE |denom| (|#3| $)))) 
((|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) 18))) 
(((|LaplaceTransform| |#1| |#2|) (CATEGORY |package| (SIGNATURE |laplace| (|#2| |#2| (|Symbol|) (|Symbol|)))) (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|))) (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| |#1|))) (T |LaplaceTransform|)) 
((|laplace| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|LaplaceTransform| *4 *2)) (|ofCategory| *2 (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *4)))))) 
(CATEGORY |package| (SIGNATURE |laplace| (|#2| |#2| (|Symbol|) (|Symbol|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 52)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|trailingCoefficient| ((|#1| $) 49)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL (|has| |#1| (|Field|)))) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) 95 (|has| |#1| (|Field|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) 83) (((|Union| |#2| "failed") $) 80)) (|retract| (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) NIL) ((|#2| $) NIL)) (|rem| (($ $ $) NIL (|has| |#1| (|Field|)))) (|reductum| (($ $) 24)) (|recip| (((|Union| $ "failed") $) 74)) (|quo| (($ $ $) NIL (|has| |#1| (|Field|)))) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL (|has| |#1| (|Field|)))) (|order| (((|Integer|) $) 19)) (|one?| (((|Boolean|) $) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) (|monomial?| (((|Boolean|) $) 36)) (|monomial| (($ |#1| (|Integer|)) 21)) (|leadingCoefficient| ((|#1| $) 51)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| |#1| (|Field|)))) (|lcm| (($ (|List| $)) NIL (|has| |#1| (|Field|))) (($ $ $) NIL (|has| |#1| (|Field|)))) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|Field|)))) (|gcd| (($ (|List| $)) NIL (|has| |#1| (|Field|))) (($ $ $) 85 (|has| |#1| (|Field|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 98 (|has| |#1| (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|exquo| (((|Union| $ "failed") $ $) 78)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) (|euclideanSize| (((|NonNegativeInteger|) $) 97 (|has| |#1| (|Field|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 96 (|has| |#1| (|Field|)))) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) 65) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|)) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|DifferentialRing|))) (($ $) NIL (|has| |#2| (|DifferentialRing|)))) (|degree| (((|Integer|) $) 34)) (|convert| (((|Fraction| |#2|) $) 42)) (|coerce| (((|OutputForm|) $) 61) (($ (|Integer|)) 32) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (($ |#1|) 31) (($ |#2|) 22)) (|coefficient| ((|#1| $ (|Integer|)) 62)) (|charthRoot| (((|Union| $ "failed") $) NIL (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) 29)) (|associates?| (((|Boolean|) $ $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 9 T CONST)) (|One| (($) 12 T CONST)) (D (($ $ (|Mapping| |#2| |#2|)) NIL) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|)) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|DifferentialRing|))) (($ $) NIL (|has| |#2| (|DifferentialRing|)))) (= (((|Boolean|) $ $) 17)) (- (($ $) 46) (($ $ $) NIL)) (+ (($ $ $) 75)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 26) (($ $ $) 44))) 
(((|LaurentPolynomial| |#1| |#2|) (|Join| (|DifferentialExtension| |#2|) (|IntegralDomain|) (|ConvertibleTo| (|Fraction| |#2|)) (|FullyRetractableTo| |#1|) (|RetractableTo| |#2|) (CATEGORY |domain| (SIGNATURE |monomial?| ((|Boolean|) $)) (SIGNATURE |degree| ((|Integer|) $)) (SIGNATURE |order| ((|Integer|) $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |leadingCoefficient| (|#1| $)) (SIGNATURE |trailingCoefficient| (|#1| $)) (SIGNATURE |coefficient| (|#1| $ (|Integer|))) (SIGNATURE |monomial| ($ |#1| (|Integer|))) (IF (|has| |#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |noBranch|) (IF (|has| |#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |noBranch|) (IF (|has| |#1| (|Field|)) (PROGN (ATTRIBUTE (|EuclideanDomain|)) (SIGNATURE |separate| ((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)))) |noBranch|))) (|IntegralDomain|) (|UnivariatePolynomialCategory| |#1|)) (T |LaurentPolynomial|)) 
((|monomial?| (*1 *2 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LaurentPolynomial| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|degree| (*1 *2 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|LaurentPolynomial| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|order| (*1 *2 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|LaurentPolynomial| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|reductum| (*1 *1 *1) (AND (|ofCategory| *2 (|IntegralDomain|)) (|isDomain| *1 (|LaurentPolynomial| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *2 (|IntegralDomain|)) (|isDomain| *1 (|LaurentPolynomial| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|trailingCoefficient| (*1 *2 *1) (AND (|ofCategory| *2 (|IntegralDomain|)) (|isDomain| *1 (|LaurentPolynomial| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|coefficient| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|IntegralDomain|)) (|isDomain| *1 (|LaurentPolynomial| *2 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)))) (|monomial| (*1 *1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|IntegralDomain|)) (|isDomain| *1 (|LaurentPolynomial| *2 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)))) (|separate| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Record| (|:| |polyPart| (|LaurentPolynomial| *4 *5)) (|:| |fracPart| (|Fraction| *5)))) (|isDomain| *1 (|LaurentPolynomial| *4 *5)) (|isDomain| *3 (|Fraction| *5))))) 
(|Join| (|DifferentialExtension| |#2|) (|IntegralDomain|) (|ConvertibleTo| (|Fraction| |#2|)) (|FullyRetractableTo| |#1|) (|RetractableTo| |#2|) (CATEGORY |domain| (SIGNATURE |monomial?| ((|Boolean|) $)) (SIGNATURE |degree| ((|Integer|) $)) (SIGNATURE |order| ((|Integer|) $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |leadingCoefficient| (|#1| $)) (SIGNATURE |trailingCoefficient| (|#1| $)) (SIGNATURE |coefficient| (|#1| $ (|Integer|))) (SIGNATURE |monomial| ($ |#1| (|Integer|))) (IF (|has| |#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |noBranch|) (IF (|has| |#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |noBranch|) (IF (|has| |#1| (|Field|)) (PROGN (ATTRIBUTE (|EuclideanDomain|)) (SIGNATURE |separate| ((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)))) |noBranch|))) 
((|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) 46)) (|normalizeIfCan| ((|#6| |#6|) 39))) 
(((|LazardSetSolvingPackage| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |normalizeIfCan| (|#6| |#6|)) (SIGNATURE |zeroSetSplit| ((|List| |#6|) (|List| |#4|) (|Boolean|)))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) (|SquareFreeRegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |LazardSetSolvingPackage|)) 
((|zeroSetSplit| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|List| *10)) (|isDomain| *1 (|LazardSetSolvingPackage| *5 *6 *7 *8 *9 *10)) (|ofCategory| *9 (|RegularTriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *10 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8)))) (|normalizeIfCan| (*1 *2 *2) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *1 (|LazardSetSolvingPackage| *3 *4 *5 *6 *7 *2)) (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *2 (|SquareFreeRegularTriangularSetCategory| *3 *4 *5 *6))))) 
(CATEGORY |package| (SIGNATURE |normalizeIfCan| (|#6| |#6|)) (SIGNATURE |zeroSetSplit| ((|List| |#6|) (|List| |#4|) (|Boolean|)))) 
((|polCase| (((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|)) 22)) (|distFact| (((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)) 51))) 
(((|LeadingCoefDetermination| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |polCase| ((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|))) (SIGNATURE |distFact| ((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)))) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|EuclideanDomain|) (|PolynomialCategory| |#3| |#2| |#1|)) (T |LeadingCoefDetermination|)) 
((|distFact| (*1 *2 *3 *4 *5 *6 *7 *6) (|partial| AND (|isDomain| *5 (|Record| (|:| |contp| *3) (|:| |factors| (|List| (|Record| (|:| |irr| *10) (|:| |pow| (|Integer|))))))) (|isDomain| *6 (|List| *3)) (|isDomain| *7 (|List| *8)) (|ofCategory| *8 (|OrderedSet|)) (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *10 (|PolynomialCategory| *3 *9 *8)) (|ofCategory| *9 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Record| (|:| |polfac| (|List| *10)) (|:| |correct| *3) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| *3))))) (|isDomain| *1 (|LeadingCoefDetermination| *8 *9 *3 *10)) (|isDomain| *4 (|List| (|SparseUnivariatePolynomial| *3))))) (|polCase| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *5 (|List| *3)) (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LeadingCoefDetermination| *6 *7 *3 *8)) (|ofCategory| *8 (|PolynomialCategory| *3 *7 *6))))) 
(CATEGORY |package| (SIGNATURE |polCase| ((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|))) (SIGNATURE |distFact| ((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)))) 
((~= (((|Boolean|) $ $) NIL)) (|varList| (((|List| |#1|) $) NIL)) (|sample| (($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|mirror| (($ $) 67)) (|log| (((|LiePolynomial| |#1| |#2|) $) 52)) (|listOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) 36)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 70)) (|identification| (((|List| (|Equation| |#2|)) $ $) 33)) (|hash| (((|SingleInteger|) $) NIL)) (|exp| (($ (|LiePolynomial| |#1| |#2|)) 48)) (|conjugate| (($ $ $) NIL)) (|commutator| (($ $ $) NIL)) (|coerce| (((|OutputForm|) $) 58) (((|XDistributedPolynomial| |#1| |#2|) $) NIL) (((|XPBWPolynomial| |#1| |#2|) $) 66)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|One| (($) 53 T CONST)) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) 31)) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) 65)) (= (((|Boolean|) $ $) 54)) (/ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ $ $) 44))) 
(((|LieExponentials| |#1| |#2| |#3|) (|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |exp| ($ (|LiePolynomial| |#1| |#2|))) (SIGNATURE |log| ((|LiePolynomial| |#1| |#2|) $)) (SIGNATURE |listOfTerms| ((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $)) (SIGNATURE |coerce| ((|XDistributedPolynomial| |#1| |#2|) $)) (SIGNATURE |coerce| ((|XPBWPolynomial| |#1| |#2|) $)) (SIGNATURE |mirror| ($ $)) (SIGNATURE |varList| ((|List| |#1|) $)) (SIGNATURE |LyndonBasis| ((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|))) (SIGNATURE |LyndonCoordinates| ((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $)) (SIGNATURE |identification| ((|List| (|Equation| |#2|)) $ $)))) (|OrderedSet|) (|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|)))) (|PositiveInteger|)) (T |LieExponentials|)) 
((|exp| (*1 *1 *2) (AND (|isDomain| *2 (|LiePolynomial| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|))))) (|isDomain| *1 (|LieExponentials| *3 *4 *5)) (|ofType| *5 (|PositiveInteger|)))) (|log| (*1 *2 *1) (AND (|isDomain| *2 (|LiePolynomial| *3 *4)) (|isDomain| *1 (|LieExponentials| *3 *4 *5)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|))))) (|ofType| *5 (|PositiveInteger|)))) (|listOfTerms| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| *3)) (|:| |c| *4)))) (|isDomain| *1 (|LieExponentials| *3 *4 *5)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|))))) (|ofType| *5 (|PositiveInteger|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|XDistributedPolynomial| *3 *4)) (|isDomain| *1 (|LieExponentials| *3 *4 *5)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|))))) (|ofType| *5 (|PositiveInteger|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|XPBWPolynomial| *3 *4)) (|isDomain| *1 (|LieExponentials| *3 *4 *5)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|))))) (|ofType| *5 (|PositiveInteger|)))) (|mirror| (*1 *1 *1) (AND (|isDomain| *1 (|LieExponentials| *2 *3 *4)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|))))) (|ofType| *4 (|PositiveInteger|)))) (|varList| (*1 *2 *1) (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|LieExponentials| *3 *4 *5)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|))))) (|ofType| *5 (|PositiveInteger|)))) (|LyndonBasis| (*1 *2 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|List| (|LiePolynomial| *4 *5))) (|isDomain| *1 (|LieExponentials| *4 *5 *6)) (|ofCategory| *5 (|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|))))) (|ofType| *6 (|PositiveInteger|)))) (|LyndonCoordinates| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |k| (|LyndonWord| *3)) (|:| |c| *4)))) (|isDomain| *1 (|LieExponentials| *3 *4 *5)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|))))) (|ofType| *5 (|PositiveInteger|)))) (|identification| (*1 *2 *1 *1) (AND (|isDomain| *2 (|List| (|Equation| *4))) (|isDomain| *1 (|LieExponentials| *3 *4 *5)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|))))) (|ofType| *5 (|PositiveInteger|))))) 
(|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |exp| ($ (|LiePolynomial| |#1| |#2|))) (SIGNATURE |log| ((|LiePolynomial| |#1| |#2|) $)) (SIGNATURE |listOfTerms| ((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $)) (SIGNATURE |coerce| ((|XDistributedPolynomial| |#1| |#2|) $)) (SIGNATURE |coerce| ((|XPBWPolynomial| |#1| |#2|) $)) (SIGNATURE |mirror| ($ $)) (SIGNATURE |varList| ((|List| |#1|) $)) (SIGNATURE |LyndonBasis| ((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|))) (SIGNATURE |LyndonCoordinates| ((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $)) (SIGNATURE |identification| ((|List| (|Equation| |#2|)) $ $)))) 
((|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) 70) (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) 56)) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) 22)) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) 69)) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) 55)) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) 26)) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) 25))) 
(((|LexTriangularPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |zeroDimensional?| ((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))))) (SIGNATURE |fglmIfCan| ((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))))) (SIGNATURE |groebner| ((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))))) (SIGNATURE |lexTriangular| ((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|))) (SIGNATURE |squareFreeLexTriangular| ((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|))) (SIGNATURE |zeroSetSplit| ((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|))) (SIGNATURE |zeroSetSplit| ((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)))) (|GcdDomain|) (|List| (|Symbol|))) (T |LexTriangularPackage|)) 
((|zeroSetSplit| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|NewSparseMultivariatePolynomial| *5 (|OrderedVariableList| *6)))) (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|)) (|ofType| *6 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|SquareFreeRegularTriangularSet| *5 (|IndexedExponents| (|OrderedVariableList| *6)) (|OrderedVariableList| *6) (|NewSparseMultivariatePolynomial| *5 (|OrderedVariableList| *6))))) (|isDomain| *1 (|LexTriangularPackage| *5 *6)))) (|zeroSetSplit| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|NewSparseMultivariatePolynomial| *5 (|OrderedVariableList| *6)))) (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|)) (|ofType| *6 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|RegularChain| *5 *6))) (|isDomain| *1 (|LexTriangularPackage| *5 *6)))) (|squareFreeLexTriangular| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|NewSparseMultivariatePolynomial| *5 (|OrderedVariableList| *6)))) (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|)) (|ofType| *6 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|SquareFreeRegularTriangularSet| *5 (|IndexedExponents| (|OrderedVariableList| *6)) (|OrderedVariableList| *6) (|NewSparseMultivariatePolynomial| *5 (|OrderedVariableList| *6))))) (|isDomain| *1 (|LexTriangularPackage| *5 *6)))) (|lexTriangular| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|NewSparseMultivariatePolynomial| *5 (|OrderedVariableList| *6)))) (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|)) (|ofType| *6 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|RegularChain| *5 *6))) (|isDomain| *1 (|LexTriangularPackage| *5 *6)))) (|groebner| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|NewSparseMultivariatePolynomial| *3 (|OrderedVariableList| *4)))) (|ofCategory| *3 (|GcdDomain|)) (|ofType| *4 (|List| (|Symbol|))) (|isDomain| *1 (|LexTriangularPackage| *3 *4)))) (|fglmIfCan| (*1 *2 *2) (|partial| AND (|isDomain| *2 (|List| (|NewSparseMultivariatePolynomial| *3 (|OrderedVariableList| *4)))) (|ofCategory| *3 (|GcdDomain|)) (|ofType| *4 (|List| (|Symbol|))) (|isDomain| *1 (|LexTriangularPackage| *3 *4)))) (|zeroDimensional?| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|NewSparseMultivariatePolynomial| *4 (|OrderedVariableList| *5)))) (|ofCategory| *4 (|GcdDomain|)) (|ofType| *5 (|List| (|Symbol|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LexTriangularPackage| *4 *5))))) 
(CATEGORY |package| (SIGNATURE |zeroDimensional?| ((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))))) (SIGNATURE |fglmIfCan| ((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))))) (SIGNATURE |groebner| ((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))))) (SIGNATURE |lexTriangular| ((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|))) (SIGNATURE |squareFreeLexTriangular| ((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|))) (SIGNATURE |zeroSetSplit| ((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|))) (SIGNATURE |zeroSetSplit| ((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)))) 
((|tanh| (($ $) 38)) (|tan| (($ $) 21)) (|sinh| (($ $) 37)) (|sin| (($ $) 22)) (|sech| (($ $) 36)) (|sec| (($ $) 23)) (|pi| (($) 48)) (|log| (($ $) 45)) (|li| (($ $) 17)) (|integral| (($ $ (|SegmentBinding| $)) 7) (($ $ (|Symbol|)) 6)) (|fresnelS| (($ $) 14)) (|fresnelC| (($ $) 13)) (|exp| (($ $) 46)) (|erf| (($ $) 15)) (|dilog| (($ $) 16)) (|csch| (($ $) 35)) (|csc| (($ $) 24)) (|coth| (($ $) 34)) (|cot| (($ $) 25)) (|cosh| (($ $) 33)) (|cos| (($ $) 26)) (|atanh| (($ $) 44)) (|atan| (($ $) 32)) (|asinh| (($ $) 43)) (|asin| (($ $) 31)) (|asech| (($ $) 42)) (|asec| (($ $) 30)) (|acsch| (($ $) 41)) (|acsc| (($ $) 29)) (|acoth| (($ $) 40)) (|acot| (($ $) 28)) (|acosh| (($ $) 39)) (|acos| (($ $) 27)) (|Si| (($ $) 19)) (|Ei| (($ $) 20)) (|Ci| (($ $) 18)) (** (($ $ $) 47))) 
(((|LiouvillianFunctionCategory|) (|Category|)) (T |LiouvillianFunctionCategory|)) 
((|Ei| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|Si| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|Ci| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|li| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|dilog| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|erf| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|fresnelS| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|fresnelC| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|)))) 
(|Join| (|PrimitiveFunctionCategory|) (|TranscendentalFunctionCategory|) (CATEGORY |domain| (SIGNATURE |Ei| ($ $)) (SIGNATURE |Si| ($ $)) (SIGNATURE |Ci| ($ $)) (SIGNATURE |li| ($ $)) (SIGNATURE |dilog| ($ $)) (SIGNATURE |erf| ($ $)) (SIGNATURE |fresnelS| ($ $)) (SIGNATURE |fresnelC| ($ $)))) 
(((|ArcHyperbolicFunctionCategory|) . T) ((|ArcTrigonometricFunctionCategory|) . T) ((|ElementaryFunctionCategory|) . T) ((|HyperbolicFunctionCategory|) . T) ((|PrimitiveFunctionCategory|) . T) ((|TranscendentalFunctionCategory|) . T) ((|TrigonometricFunctionCategory|) . T)) 
((|operator| (((|BasicOperator|) (|BasicOperator|)) 87)) (|li| ((|#2| |#2|) 32)) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) 83) ((|#2| |#2| (|Symbol|)) 56)) (|fresnelS| ((|#2| |#2|) 34)) (|fresnelC| ((|#2| |#2|) 35)) (|erf| ((|#2| |#2|) 31)) (|dilog| ((|#2| |#2|) 33)) (|belong?| (((|Boolean|) (|BasicOperator|)) 38)) (|Si| ((|#2| |#2|) 28)) (|Ei| ((|#2| |#2|) 30)) (|Ci| ((|#2| |#2|) 29))) 
(((|LiouvillianFunction| |#1| |#2|) (CATEGORY |package| (SIGNATURE |belong?| ((|Boolean|) (|BasicOperator|))) (SIGNATURE |operator| ((|BasicOperator|) (|BasicOperator|))) (SIGNATURE |Ei| (|#2| |#2|)) (SIGNATURE |Si| (|#2| |#2|)) (SIGNATURE |Ci| (|#2| |#2|)) (SIGNATURE |li| (|#2| |#2|)) (SIGNATURE |erf| (|#2| |#2|)) (SIGNATURE |dilog| (|#2| |#2|)) (SIGNATURE |fresnelS| (|#2| |#2|)) (SIGNATURE |fresnelC| (|#2| |#2|)) (SIGNATURE |integral| (|#2| |#2| (|Symbol|))) (SIGNATURE |integral| (|#2| |#2| (|SegmentBinding| |#2|)))) (|Join| (|OrderedSet|) (|IntegralDomain|)) (|Join| (|FunctionSpace| |#1|) (|RadicalCategory|) (|TranscendentalFunctionCategory|))) (T |LiouvillianFunction|)) 
((|integral| (*1 *2 *2 *3) (AND (|isDomain| *3 (|SegmentBinding| *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *4) (|RadicalCategory|) (|TranscendentalFunctionCategory|))) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|LiouvillianFunction| *4 *2)))) (|integral| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|LiouvillianFunction| *4 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *4) (|RadicalCategory|) (|TranscendentalFunctionCategory|))))) (|fresnelC| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|LiouvillianFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|) (|TranscendentalFunctionCategory|))))) (|fresnelS| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|LiouvillianFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|) (|TranscendentalFunctionCategory|))))) (|dilog| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|LiouvillianFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|) (|TranscendentalFunctionCategory|))))) (|erf| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|LiouvillianFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|) (|TranscendentalFunctionCategory|))))) (|li| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|LiouvillianFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|) (|TranscendentalFunctionCategory|))))) (|Ci| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|LiouvillianFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|) (|TranscendentalFunctionCategory|))))) (|Si| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|LiouvillianFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|) (|TranscendentalFunctionCategory|))))) (|Ei| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|LiouvillianFunction| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|) (|TranscendentalFunctionCategory|))))) (|operator| (*1 *2 *2) (AND (|isDomain| *2 (|BasicOperator|)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|LiouvillianFunction| *3 *4)) (|ofCategory| *4 (|Join| (|FunctionSpace| *3) (|RadicalCategory|) (|TranscendentalFunctionCategory|))))) (|belong?| (*1 *2 *3) (AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LiouvillianFunction| *4 *5)) (|ofCategory| *5 (|Join| (|FunctionSpace| *4) (|RadicalCategory|) (|TranscendentalFunctionCategory|)))))) 
(CATEGORY |package| (SIGNATURE |belong?| ((|Boolean|) (|BasicOperator|))) (SIGNATURE |operator| ((|BasicOperator|) (|BasicOperator|))) (SIGNATURE |Ei| (|#2| |#2|)) (SIGNATURE |Si| (|#2| |#2|)) (SIGNATURE |Ci| (|#2| |#2|)) (SIGNATURE |li| (|#2| |#2|)) (SIGNATURE |erf| (|#2| |#2|)) (SIGNATURE |dilog| (|#2| |#2|)) (SIGNATURE |fresnelS| (|#2| |#2|)) (SIGNATURE |fresnelC| (|#2| |#2|)) (SIGNATURE |integral| (|#2| |#2| (|Symbol|))) (SIGNATURE |integral| (|#2| |#2| (|SegmentBinding| |#2|)))) 
((|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) 52)) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) 67)) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) 69) (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) 68)) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) 105)) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) 82)) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) 116)) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) 57)) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) 39)) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) 49)) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) 89))) 
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(((|Library|) (|Join| (|TableAggregate| (|String|) (|Any|)) (CATEGORY |domain| (SIGNATURE |library| ($ (|FileName|))) (SIGNATURE |pack!| ($ $)) (SIGNATURE |elt| ((|Any|) $ (|Symbol|))) (SIGNATURE |setelt| ((|Any|) $ (|Symbol|) (|Any|))) (SIGNATURE |close!| ($ $))))) (T |Library|)) 
((|library| (*1 *1 *2) (AND (|isDomain| *2 (|FileName|)) (|isDomain| *1 (|Library|)))) (|pack!| (*1 *1 *1) (|isDomain| *1 (|Library|))) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|Library|)))) (|setelt| (*1 *2 *1 *3 *2) (AND (|isDomain| *2 (|Any|)) (|isDomain| *3 (|Symbol|)) (|isDomain| *1 (|Library|)))) (|close!| (*1 *1 *1) (|isDomain| *1 (|Library|)))) 
(|Join| (|TableAggregate| (|String|) (|Any|)) (CATEGORY |domain| (SIGNATURE |library| ($ (|FileName|))) (SIGNATURE |pack!| ($ $)) (SIGNATURE |elt| ((|Any|) $ (|Symbol|))) (SIGNATURE |setelt| ((|Any|) $ (|Symbol|) (|Any|))) (SIGNATURE |close!| ($ $)))) 
((/ (($ $ |#2|) 10))) 
(((|LieAlgebra&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE / (|#1| |#1| |#2|))) (|LieAlgebra| |#2|) (|CommutativeRing|)) (T |LieAlgebra&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE / (|#1| |#1| |#2|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|construct| (($ $ $) 26)) (|coerce| (((|OutputForm|) $) 11)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (/ (($ $ |#1|) 25 (|has| |#1| (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ |#1| $) 22) (($ $ |#1|) 24))) 
(((|LieAlgebra| |#1|) (|Category|) (|CommutativeRing|)) (T |LieAlgebra|)) 
((|construct| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|LieAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (/ (*1 *1 *1 *2) (AND (|ofCategory| *1 (|LieAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|Field|))))) 
(|Join| (|Module| |t#1|) (CATEGORY |domain| (SIGNATURE |construct| ($ $ $)) (ATTRIBUTE |NullSquare|) (ATTRIBUTE |JacobiIdentity|) (IF (|has| |t#1| (|Field|)) (SIGNATURE / ($ $ |t#1|)) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| |#1|) . T) ((|Module| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T)) 
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(|FiniteRankNonAssociativeAlgebra| |#1|)))) (|recip| (((|Union| $ "failed") $) NIL (OR (AND (|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)) (|has| |#1| (|IntegralDomain|))) (AND (|has| |#2| (|FramedNonAssociativeAlgebra| |#1|)) (|has| |#1| (|IntegralDomain|)))))) (|rank| (((|PositiveInteger|)) NIL (|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)))) (|powerAssociative?| (((|Boolean|)) NIL (|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)))) (|plenaryPower| (($ $ (|PositiveInteger|)) NIL)) (|noncommutativeJordanAlgebra?| (((|Boolean|)) NIL (|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)))) (|lieAlgebra?| (((|Boolean|)) NIL (|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)))) (|lieAdmissible?| (((|Boolean|)) NIL (|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)))) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) NIL (OR (AND (|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)) (|has| |#1| (|IntegralDomain|))) (AND (|has| 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$ $) NIL)) (|antiCommutative?| (((|Boolean|)) NIL (|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)))) (|antiAssociative?| (((|Boolean|)) NIL (|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)))) (|alternative?| (((|Boolean|)) NIL (|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)))) (|Zero| (($) 15 T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) 17)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 11) (($ $ |#1|) NIL) (($ |#1| $) NIL))) 
(((|AssociatedLieAlgebra| |#1| |#2|) (|Join| (|NonAssociativeAlgebra| |#1|) (|CoercibleTo| |#2|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#2|)) (IF (|has| |#2| (|FramedNonAssociativeAlgebra| |#1|)) (ATTRIBUTE (|FramedNonAssociativeAlgebra| |#1|)) |noBranch|) (IF (|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)) (ATTRIBUTE (|FiniteRankNonAssociativeAlgebra| |#1|)) |noBranch|))) (|CommutativeRing|) (|NonAssociativeAlgebra| |#1|)) (T |AssociatedLieAlgebra|)) 
((|coerce| (*1 *1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *1 (|AssociatedLieAlgebra| *3 *2)) (|ofCategory| *2 (|NonAssociativeAlgebra| *3))))) 
(|Join| (|NonAssociativeAlgebra| |#1|) (|CoercibleTo| |#2|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#2|)) (IF (|has| |#2| (|FramedNonAssociativeAlgebra| |#1|)) (ATTRIBUTE (|FramedNonAssociativeAlgebra| |#1|)) |noBranch|) (IF (|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)) (ATTRIBUTE (|FiniteRankNonAssociativeAlgebra| |#1|)) |noBranch|))) 
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(((|PowerSeriesLimitPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |limit| ((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|)))) (SIGNATURE |complexLimit| ((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|)))) (SIGNATURE |limit| ((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)))) (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|))) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |PowerSeriesLimitPackage|)) 
((|limit| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *4 (|Equation| *3)) (|isDomain| *5 (|String|)) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *6))) (|ofCategory| *6 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|OrderedCompletion| *3)) (|isDomain| *1 (|PowerSeriesLimitPackage| *6 *3)))) (|complexLimit| (*1 *2 *3 *4) (|partial| AND (|isDomain| *4 (|Equation| (|OnePointCompletion| *3))) (|ofCategory| *5 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|OnePointCompletion| *3)) (|isDomain| *1 (|PowerSeriesLimitPackage| *5 *3)) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *5))))) (|limit| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Equation| (|OrderedCompletion| *3))) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *5))) (|ofCategory| *5 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Union| (|OrderedCompletion| *3) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| *3) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| *3) "failed"))) "failed")) (|isDomain| *1 (|PowerSeriesLimitPackage| *5 *3))))) 
(CATEGORY |package| (SIGNATURE |limit| ((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|)))) (SIGNATURE |complexLimit| ((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|)))) (SIGNATURE |limit| ((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)))) 
((|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) 79) (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) 18) (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) 34)) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) 21) (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) 42))) 
(((|RationalFunctionLimitPackage| |#1|) (CATEGORY |package| (SIGNATURE |limit| ((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|))))) (SIGNATURE |limit| ((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |complexLimit| ((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|))))) (SIGNATURE |complexLimit| ((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |limit| ((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)))) (|GcdDomain|)) (T |RationalFunctionLimitPackage|)) 
((|limit| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *4 (|Equation| (|Fraction| (|Polynomial| *6)))) (|isDomain| *5 (|String|)) (|isDomain| *3 (|Fraction| (|Polynomial| *6))) (|ofCategory| *6 (|GcdDomain|)) (|isDomain| *2 (|OrderedCompletion| *3)) (|isDomain| *1 (|RationalFunctionLimitPackage| *6)))) (|complexLimit| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Equation| (|Fraction| (|Polynomial| *5)))) (|isDomain| *3 (|Fraction| (|Polynomial| *5))) (|ofCategory| *5 (|GcdDomain|)) (|isDomain| *2 (|OnePointCompletion| *3)) (|isDomain| *1 (|RationalFunctionLimitPackage| *5)))) (|complexLimit| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Equation| (|OnePointCompletion| (|Polynomial| *5)))) (|ofCategory| *5 (|GcdDomain|)) (|isDomain| *2 (|OnePointCompletion| (|Fraction| (|Polynomial| *5)))) (|isDomain| *1 (|RationalFunctionLimitPackage| *5)) (|isDomain| *3 (|Fraction| (|Polynomial| *5))))) (|limit| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Equation| (|Fraction| (|Polynomial| *5)))) (|isDomain| *3 (|Fraction| (|Polynomial| *5))) (|ofCategory| *5 (|GcdDomain|)) (|isDomain| *2 (|Union| (|OrderedCompletion| *3) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| *3) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| *3) "failed"))) "failed")) (|isDomain| *1 (|RationalFunctionLimitPackage| *5)))) (|limit| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Equation| (|OrderedCompletion| (|Polynomial| *5)))) (|ofCategory| *5 (|GcdDomain|)) (|isDomain| *2 (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| *5))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| *5))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| *5))) "failed"))) "failed")) (|isDomain| *1 (|RationalFunctionLimitPackage| *5)) (|isDomain| *3 (|Fraction| (|Polynomial| *5)))))) 
(CATEGORY |package| (SIGNATURE |limit| ((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|))))) (SIGNATURE |limit| ((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |complexLimit| ((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|))))) (SIGNATURE |complexLimit| ((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |limit| ((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)))) 
((|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) 57 (|not| (|has| |#1| (|Field|)))) (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) 42 (|has| |#1| (|Field|)))) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) 30)) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) 33))) 
(((|LinearDependence| |#1| |#2|) (CATEGORY |package| (SIGNATURE |linearlyDependent?| ((|Boolean|) (|Vector| |#2|))) (SIGNATURE |linearDependence| ((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|))) (IF (|has| |#1| (|Field|)) (SIGNATURE |solveLinear| ((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|)) (SIGNATURE |solveLinear| ((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|)))) (|IntegralDomain|) (|LinearlyExplicitRingOver| |#1|)) (T |LinearDependence|)) 
((|solveLinear| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Vector| *4)) (|ofCategory| *4 (|LinearlyExplicitRingOver| *5)) (|not| (|ofCategory| *5 (|Field|))) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|Vector| (|Fraction| *5))) (|isDomain| *1 (|LinearDependence| *5 *4)))) (|solveLinear| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Vector| *4)) (|ofCategory| *4 (|LinearlyExplicitRingOver| *5)) (|ofCategory| *5 (|Field|)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|Vector| *5)) (|isDomain| *1 (|LinearDependence| *5 *4)))) (|linearDependence| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|Vector| *5)) (|ofCategory| *5 (|LinearlyExplicitRingOver| *4)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Vector| *4)) (|isDomain| *1 (|LinearDependence| *4 *5)))) (|linearlyDependent?| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *5)) (|ofCategory| *5 (|LinearlyExplicitRingOver| *4)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LinearDependence| *4 *5))))) 
(CATEGORY |package| (SIGNATURE |linearlyDependent?| ((|Boolean|) (|Vector| |#2|))) (SIGNATURE |linearDependence| ((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|))) (IF (|has| |#1| (|Field|)) (SIGNATURE |solveLinear| ((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|)) (SIGNATURE |solveLinear| ((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|reducedSystem| (((|Matrix| |#1|) (|Matrix| $)) 35) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) 34)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|LinearlyExplicitRingOver| |#1|) (|Category|) (|Ring|)) (T |LinearlyExplicitRingOver|)) 
((|reducedSystem| (*1 *2 *3) (AND (|isDomain| *3 (|Matrix| *1)) (|ofCategory| *1 (|LinearlyExplicitRingOver| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Matrix| *4)))) (|reducedSystem| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Matrix| *1)) (|isDomain| *4 (|Vector| *1)) (|ofCategory| *1 (|LinearlyExplicitRingOver| *5)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Record| (|:| |mat| (|Matrix| *5)) (|:| |vec| (|Vector| *5))))))) 
(|Join| (|Ring|) (CATEGORY |domain| (SIGNATURE |reducedSystem| ((|Matrix| |t#1|) (|Matrix| $))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| |t#1|)) (|:| |vec| (|Vector| |t#1|))) (|Matrix| $) (|Vector| $))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) 18) (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) 19) ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) 16) (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) 17) ((|#2| (|List| |#1|) (|List| |#2|) |#1|) 10) (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) 12))) 
(((|ListToMap| |#1| |#2|) (CATEGORY |package| (SIGNATURE |match| ((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|))) (SIGNATURE |match| (|#2| (|List| |#1|) (|List| |#2|) |#1|)) (SIGNATURE |match| ((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|)) (SIGNATURE |match| (|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|)) (SIGNATURE |match| ((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|))) (SIGNATURE |match| (|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)))) (|SetCategory|) (|Type|)) (T |ListToMap|)) 
((|match| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|List| *2)) (|isDomain| *6 (|Mapping| *2 *5)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *2 (|Type|)) (|isDomain| *1 (|ListToMap| *5 *2)))) (|match| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|Mapping| *6 *5)) (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|List| *6)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|Type|)) (|isDomain| *1 (|ListToMap| *5 *6)))) (|match| (*1 *2 *3 *4 *5 *2) (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|List| *2)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *2 (|Type|)) (|isDomain| *1 (|ListToMap| *5 *2)))) (|match| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|List| *5)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *5 (|Type|)) (|isDomain| *2 (|Mapping| *5 *6)) (|isDomain| *1 (|ListToMap| *6 *5)))) (|match| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|List| *2)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *2 (|Type|)) (|isDomain| *1 (|ListToMap| *5 *2)))) (|match| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|List| *6)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|Mapping| *6 *5)) (|isDomain| *1 (|ListToMap| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |match| ((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|))) (SIGNATURE |match| (|#2| (|List| |#1|) (|List| |#2|) |#1|)) (SIGNATURE |match| ((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|)) (SIGNATURE |match| (|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|)) (SIGNATURE |match| ((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|))) (SIGNATURE |match| (|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)))) 
((|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) 16)) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) 18)) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) 13))) 
(((|ListFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |scan| ((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|)) (SIGNATURE |map| ((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)))) (|Type|) (|Type|)) (T |ListFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|List| *5)) (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|List| *6)) (|isDomain| *1 (|ListFunctions2| *5 *6)))) (|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) (|isDomain| *4 (|List| *5)) (|ofCategory| *5 (|Type|)) (|ofCategory| *2 (|Type|)) (|isDomain| *1 (|ListFunctions2| *5 *2)))) (|scan| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *5 *6 *5)) (|isDomain| *4 (|List| *6)) (|ofCategory| *6 (|Type|)) (|ofCategory| *5 (|Type|)) (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|ListFunctions2| *6 *5))))) 
(CATEGORY |package| (SIGNATURE |scan| ((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|)) (SIGNATURE |map| ((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)))) 
((|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) 13))) 
(((|ListFunctions3| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |map| ((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)))) (|Type|) (|Type|) (|Type|)) (T |ListFunctions3|)) 
((|map| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *8 *6 *7)) (|isDomain| *4 (|List| *6)) (|isDomain| *5 (|List| *7)) (|ofCategory| *6 (|Type|)) (|ofCategory| *7 (|Type|)) (|ofCategory| *8 (|Type|)) (|isDomain| *2 (|List| *8)) (|isDomain| *1 (|ListFunctions3| *6 *7 *8))))) 
(CATEGORY |package| (SIGNATURE |map| ((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)))) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) NIL)) (|third| ((|#1| $) NIL)) (|tail| (($ $) NIL)) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|split!| (($ $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) $) NIL (|has| |#1| (|OrderedSet|))) (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) NIL)) (|sort!| (($ $) NIL (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|has| |#1| (|OrderedSet|)))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sort| (($ $) NIL (|has| |#1| (|OrderedSet|))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setvalue!| ((|#1| $ |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setrest!| (($ $ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setlast!| ((|#1| $ |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setfirst!| ((|#1| $ |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ "first" |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "rest" $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ "last" |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|Integer|) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setUnion| (($ $ $) 31 (|has| |#1| (|SetCategory|)))) (|setIntersection| (($ $ $) 33 (|has| |#1| (|SetCategory|)))) (|setDifference| (($ $ $) 36 (|has| |#1| (|SetCategory|)))) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) NIL)) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|second| ((|#1| $) NIL)) (|sample| (($) NIL T CONST)) (|reverse!| (($ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) NIL)) (|rest| (($ $) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|removeDuplicates!| (($ $) NIL (|has| |#1| (|SetCategory|)))) (|removeDuplicates| (($ $) 30 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|remove!| (($ |#1| $) NIL (|has| |#1| (|SetCategory|))) (($ (|Mapping| (|Boolean|) |#1|) $) NIL)) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|qsetelt!| ((|#1| $ (|Integer|) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#1| $ (|Integer|)) NIL)) (|possiblyInfinite?| (((|Boolean|) $) NIL)) (|position| (((|Integer|) |#1| $ (|Integer|)) NIL (|has| |#1| (|SetCategory|))) (((|Integer|) |#1| $) NIL (|has| |#1| (|SetCategory|))) (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) NIL)) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|null| (((|Boolean|) $) 9)) (|nodes| (((|List| $) $) NIL)) (|node?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|nil| (($) 7)) (|new| (($ (|NonNegativeInteger|) |#1|) NIL)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|merge!| (($ $ $) NIL (|has| |#1| (|OrderedSet|))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) NIL)) (|merge| (($ $ $) NIL (|has| |#1| (|OrderedSet|))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 32 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|maxIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL)) (|list| (($ |#1|) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|leaves| (((|List| |#1|) $) NIL)) (|leaf?| (((|Boolean|) $) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|last| ((|#1| $) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|insert!| (($ $ $ (|Integer|)) NIL) (($ |#1| $ (|Integer|)) NIL)) (|insert| (($ $ $ (|Integer|)) NIL) (($ |#1| $ (|Integer|)) NIL)) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|first| ((|#1| $) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) NIL)) (|fill!| (($ $ |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|explicitlyFinite?| (((|Boolean|) $) NIL)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|entry?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|entries| (((|List| |#1|) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#1| $ "value") NIL) ((|#1| $ "first") NIL) (($ $ "rest") NIL) ((|#1| $ "last") NIL) (($ $ (|UniversalSegment| (|Integer|))) NIL) ((|#1| $ (|Integer|)) 35) ((|#1| $ (|Integer|) |#1|) NIL)) (|distance| (((|Integer|) $ $) NIL)) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) NIL) (($ $ (|Integer|)) NIL)) (|delete| (($ $ (|UniversalSegment| (|Integer|))) NIL) (($ $ (|Integer|)) NIL)) (|cyclic?| (((|Boolean|) $) NIL)) (|cycleTail| (($ $) NIL)) (|cycleSplit!| (($ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|cycleLength| (((|NonNegativeInteger|) $) NIL)) (|cycleEntry| (($ $) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copyInto!| (($ $ $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) 44 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) NIL)) (|cons| (($ |#1| $) 10)) (|concat!| (($ $ $) NIL) (($ $ |#1|) NIL)) (|concat| (($ $ $) 29) (($ |#1| $) NIL) (($ (|List| $)) NIL) (($ $ |#1|) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|)))) (|children| (((|List| $) $) NIL)) (|child?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|append| (($ $ $) 11)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|OMwrite| (((|String|) $) 25 (|has| |#1| (|OpenMath|))) (((|String|) $ (|Boolean|)) 26 (|has| |#1| (|OpenMath|))) (((|Void|) (|OpenMathDevice|) $) 27 (|has| |#1| (|OpenMath|))) (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) 28 (|has| |#1| (|OpenMath|)))) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|List| |#1|) (|Join| (|ListAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |nil| ($)) (SIGNATURE |null| ((|Boolean|) $)) (SIGNATURE |cons| ($ |#1| $)) (SIGNATURE |append| ($ $ $)) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |setUnion| ($ $ $)) (SIGNATURE |setIntersection| ($ $ $)) (SIGNATURE |setDifference| ($ $ $))) |noBranch|) (IF (|has| |#1| (|OpenMath|)) (ATTRIBUTE (|OpenMath|)) |noBranch|))) (|Type|)) (T |List|)) 
((|nil| (*1 *1) (AND (|isDomain| *1 (|List| *2)) (|ofCategory| *2 (|Type|)))) (|null| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|List| *3)) (|ofCategory| *3 (|Type|)))) (|cons| (*1 *1 *2 *1) (AND (|isDomain| *1 (|List| *2)) (|ofCategory| *2 (|Type|)))) (|append| (*1 *1 *1 *1) (AND (|isDomain| *1 (|List| *2)) (|ofCategory| *2 (|Type|)))) (|setUnion| (*1 *1 *1 *1) (AND (|isDomain| *1 (|List| *2)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|Type|)))) (|setIntersection| (*1 *1 *1 *1) (AND (|isDomain| *1 (|List| *2)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|Type|)))) (|setDifference| (*1 *1 *1 *1) (AND (|isDomain| *1 (|List| *2)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|ListAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |nil| ($)) (SIGNATURE |null| ((|Boolean|) $)) (SIGNATURE |cons| ($ |#1| $)) (SIGNATURE |append| ($ $ $)) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |setUnion| ($ $ $)) (SIGNATURE |setIntersection| ($ $ $)) (SIGNATURE |setDifference| ($ $ $))) |noBranch|) (IF (|has| |#1| (|OpenMath|)) (ATTRIBUTE (|OpenMath|)) |noBranch|))) 
((|finiteSeries2Vector| (((|List| |#1|) |#2| (|Integer|)) 21)) (|finiteSeries2LinSysWOVectorise| (((|Matrix| |#1|) (|List| |#2|) (|Integer|)) 30)) (|finiteSeries2LinSys| (((|Matrix| |#1|) (|List| |#2|) (|Integer|)) 28))) 
(((|LinearSystemFromPowerSeriesPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |finiteSeries2LinSysWOVectorise| ((|Matrix| |#1|) (|List| |#2|) (|Integer|))) (SIGNATURE |finiteSeries2LinSys| ((|Matrix| |#1|) (|List| |#2|) (|Integer|))) (SIGNATURE |finiteSeries2Vector| ((|List| |#1|) |#2| (|Integer|)))) (|Field|) (|LocalPowerSeriesCategory| |#1|)) (T |LinearSystemFromPowerSeriesPackage|)) 
((|finiteSeries2Vector| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Integer|)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|LinearSystemFromPowerSeriesPackage| *5 *3)) (|ofCategory| *3 (|LocalPowerSeriesCategory| *5)))) (|finiteSeries2LinSys| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|Integer|)) (|ofCategory| *6 (|LocalPowerSeriesCategory| *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Matrix| *5)) (|isDomain| *1 (|LinearSystemFromPowerSeriesPackage| *5 *6)))) (|finiteSeries2LinSysWOVectorise| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|Integer|)) (|ofCategory| *6 (|LocalPowerSeriesCategory| *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Matrix| *5)) (|isDomain| *1 (|LinearSystemFromPowerSeriesPackage| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |finiteSeries2LinSysWOVectorise| ((|Matrix| |#1|) (|List| |#2|) (|Integer|))) (SIGNATURE |finiteSeries2LinSys| ((|Matrix| |#1|) (|List| |#2|) (|Integer|))) (SIGNATURE |finiteSeries2Vector| ((|List| |#1|) |#2| (|Integer|)))) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|substitute| (($ |#1| |#1| $) 43)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) 56 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) NIL T CONST)) (|removeDuplicates!| (($ $) 45)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|remove!| (($ |#1| $) 51 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) |#1|) $) 53 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remove| (($ |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|parts| (((|List| |#1|) $) 9 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 37)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|inspect| ((|#1| $) 46)) (|insert!| (($ |#1| $) 26) (($ |#1| $ (|NonNegativeInteger|)) 42)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) NIL)) (|extract!| ((|#1| $) 48)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) 21)) (|empty| (($) 25)) (|duplicates?| (((|Boolean|) $) 49)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) 60)) (|dictionary| (($) 23) (($ (|List| |#1|)) 18)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 57 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) 19)) (|convert| (((|InputForm|) $) 34 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) NIL)) (|coerce| (((|OutputForm|) $) 14 (|has| |#1| (|SetCategory|)))) (|bag| (($ (|List| |#1|)) 22)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 62 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 16 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|ListMultiDictionary| |#1|) (|Join| (|MultiDictionary| |#1|) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (SIGNATURE |duplicates?| ((|Boolean|) $)) (SIGNATURE |substitute| ($ |#1| |#1| $)))) (|SetCategory|)) (T |ListMultiDictionary|)) 
((|duplicates?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ListMultiDictionary| *3)) (|ofCategory| *3 (|SetCategory|)))) (|substitute| (*1 *1 *2 *2 *1) (AND (|isDomain| *1 (|ListMultiDictionary| *2)) (|ofCategory| *2 (|SetCategory|))))) 
(|Join| (|MultiDictionary| |#1|) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (SIGNATURE |duplicates?| ((|Boolean|) $)) (SIGNATURE |substitute| ($ |#1| |#1| $)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ |#1| $) 22))) 
(((|LeftModule| |#1|) (|Category|) (|Rng|)) (T |LeftModule|)) 
((* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|LeftModule| *2)) (|ofCategory| *2 (|Rng|))))) 
(|Join| (|AbelianGroup|) (CATEGORY |domain| (SIGNATURE * ($ |t#1| $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|size| (((|NonNegativeInteger|) $) 15)) (|rightMult| (($ $ |#1|) 55)) (|reverse!| (($ $) 32)) (|reverse| (($ $) 31)) (|retractIfCan| (((|Union| |#1| "failed") $) 47)) (|retract| ((|#1| $) NIL)) (|plus| (($ |#1| |#2| $) 60) (($ $ $) 61)) (|outputForm| (((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|)) 45)) (|nthFactor| ((|#1| $ (|Integer|)) 30)) (|nthExpon| ((|#2| $ (|Integer|)) 29)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 34)) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) 38)) (|makeUnit| (($) 10)) (|makeTerm| (($ |#1| |#2|) 22)) (|makeMulti| (($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) 23)) (|listOfMonoms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) 13)) (|leftMult| (($ |#1| $) 56)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|commutativeEquality| (((|Boolean|) $ $) 58)) (|coerce| (((|OutputForm|) $) 19) (($ |#1|) 16)) (= (((|Boolean|) $ $) 25))) 
(((|ListMonoidOps| |#1| |#2| |#3|) (|Join| (|SetCategory|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |outputForm| ((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|))) (SIGNATURE |listOfMonoms| ((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $)) (SIGNATURE |makeTerm| ($ |#1| |#2|)) (SIGNATURE |makeMulti| ($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))))) (SIGNATURE |nthExpon| (|#2| $ (|Integer|))) (SIGNATURE |nthFactor| (|#1| $ (|Integer|))) (SIGNATURE |reverse| ($ $)) (SIGNATURE |reverse!| ($ $)) (SIGNATURE |size| ((|NonNegativeInteger|) $)) (SIGNATURE |makeUnit| ($)) (SIGNATURE |rightMult| ($ $ |#1|)) (SIGNATURE |leftMult| ($ |#1| $)) (SIGNATURE |plus| ($ |#1| |#2| $)) (SIGNATURE |plus| ($ $ $)) (SIGNATURE |commutativeEquality| ((|Boolean|) $ $)) (SIGNATURE |mapExpon| ($ (|Mapping| |#2| |#2|) $)) (SIGNATURE |mapGen| ($ (|Mapping| |#1| |#1|) $)))) (|SetCategory|) (|AbelianMonoid|) |#2|) (T |ListMonoidOps|)) 
((|outputForm| (*1 *2 *1 *3 *3 *4) (AND (|isDomain| *3 (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|))) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|ListMonoidOps| *5 *6 *7)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|AbelianMonoid|)) (|ofType| *7 *6))) (|listOfMonoms| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| *4)))) (|isDomain| *1 (|ListMonoidOps| *3 *4 *5)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 *4))) (|makeTerm| (*1 *1 *2 *3) (AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 *3))) (|makeMulti| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| *4)))) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 *4) (|isDomain| *1 (|ListMonoidOps| *3 *4 *5)))) (|nthExpon| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|AbelianMonoid|)) (|isDomain| *1 (|ListMonoidOps| *4 *2 *5)) (|ofCategory| *4 (|SetCategory|)) (|ofType| *5 *2))) (|nthFactor| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|SetCategory|)) (|isDomain| *1 (|ListMonoidOps| *2 *4 *5)) (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 *4))) (|reverse| (*1 *1 *1) (AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 *3))) (|reverse!| (*1 *1 *1) (AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 *3))) (|size| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ListMonoidOps| *3 *4 *5)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 *4))) (|makeUnit| (*1 *1) (AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 *3))) (|rightMult| (*1 *1 *1 *2) (AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 *3))) (|leftMult| (*1 *1 *2 *1) (AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 *3))) (|plus| (*1 *1 *2 *3 *1) (AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 *3))) (|plus| (*1 *1 *1 *1) (AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 *3))) (|commutativeEquality| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ListMonoidOps| *3 *4 *5)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 *4))) (|mapExpon| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 *4) (|isDomain| *1 (|ListMonoidOps| *3 *4 *5)) (|ofCategory| *3 (|SetCategory|)))) (|mapGen| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|ListMonoidOps| *3 *4 *5)) (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 *4)))) 
(|Join| (|SetCategory|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |outputForm| ((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|))) (SIGNATURE |listOfMonoms| ((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $)) (SIGNATURE |makeTerm| ($ |#1| |#2|)) (SIGNATURE |makeMulti| ($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))))) (SIGNATURE |nthExpon| (|#2| $ (|Integer|))) (SIGNATURE |nthFactor| (|#1| $ (|Integer|))) (SIGNATURE |reverse| ($ $)) (SIGNATURE |reverse!| ($ $)) (SIGNATURE |size| ((|NonNegativeInteger|) $)) (SIGNATURE |makeUnit| ($)) (SIGNATURE |rightMult| ($ $ |#1|)) (SIGNATURE |leftMult| ($ |#1| $)) (SIGNATURE |plus| ($ |#1| |#2| $)) (SIGNATURE |plus| ($ $ $)) (SIGNATURE |commutativeEquality| ((|Boolean|) $ $)) (SIGNATURE |mapExpon| ($ (|Mapping| |#2| |#2|) $)) (SIGNATURE |mapGen| ($ (|Mapping| |#1| |#1|) $)))) 
((|maxIndex| (((|Integer|) $) 23)) (|insert| (($ |#2| $ (|Integer|)) 21) (($ $ $ (|Integer|)) NIL)) (|indices| (((|List| (|Integer|)) $) 12)) (|index?| (((|Boolean|) (|Integer|) $) 14)) (|concat| (($ $ |#2|) 18) (($ |#2| $) 19) (($ $ $) NIL) (($ (|List| $)) NIL))) 
(((|LinearAggregate&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |insert| (|#1| |#1| |#1| (|Integer|))) (SIGNATURE |insert| (|#1| |#2| |#1| (|Integer|))) (SIGNATURE |concat| (|#1| (|List| |#1|))) (SIGNATURE |concat| (|#1| |#1| |#1|)) (SIGNATURE |concat| (|#1| |#2| |#1|)) (SIGNATURE |concat| (|#1| |#1| |#2|)) (SIGNATURE |maxIndex| ((|Integer|) |#1|)) (SIGNATURE |indices| ((|List| (|Integer|)) |#1|)) (SIGNATURE |index?| ((|Boolean|) (|Integer|) |#1|))) (|LinearAggregate| |#2|) (|Type|)) (T |LinearAggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |insert| (|#1| |#1| |#1| (|Integer|))) (SIGNATURE |insert| (|#1| |#2| |#1| (|Integer|))) (SIGNATURE |concat| (|#1| (|List| |#1|))) (SIGNATURE |concat| (|#1| |#1| |#1|)) (SIGNATURE |concat| (|#1| |#2| |#1|)) (SIGNATURE |concat| (|#1| |#1| |#2|)) (SIGNATURE |maxIndex| ((|Integer|) |#1|)) (SIGNATURE |indices| ((|List| (|Integer|)) |#1|)) (SIGNATURE |index?| ((|Boolean|) (|Integer|) |#1|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setelt| ((|#1| $ (|Integer|) |#1|) 49 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) 53 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 70 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) 7 T CONST)) (|removeDuplicates| (($ $) 73 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove| (($ |#1| $) 72 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#1|) $) 69 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 71 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 68 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 67 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| ((|#1| $ (|Integer|) |#1|) 50 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#1| $ (|Integer|)) 48)) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|new| (($ (|NonNegativeInteger|) |#1|) 64)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|minIndex| (((|Integer|) $) 40 (|has| (|Integer|) (|OrderedSet|)))) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|maxIndex| (((|Integer|) $) 41 (|has| (|Integer|) (|OrderedSet|)))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35) (($ (|Mapping| |#1| |#1| |#1|) $ $) 59)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|insert| (($ |#1| $ (|Integer|)) 55) (($ $ $ (|Integer|)) 54)) (|indices| (((|List| (|Integer|)) $) 43)) (|index?| (((|Boolean|) (|Integer|) $) 44)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|first| ((|#1| $) 39 (|has| (|Integer|) (|OrderedSet|)))) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) 66)) (|fill!| (($ $ |#1|) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|entry?| (((|Boolean|) |#1| $) 42 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|entries| (((|List| |#1|) $) 45)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| ((|#1| $ (|Integer|) |#1|) 47) ((|#1| $ (|Integer|)) 46) (($ $ (|UniversalSegment| (|Integer|))) 58)) (|delete| (($ $ (|Integer|)) 57) (($ $ (|UniversalSegment| (|Integer|))) 56)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|convert| (((|InputForm|) $) 74 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 65)) (|concat| (($ $ |#1|) 63) (($ |#1| $) 62) (($ $ $) 61) (($ (|List| $)) 60)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|LinearAggregate| |#1|) (|Category|) (|Type|)) (T |LinearAggregate|)) 
((|new| (*1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|concat| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|concat| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|concat| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|concat| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|map| (*1 *1 *2 *1 *1) (AND (|isDomain| *2 (|Mapping| *3 *3 *3)) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|elt| (*1 *1 *1 *2) (AND (|isDomain| *2 (|UniversalSegment| (|Integer|))) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|delete| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|delete| (*1 *1 *1 *2) (AND (|isDomain| *2 (|UniversalSegment| (|Integer|))) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|insert| (*1 *1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|insert| (*1 *1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|setelt| (*1 *2 *1 *3 *2) (AND (|isDomain| *3 (|UniversalSegment| (|Integer|))) (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|IndexedAggregate| (|Integer|) |t#1|) (|Collection| |t#1|) (CATEGORY |domain| (SIGNATURE |new| ($ (|NonNegativeInteger|) |t#1|)) (SIGNATURE |concat| ($ $ |t#1|)) (SIGNATURE |concat| ($ |t#1| $)) (SIGNATURE |concat| ($ $ $)) (SIGNATURE |concat| ($ (|List| $))) (SIGNATURE |map| ($ (|Mapping| |t#1| |t#1| |t#1|) $ $)) (SIGNATURE |elt| ($ $ (|UniversalSegment| (|Integer|)))) (SIGNATURE |delete| ($ $ (|Integer|))) (SIGNATURE |delete| ($ $ (|UniversalSegment| (|Integer|)))) (SIGNATURE |insert| ($ |t#1| $ (|Integer|))) (SIGNATURE |insert| ($ $ $ (|Integer|))) (IF (|has| $ (ATTRIBUTE |shallowlyMutable|)) (SIGNATURE |setelt| (|t#1| $ (|UniversalSegment| (|Integer|)) |t#1|)) |noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| (|Integer|) |#1|) . T) ((|EltableAggregate| (|Integer|) |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| (|Integer|) |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) 117)) (|variable| (((|Symbol|) $) 122)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|truncate| (($ $ (|Integer|) (|Integer|)) 128) (($ $ (|Integer|)) 127)) (|terms| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) 120)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 73)) (|squareFree| (((|Factored| $) $) 72)) (|sizeLess?| (((|Boolean|) $ $) 58)) (|shift| (($ $ (|Integer|)) 88)) (|series| (($ (|Integer|) |#1| $) 89)) (|sbt| (($ $ $) 94)) (|sample| (($) 16 T CONST)) (|removeZeroes| (($ (|Integer|) $) 91) (($ $) 90)) (|removeFirstZeroes| (($ $) 95)) (|rem| (($ $ $) 54)) (|reductum| (($ $) 110)) (|recip| (((|Union| $ "failed") $) 33)) (|quo| (($ $ $) 55)) (|printInfo| (((|Boolean|) (|Boolean|)) 85) (((|Boolean|)) 84)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 50)) (|prime?| (((|Boolean|) $) 71)) (|posExpnPart| (($ $) 97)) (|pole?| (((|Boolean|) $) 118)) (|orderIfNegative| (((|Union| (|Integer|) "failed") $) 96)) (|order| (((|Integer|) $ (|Integer|)) 126) (((|Integer|) $) 125) (((|Integer|) $) 101)) (|one?| (((|Boolean|) $) 30)) (|multiplyExponents| (($ $ (|PositiveInteger|)) 124)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 51)) (|monomial?| (((|Boolean|) $) 108)) (|monomial2series| (($ (|List| $) (|List| (|NonNegativeInteger|)) (|Integer|)) 92)) (|monomial| (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|Integer|))) 116) (($ $ (|SingletonAsOrderedSet|) (|Integer|)) 115) (($ |#1| (|Integer|)) 109)) (|map| (($ (|Mapping| |#1| |#1|) $) 107)) (|leadingMonomial| (($ $) 105)) (|leadingCoefficient| ((|#1| $) 104)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 70)) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|findCoef| ((|#1| $ (|Integer|)) 100)) (|filterUpTo| (($ $ (|Integer|)) 87)) (|factor| (((|Factored| $) $) 74)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 53) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 52)) (|extend| (($ $ (|Integer|)) 130)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 49)) (|eval| (((|Stream| |#1|) $ |#1|) 131 (|has| |#1| (SIGNATURE ** (|#1| |#1| (|Integer|)))))) (|euclideanSize| (((|NonNegativeInteger|) $) 57)) (|elt| (($ $ $) 144 (|has| (|Integer|) (|SemiGroup|))) ((|#1| $ (|Integer|)) 121)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 56)) (|differentiate| (($ $) 143 (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) (($ $ (|NonNegativeInteger|)) 141 (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) (($ $ (|Symbol|)) 139 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) (($ $ (|List| (|Symbol|))) 138 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 137 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 136 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))))) (|delay| (($ (|Mapping| $)) 93)) (|degree| (((|Integer|) $) 106)) (|complete| (($ $) 119)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42) (($ (|Fraction| (|Integer|))) 65) (($ |#1|) 114 (|has| |#1| (|CommutativeRing|))) (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) 99) (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) 98)) (|coefficient| ((|#1| $ (|Integer|)) 111)) (|coefOfFirstNonZeroTerm| ((|#1| $) 86)) (|charthRoot| (((|Union| $ "failed") $) 113 (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|center| ((|#1| $) 123)) (|associates?| (((|Boolean|) $ $) 38)) (|approximate| ((|#1| $ (|Integer|)) 129 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| (|Integer|)))) (|has| |#1| (SIGNATURE |coerce| (|#1| (|Symbol|))))))) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 69)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $) 142 (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) (($ $ (|NonNegativeInteger|)) 140 (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) (($ $ (|Symbol|)) 135 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) (($ $ (|List| (|Symbol|))) 134 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 133 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 132 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))))) (= (((|Boolean|) $ $) 6)) (/ (($ $ $) 64) (($ $ |#1|) 112 (|has| |#1| (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 68)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ (|Fraction| (|Integer|))) 67) (($ (|Fraction| (|Integer|)) $) 66) (($ |#1| $) 103) (($ $ |#1|) 102))) 
(((|LocalPowerSeriesCategory| |#1|) (|Category|) (|Field|)) (T |LocalPowerSeriesCategory|)) 
((|order| (*1 *2 *1) (AND (|ofCategory| *1 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Integer|)))) (|order| (*1 *2 *1) (AND (|ofCategory| *1 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Integer|)))) (|findCoef| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|LocalPowerSeriesCategory| *2)) (|ofCategory| *2 (|Field|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| *3)))) (|ofCategory| *3 (|Field|)) (|ofCategory| *1 (|LocalPowerSeriesCategory| *3)))) (|coerce| (*1 *2 *1) (AND (|ofCategory| *1 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| *3)))))) (|posExpnPart| (*1 *1 *1) (AND (|ofCategory| *1 (|LocalPowerSeriesCategory| *2)) (|ofCategory| *2 (|Field|)))) (|orderIfNegative| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Integer|)))) (|removeFirstZeroes| (*1 *1 *1) (AND (|ofCategory| *1 (|LocalPowerSeriesCategory| *2)) (|ofCategory| *2 (|Field|)))) (|sbt| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|LocalPowerSeriesCategory| *2)) (|ofCategory| *2 (|Field|)))) (|delay| (*1 *1 *2) (AND (|isDomain| *2 (|Mapping| *1)) (|ofCategory| *1 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *3 (|Field|)))) (|monomial2series| (*1 *1 *2 *3 *4) (AND (|isDomain| *2 (|List| *1)) (|isDomain| *3 (|List| (|NonNegativeInteger|))) (|isDomain| *4 (|Integer|)) (|ofCategory| *1 (|LocalPowerSeriesCategory| *5)) (|ofCategory| *5 (|Field|)))) (|removeZeroes| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *3 (|Field|)))) (|removeZeroes| (*1 *1 *1) (AND (|ofCategory| *1 (|LocalPowerSeriesCategory| *2)) (|ofCategory| *2 (|Field|)))) (|series| (*1 *1 *2 *3 *1) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *3 (|Field|)))) (|shift| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *3 (|Field|)))) (|filterUpTo| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *3 (|Field|)))) (|coefOfFirstNonZeroTerm| (*1 *2 *1) (AND (|ofCategory| *1 (|LocalPowerSeriesCategory| *2)) (|ofCategory| *2 (|Field|)))) (|printInfo| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|ofCategory| *1 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *3 (|Field|)))) (|printInfo| (*1 *2) (AND (|ofCategory| *1 (|LocalPowerSeriesCategory| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Boolean|))))) 
(|Join| (|Field|) (|UnivariatePowerSeriesCategory| |t#1| (|Integer|)) (CATEGORY |domain| (SIGNATURE |order| ((|Integer|) $)) (SIGNATURE |findCoef| (|t#1| $ (|Integer|))) (SIGNATURE |coerce| ($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |t#1|))))) (SIGNATURE |coerce| ((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |t#1|))) $)) (SIGNATURE |posExpnPart| ($ $)) (SIGNATURE |orderIfNegative| ((|Union| (|Integer|) "failed") $)) (SIGNATURE |removeFirstZeroes| ($ $)) (SIGNATURE |sbt| ($ $ $)) (SIGNATURE |delay| ($ (|Mapping| $))) (SIGNATURE |monomial2series| ($ (|List| $) (|List| (|NonNegativeInteger|)) (|Integer|))) (SIGNATURE |removeZeroes| ($ (|Integer|) $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |series| ($ (|Integer|) |t#1| $)) (SIGNATURE |shift| ($ $ (|Integer|))) (SIGNATURE |filterUpTo| ($ $ (|Integer|))) (SIGNATURE |coefOfFirstNonZeroTerm| (|t#1| $)) (SIGNATURE |printInfo| ((|Boolean|) (|Boolean|))) (SIGNATURE |printInfo| ((|Boolean|))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| (|Integer|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) . T) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) . T) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) ((|DivisionRing|) . T) ((|Eltable| $ $) |has| (|Integer|) (|SemiGroup|)) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| (|Fraction| (|Integer|))) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| (|Fraction| (|Integer|))) . T) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) . T) ((|Monoid|) . T) ((|PartialDifferentialRing| (|Symbol|)) AND (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PowerSeriesCategory| |#1| (|Integer|) (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) . T) ((|RightModule| (|Fraction| (|Integer|))) . T) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|UniqueFactorizationDomain|) . T) ((|UnivariatePowerSeriesCategory| |#1| (|Integer|)) . T)) 
((|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) 159) (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) 43))) 
(((|ElementaryFunctionLODESolver| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|))) (SIGNATURE |solve| ((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)))) (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|)) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|)) (|LinearOrdinaryDifferentialOperatorCategory| |#2|)) (T |ElementaryFunctionLODESolver|)) 
((|solve| (*1 *2 *3 *2 *4 *2 *5) (|partial| AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|List| *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedFunctionSpace| *6) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (|ofCategory| *6 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *1 (|ElementaryFunctionLODESolver| *6 *2 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2)))) (|solve| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *5 (|Symbol|)) (|ofCategory| *6 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|ofCategory| *4 (|Join| (|AlgebraicallyClosedFunctionSpace| *6) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (|isDomain| *2 (|Record| (|:| |particular| *4) (|:| |basis| (|List| *4)))) (|isDomain| *1 (|ElementaryFunctionLODESolver| *6 *4 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|))) (SIGNATURE |solve| ((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|symmetricSquare| (($ $) NIL (|has| |#1| (|Field|)))) (|symmetricProduct| (($ $ $) NIL (|has| |#1| (|Field|)))) (|symmetricPower| (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Field|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|rightRemainder| (($ $ $) NIL (|has| |#1| (|Field|)))) (|rightQuotient| (($ $ $) NIL (|has| |#1| (|Field|)))) (|rightLcm| (($ $ $) NIL (|has| |#1| (|Field|)))) (|rightGcd| (($ $ $) NIL (|has| |#1| (|Field|)))) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|rightExactQuotient| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|Field|)))) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|Field|)))) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) NIL)) (|retract| (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) NIL)) (|reductum| (($ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|primitivePart| (($ $) NIL (|has| |#1| (|GcdDomain|)))) (|one?| (((|Boolean|) $) NIL)) (|monomial| (($ |#1| (|NonNegativeInteger|)) NIL)) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|minimumDegree| (((|NonNegativeInteger|) $) NIL)) (|leftRemainder| (($ $ $) NIL (|has| |#1| (|Field|)))) (|leftQuotient| (($ $ $) NIL (|has| |#1| (|Field|)))) (|leftLcm| (($ $ $) NIL (|has| |#1| (|Field|)))) (|leftGcd| (($ $ $) NIL (|has| |#1| (|Field|)))) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|leftExactQuotient| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|Field|)))) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|Field|)))) (|leadingCoefficient| ((|#1| $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|exquo| (((|Union| $ "failed") $ |#1|) NIL (|has| |#1| (|IntegralDomain|)))) (|elt| ((|#1| $ |#1|) NIL)) (|directSum| (($ $ $) NIL (|has| |#1| (|Field|)))) (|degree| (((|NonNegativeInteger|) $) NIL)) (|content| ((|#1| $) NIL (|has| |#1| (|GcdDomain|)))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ (|Fraction| (|Integer|))) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (($ |#1|) NIL)) (|coefficients| (((|List| |#1|) $) NIL)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|apply| ((|#1| $ |#1| |#1|) NIL)) (|adjoint| (($ $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($) NIL)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ |#1|) NIL) (($ |#1| $) NIL))) 
(((|LinearOrdinaryDifferentialOperator1| |#1|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|DifferentialRing|)) (T |LinearOrdinaryDifferentialOperator1|)) 
NIL 
(|LinearOrdinaryDifferentialOperatorCategory| |#1|) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|symmetricSquare| (($ $) NIL (|has| |#1| (|Field|)))) (|symmetricProduct| (($ $ $) NIL (|has| |#1| (|Field|)))) (|symmetricPower| (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Field|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|rightRemainder| (($ $ $) NIL (|has| |#1| (|Field|)))) (|rightQuotient| (($ $ $) NIL (|has| |#1| (|Field|)))) (|rightLcm| (($ $ $) NIL (|has| |#1| (|Field|)))) (|rightGcd| (($ $ $) NIL (|has| |#1| (|Field|)))) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|rightExactQuotient| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|Field|)))) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|Field|)))) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) NIL)) (|retract| (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) NIL)) (|reductum| (($ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|primitivePart| (($ $) NIL (|has| |#1| (|GcdDomain|)))) (|one?| (((|Boolean|) $) NIL)) (|monomial| (($ |#1| (|NonNegativeInteger|)) NIL)) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|minimumDegree| (((|NonNegativeInteger|) $) NIL)) (|leftRemainder| (($ $ $) NIL (|has| |#1| (|Field|)))) (|leftQuotient| (($ $ $) NIL (|has| |#1| (|Field|)))) (|leftLcm| (($ $ $) NIL (|has| |#1| (|Field|)))) (|leftGcd| (($ $ $) NIL (|has| |#1| (|Field|)))) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|leftExactQuotient| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|Field|)))) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|Field|)))) (|leadingCoefficient| ((|#1| $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|exquo| (((|Union| $ "failed") $ |#1|) NIL (|has| |#1| (|IntegralDomain|)))) (|elt| ((|#1| $ |#1|) NIL) ((|#2| $ |#2|) 13)) (|directSum| (($ $ $) NIL (|has| |#1| (|Field|)))) (|degree| (((|NonNegativeInteger|) $) NIL)) (|content| ((|#1| $) NIL (|has| |#1| (|GcdDomain|)))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ (|Fraction| (|Integer|))) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (($ |#1|) NIL)) (|coefficients| (((|List| |#1|) $) NIL)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|apply| ((|#1| $ |#1| |#1|) NIL)) (|adjoint| (($ $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($) NIL)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ |#1|) NIL) (($ |#1| $) NIL))) 
(((|LinearOrdinaryDifferentialOperator2| |#1| |#2|) (|Join| (|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|Eltable| |#2| |#2|)) (|DifferentialRing|) (|Join| (|LeftModule| |#1|) (CATEGORY |domain| (SIGNATURE |differentiate| ($ $))))) (T |LinearOrdinaryDifferentialOperator2|)) 
NIL 
(|Join| (|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|Eltable| |#2| |#2|)) 
((|symmetricSquare| (($ $) 26)) (|adjoint| (($ $) 24)) (D (($) 12))) 
(((|LinearOrdinaryDifferentialOperatorCategory&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |symmetricSquare| (|#1| |#1|)) (SIGNATURE |adjoint| (|#1| |#1|)) (SIGNATURE D (|#1|))) (|LinearOrdinaryDifferentialOperatorCategory| |#2|) (|Ring|)) (T |LinearOrdinaryDifferentialOperatorCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |symmetricSquare| (|#1| |#1|)) (SIGNATURE |adjoint| (|#1| |#1|)) (SIGNATURE D (|#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|symmetricSquare| (($ $) 79 (|has| |#1| (|Field|)))) (|symmetricProduct| (($ $ $) 81 (|has| |#1| (|Field|)))) (|symmetricPower| (($ $ (|NonNegativeInteger|)) 80 (|has| |#1| (|Field|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|rightRemainder| (($ $ $) 44 (|has| |#1| (|Field|)))) (|rightQuotient| (($ $ $) 45 (|has| |#1| (|Field|)))) (|rightLcm| (($ $ $) 47 (|has| |#1| (|Field|)))) (|rightGcd| (($ $ $) 42 (|has| |#1| (|Field|)))) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 41 (|has| |#1| (|Field|)))) (|rightExactQuotient| (((|Union| $ "failed") $ $) 43 (|has| |#1| (|Field|)))) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 46 (|has| |#1| (|Field|)))) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 73 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) 71 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) 68)) (|retract| (((|Integer|) $) 74 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) 72 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) 67)) (|reductum| (($ $) 63)) (|recip| (((|Union| $ "failed") $) 33)) (|primitivePart| (($ $) 54 (|has| |#1| (|GcdDomain|)))) (|one?| (((|Boolean|) $) 30)) (|monomial| (($ |#1| (|NonNegativeInteger|)) 61)) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 56 (|has| |#1| (|IntegralDomain|)))) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 57 (|has| |#1| (|IntegralDomain|)))) (|minimumDegree| (((|NonNegativeInteger|) $) 65)) (|leftRemainder| (($ $ $) 51 (|has| |#1| (|Field|)))) (|leftQuotient| (($ $ $) 52 (|has| |#1| (|Field|)))) (|leftLcm| (($ $ $) 40 (|has| |#1| (|Field|)))) (|leftGcd| (($ $ $) 49 (|has| |#1| (|Field|)))) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 48 (|has| |#1| (|Field|)))) (|leftExactQuotient| (((|Union| $ "failed") $ $) 50 (|has| |#1| (|Field|)))) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 53 (|has| |#1| (|Field|)))) (|leadingCoefficient| ((|#1| $) 64)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|exquo| (((|Union| $ "failed") $ |#1|) 58 (|has| |#1| (|IntegralDomain|)))) (|elt| ((|#1| $ |#1|) 84)) (|directSum| (($ $ $) 78 (|has| |#1| (|Field|)))) (|degree| (((|NonNegativeInteger|) $) 66)) (|content| ((|#1| $) 55 (|has| |#1| (|GcdDomain|)))) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ (|Fraction| (|Integer|))) 70 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (($ |#1|) 69)) (|coefficients| (((|List| |#1|) $) 60)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) 62)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|apply| ((|#1| $ |#1| |#1|) 59)) (|adjoint| (($ $) 82)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($) 83)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 76) (($ |#1| $) 75))) 
(((|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|Category|) (|Ring|)) (T |LinearOrdinaryDifferentialOperatorCategory|)) 
((D (*1 *1) (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|adjoint| (*1 *1 *1) (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|symmetricProduct| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|symmetricPower| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|Field|)))) (|symmetricSquare| (*1 *1 *1) (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|directSum| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) 
(|Join| (|UnivariateSkewPolynomialCategory| |t#1|) (|Eltable| |t#1| |t#1|) (CATEGORY |domain| (SIGNATURE D ($)) (SIGNATURE |adjoint| ($ $)) (IF (|has| |t#1| (|Field|)) (PROGN (SIGNATURE |symmetricProduct| ($ $ $)) (SIGNATURE |symmetricPower| ($ $ (|NonNegativeInteger|))) (SIGNATURE |symmetricSquare| ($ $)) (SIGNATURE |directSum| ($ $ $))) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Eltable| |#1| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|UnivariateSkewPolynomialCategory| |#1|) . T)) 
((|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) 72 (|has| |#1| (|AlgebraicallyClosedField|)))) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) 71 (|has| |#1| (|AlgebraicallyClosedField|))) (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) 15))) 
(((|LinearOrdinaryDifferentialOperatorFactorizer| |#1| |#2|) (CATEGORY |package| (SIGNATURE |factor| ((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|))) (IF (|has| |#1| (|AlgebraicallyClosedField|)) (PROGN (SIGNATURE |factor| ((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)))) (SIGNATURE |factor1| ((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))))) |noBranch|)) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|)))) (|UnivariatePolynomialCategory| |#1|)) (T |LinearOrdinaryDifferentialOperatorFactorizer|)) 
((|factor1| (*1 *2 *3) (AND (|ofCategory| *4 (|AlgebraicallyClosedField|)) (|ofCategory| *4 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| *5)))) (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorFactorizer| *4 *5)) (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| (|Fraction| *5))))) (|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|AlgebraicallyClosedField|)) (|ofCategory| *4 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| *5)))) (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorFactorizer| *4 *5)) (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| (|Fraction| *5))))) (|factor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| (|List| *5) *6)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| *6)))) (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorFactorizer| *5 *6)) (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| (|Fraction| *6)))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|))) (IF (|has| |#1| (|AlgebraicallyClosedField|)) (PROGN (SIGNATURE |factor| ((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)))) (SIGNATURE |factor1| ((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))))) |noBranch|)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|symmetricSquare| (($ $) NIL (|has| |#1| (|Field|)))) (|symmetricProduct| (($ $ $) 28 (|has| |#1| (|Field|)))) (|symmetricPower| (($ $ (|NonNegativeInteger|)) 31 (|has| |#1| (|Field|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|rightRemainder| (($ $ $) NIL (|has| |#1| (|Field|)))) (|rightQuotient| (($ $ $) NIL (|has| |#1| (|Field|)))) (|rightLcm| (($ $ $) NIL (|has| |#1| (|Field|)))) (|rightGcd| (($ $ $) NIL (|has| |#1| (|Field|)))) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|rightExactQuotient| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|Field|)))) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|Field|)))) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) NIL)) (|retract| (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) NIL)) (|reductum| (($ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|primitivePart| (($ $) NIL (|has| |#1| (|GcdDomain|)))) (|one?| (((|Boolean|) $) NIL)) (|monomial| (($ |#1| (|NonNegativeInteger|)) NIL)) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|minimumDegree| (((|NonNegativeInteger|) $) NIL)) (|leftRemainder| (($ $ $) NIL (|has| |#1| (|Field|)))) (|leftQuotient| (($ $ $) NIL (|has| |#1| (|Field|)))) (|leftLcm| (($ $ $) NIL (|has| |#1| (|Field|)))) (|leftGcd| (($ $ $) NIL (|has| |#1| (|Field|)))) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|leftExactQuotient| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|Field|)))) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|Field|)))) (|leadingCoefficient| ((|#1| $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|exquo| (((|Union| $ "failed") $ |#1|) NIL (|has| |#1| (|IntegralDomain|)))) (|elt| ((|#1| $ |#1|) 24)) (|directSum| (($ $ $) 33 (|has| |#1| (|Field|)))) (|degree| (((|NonNegativeInteger|) $) NIL)) (|content| ((|#1| $) NIL (|has| |#1| (|GcdDomain|)))) (|coerce| (((|OutputForm|) $) 20) (($ (|Integer|)) NIL) (($ (|Fraction| (|Integer|))) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (($ |#1|) NIL)) (|coefficients| (((|List| |#1|) $) NIL)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|apply| ((|#1| $ |#1| |#1|) 23)) (|adjoint| (($ $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 21 T CONST)) (|One| (($) 8 T CONST)) (D (($) NIL)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ |#1|) NIL) (($ |#1| $) NIL))) 
(((|LinearOrdinaryDifferentialOperator| |#1| |#2|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|Ring|) (|Mapping| |#1| |#1|)) (T |LinearOrdinaryDifferentialOperator|)) 
NIL 
(|LinearOrdinaryDifferentialOperatorCategory| |#1|) 
((|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) 61)) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) 42)) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) 63))) 
(((|LinearOrdinaryDifferentialOperatorsOps| |#1| |#2|) (CATEGORY |package| (SIGNATURE |symmetricProduct| (|#2| |#2| |#2| (|Mapping| |#1| |#1|))) (SIGNATURE |symmetricPower| (|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|))) (SIGNATURE |directSum| (|#2| |#2| |#2| (|Mapping| |#1| |#1|)))) (|Field|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|)) (T |LinearOrdinaryDifferentialOperatorsOps|)) 
((|directSum| (*1 *2 *2 *2 *3) (AND (|isDomain| *3 (|Mapping| *4 *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorsOps| *4 *2)) (|ofCategory| *2 (|LinearOrdinaryDifferentialOperatorCategory| *4)))) (|symmetricPower| (*1 *2 *2 *3 *4) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|Mapping| *5 *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorsOps| *5 *2)) (|ofCategory| *2 (|LinearOrdinaryDifferentialOperatorCategory| *5)))) (|symmetricProduct| (*1 *2 *2 *2 *3) (AND (|isDomain| *3 (|Mapping| *4 *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorsOps| *4 *2)) (|ofCategory| *2 (|LinearOrdinaryDifferentialOperatorCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |symmetricProduct| (|#2| |#2| |#2| (|Mapping| |#1| |#1|))) (SIGNATURE |symmetricPower| (|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|))) (SIGNATURE |directSum| (|#2| |#2| |#2| (|Mapping| |#1| |#1|)))) 
((|\\/| (($ $ $) 9))) 
(((|Logic&| |#1|) (CATEGORY |domain| (SIGNATURE |\\/| (|#1| |#1| |#1|))) (|Logic|)) (T |Logic&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |\\/| (|#1| |#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (~ (($ $) 10)) (|\\/| (($ $ $) 8)) (= (((|Boolean|) $ $) 6)) (|/\\| (($ $ $) 9))) 
(((|Logic|) (|Category|)) (T |Logic|)) 
((~ (*1 *1 *1) (|ofCategory| *1 (|Logic|))) (|/\\| (*1 *1 *1 *1) (|ofCategory| *1 (|Logic|))) (|\\/| (*1 *1 *1 *1) (|ofCategory| *1 (|Logic|)))) 
(|Join| (|BasicType|) (CATEGORY |domain| (SIGNATURE ~ ($ $)) (SIGNATURE |/\\| ($ $ $)) (SIGNATURE |\\/| ($ $ $)))) 
(((|BasicType|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|numer| ((|#1| $) 21)) (|min| (($ $ $) NIL (|has| |#1| (|OrderedAbelianGroup|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedAbelianGroup|)))) (|latex| (((|String|) $) 46)) (|hash| (((|SingleInteger|) $) NIL)) (|denom| ((|#3| $) 22)) (|coerce| (((|OutputForm|) $) 42)) (|Zero| (($) 10 T CONST)) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedAbelianGroup|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedAbelianGroup|)))) (= (((|Boolean|) $ $) 20)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedAbelianGroup|)))) (< (((|Boolean|) $ $) 24 (|has| |#1| (|OrderedAbelianGroup|)))) (/ (($ $ |#3|) 34) (($ |#1| |#3|) 35)) (- (($ $) 17) (($ $ $) NIL)) (+ (($ $ $) 27)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 30) (($ |#2| $) 32) (($ $ |#2|) NIL))) 
(((|Localize| |#1| |#2| |#3|) (|Join| (|Module| |#2|) (CATEGORY |domain| (IF (|has| |#1| (|OrderedAbelianGroup|)) (ATTRIBUTE (|OrderedAbelianGroup|)) |noBranch|) (SIGNATURE / ($ $ |#3|)) (SIGNATURE / ($ |#1| |#3|)) (SIGNATURE |numer| (|#1| $)) (SIGNATURE |denom| (|#3| $)))) (|Module| |#2|) (|CommutativeRing|) (|SubsetCategory| (|Monoid|) |#2|)) (T |Localize|)) 
((/ (*1 *1 *1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *1 (|Localize| *3 *4 *2)) (|ofCategory| *3 (|Module| *4)) (|ofCategory| *2 (|SubsetCategory| (|Monoid|) *4)))) (/ (*1 *1 *2 *3) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *1 (|Localize| *2 *4 *3)) (|ofCategory| *2 (|Module| *4)) (|ofCategory| *3 (|SubsetCategory| (|Monoid|) *4)))) (|numer| (*1 *2 *1) (AND (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *2 (|Module| *3)) (|isDomain| *1 (|Localize| *2 *3 *4)) (|ofCategory| *4 (|SubsetCategory| (|Monoid|) *3)))) (|denom| (*1 *2 *1) (AND (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *2 (|SubsetCategory| (|Monoid|) *4)) (|isDomain| *1 (|Localize| *3 *4 *2)) (|ofCategory| *3 (|Module| *4))))) 
(|Join| (|Module| |#2|) (CATEGORY |domain| (IF (|has| |#1| (|OrderedAbelianGroup|)) (ATTRIBUTE (|OrderedAbelianGroup|)) |noBranch|) (SIGNATURE / ($ $ |#3|)) (SIGNATURE / ($ |#1| |#3|)) (SIGNATURE |numer| (|#1| $)) (SIGNATURE |denom| (|#3| $)))) 
((|rowEchWoZeroLinesWOVectorise| (((|Matrix| |#1|) (|Matrix| |#1|)) 27)) (|rowEchWoZeroLines| (((|Matrix| |#1|) (|Matrix| |#1|)) 26)) (|reduceRowOnList| (((|List| (|List| |#1|)) (|List| |#1|) (|List| (|List| |#1|))) 44)) (|reduceRow| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) 29)) (|reduceLineOverLine| (((|List| |#1|) (|List| |#1|) (|List| |#1|) |#1|) 43)) (|quotVecSpaceBasis| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| |#1|))) 34))) 
(((|LinesOpPack| |#1|) (CATEGORY |package| (SIGNATURE |rowEchWoZeroLinesWOVectorise| ((|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |rowEchWoZeroLines| ((|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |reduceRow| ((|List| (|List| |#1|)) (|List| (|List| |#1|)))) (SIGNATURE |quotVecSpaceBasis| ((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| |#1|)))) (SIGNATURE |reduceLineOverLine| ((|List| |#1|) (|List| |#1|) (|List| |#1|) |#1|)) (SIGNATURE |reduceRowOnList| ((|List| (|List| |#1|)) (|List| |#1|) (|List| (|List| |#1|))))) (|Field|)) (T |LinesOpPack|)) 
((|reduceRowOnList| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| (|List| *4))) (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *1 (|LinesOpPack| *4)))) (|reduceLineOverLine| (*1 *2 *2 *2 *3) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|LinesOpPack| *3)))) (|quotVecSpaceBasis| (*1 *2 *2 *2) (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|LinesOpPack| *3)))) (|reduceRow| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|LinesOpPack| *3)))) (|rowEchWoZeroLines| (*1 *2 *2) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|LinesOpPack| *3)))) (|rowEchWoZeroLinesWOVectorise| (*1 *2 *2) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|LinesOpPack| *3))))) 
(CATEGORY |package| (SIGNATURE |rowEchWoZeroLinesWOVectorise| ((|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |rowEchWoZeroLines| ((|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |reduceRow| ((|List| (|List| |#1|)) (|List| (|List| |#1|)))) (SIGNATURE |quotVecSpaceBasis| ((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| |#1|)))) (SIGNATURE |reduceLineOverLine| ((|List| |#1|) (|List| |#1|) (|List| |#1|) |#1|)) (SIGNATURE |reduceRowOnList| ((|List| (|List| |#1|)) (|List| |#1|) (|List| (|List| |#1|))))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 35)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|LeftOreRing|) (|Category|)) (T |LeftOreRing|)) 
((|lcmCoef| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |llcmres| *1) (|:| |coeff1| *1) (|:| |coeff2| *1))) (|ofCategory| *1 (|LeftOreRing|))))) 
(|Join| (|EntireRing|) (CATEGORY |domain| (SIGNATURE |lcmCoef| ((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|EntireRing|) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|printInfo| (((|Boolean|)) 46) (((|Boolean|) (|Boolean|)) 47)) (|pointToPlace| ((|#7| |#5| |#3|) 44)) (|pointDominateBy| ((|#5| |#7|) 29)) (|localize| (((|Record| (|:| |fnc| |#3|) (|:| |crv| |#3|) (|:| |chart| (|List| (|Integer|)))) |#3| |#5| |#3| (|Integer|)) 99)) (|localParamOfSimplePt| (((|List| |#6|) |#5| |#3| (|Integer|)) 35))) 
(((|LocalParametrizationOfSimplePointPackage| |#1| |#2| |#3| |#4| |#5| |#6| |#7|) (CATEGORY |package| (SIGNATURE |printInfo| ((|Boolean|) (|Boolean|))) (SIGNATURE |printInfo| ((|Boolean|))) (SIGNATURE |pointToPlace| (|#7| |#5| |#3|)) (SIGNATURE |localParamOfSimplePt| ((|List| |#6|) |#5| |#3| (|Integer|))) (SIGNATURE |pointDominateBy| (|#5| |#7|)) (SIGNATURE |localize| ((|Record| (|:| |fnc| |#3|) (|:| |crv| |#3|) (|:| |chart| (|List| (|Integer|)))) |#3| |#5| |#3| (|Integer|)))) (|Field|) (|List| (|Symbol|)) (|PolynomialCategory| |#1| |#4| (|OrderedVariableList| |#2|)) (|DirectProductCategory| (|#| |#2|) (|NonNegativeInteger|)) (|ProjectiveSpaceCategory| |#1|) (|LocalPowerSeriesCategory| |#1|) (|PlacesCategory| |#1| |#6|)) (T |LocalParametrizationOfSimplePointPackage|)) 
((|localize| (*1 *2 *3 *4 *3 *5) (AND (|ofCategory| *6 (|Field|)) (|ofType| *7 (|List| (|Symbol|))) (|ofCategory| *8 (|DirectProductCategory| (|#| *7) (|NonNegativeInteger|))) (|ofCategory| *9 (|LocalPowerSeriesCategory| *6)) (|isDomain| *2 (|Record| (|:| |fnc| *3) (|:| |crv| *3) (|:| |chart| (|List| (|Integer|))))) (|isDomain| *1 (|LocalParametrizationOfSimplePointPackage| *6 *7 *3 *8 *4 *9 *10)) (|isDomain| *5 (|Integer|)) (|ofCategory| *3 (|PolynomialCategory| *6 *8 (|OrderedVariableList| *7))) (|ofCategory| *4 (|ProjectiveSpaceCategory| *6)) (|ofCategory| *10 (|PlacesCategory| *6 *9)))) (|pointDominateBy| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *8 (|LocalPowerSeriesCategory| *4)) (|ofCategory| *2 (|ProjectiveSpaceCategory| *4)) (|isDomain| *1 (|LocalParametrizationOfSimplePointPackage| *4 *5 *6 *7 *2 *8 *3)) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *3 (|PlacesCategory| *4 *8)))) (|localParamOfSimplePt| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|Integer|)) (|ofCategory| *6 (|Field|)) (|ofType| *7 (|List| (|Symbol|))) (|ofCategory| *8 (|DirectProductCategory| (|#| *7) (|NonNegativeInteger|))) (|ofCategory| *9 (|LocalPowerSeriesCategory| *6)) (|isDomain| *2 (|List| *9)) (|isDomain| *1 (|LocalParametrizationOfSimplePointPackage| *6 *7 *4 *8 *3 *9 *10)) (|ofCategory| *4 (|PolynomialCategory| *6 *8 (|OrderedVariableList| *7))) (|ofCategory| *3 (|ProjectiveSpaceCategory| *6)) (|ofCategory| *10 (|PlacesCategory| *6 *9)))) (|pointToPlace| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|DirectProductCategory| (|#| *6) (|NonNegativeInteger|))) (|ofCategory| *2 (|PlacesCategory| *5 *8)) (|isDomain| *1 (|LocalParametrizationOfSimplePointPackage| *5 *6 *4 *7 *3 *8 *2)) (|ofCategory| *4 (|PolynomialCategory| *5 *7 (|OrderedVariableList| *6))) (|ofCategory| *3 (|ProjectiveSpaceCategory| *5)) (|ofCategory| *8 (|LocalPowerSeriesCategory| *5)))) (|printInfo| (*1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LocalParametrizationOfSimplePointPackage| *3 *4 *5 *6 *7 *8 *9)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8)))) (|printInfo| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *6 (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|))) (|ofCategory| *8 (|LocalPowerSeriesCategory| *3)) (|isDomain| *1 (|LocalParametrizationOfSimplePointPackage| *3 *4 *5 *6 *7 *8 *9)) (|ofCategory| *5 (|PolynomialCategory| *3 *6 (|OrderedVariableList| *4))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *9 (|PlacesCategory| *3 *8))))) 
(CATEGORY |package| (SIGNATURE |printInfo| ((|Boolean|) (|Boolean|))) (SIGNATURE |printInfo| ((|Boolean|))) (SIGNATURE |pointToPlace| (|#7| |#5| |#3|)) (SIGNATURE |localParamOfSimplePt| ((|List| |#6|) |#5| |#3| (|Integer|))) (SIGNATURE |pointDominateBy| (|#5| |#7|)) (SIGNATURE |localize| ((|Record| (|:| |fnc| |#3|) (|:| |crv| |#3|) (|:| |chart| (|List| (|Integer|)))) |#3| |#5| |#3| (|Integer|)))) 
((|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) 33))) 
(((|LinearPolynomialEquationByFractions| |#1|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquationByFractions| ((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)))) (|PolynomialFactorizationExplicit|)) (T |LinearPolynomialEquationByFractions|)) 
((|solveLinearPolynomialEquationByFractions| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *4))) (|isDomain| *3 (|SparseUnivariatePolynomial| *4)) (|ofCategory| *4 (|PolynomialFactorizationExplicit|)) (|isDomain| *1 (|LinearPolynomialEquationByFractions| *4))))) 
(CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquationByFractions| ((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|varList| (((|List| |#1|) $) 82)) (|trunc| (($ $ (|NonNegativeInteger|)) 90)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) 48)) (|retractIfCan| (((|Union| (|LyndonWord| |#1|) "failed") $) NIL)) (|retract| (((|LyndonWord| |#1|) $) NIL)) (|reductum| (($ $) 89)) (|numberOfMonomials| (((|NonNegativeInteger|) $) NIL)) (|monomials| (((|List| $) $) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monom| (($ (|LyndonWord| |#1|) |#2|) 68)) (|mirror| (($ $) 86)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL)) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) 47)) (|listOfTerms| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) NIL)) (|leadingTerm| (((|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|)) $) NIL)) (|leadingMonomial| (((|LyndonWord| |#1|) $) NIL)) (|leadingCoefficient| ((|#2| $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|eval| (($ $ |#1| $) 30) (($ $ (|List| |#1|) (|List| $)) 32)) (|degree| (((|NonNegativeInteger|) $) 88)) (|construct| (($ $ $) 20) (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) 77) (($ (|LyndonWord| |#1|) $) 75) (($ $ (|LyndonWord| |#1|)) 76)) (|coerce| (((|OutputForm|) $) NIL) (($ |#1|) 74) (((|XDistributedPolynomial| |#1| |#2|) $) 58) (((|XRecursivePolynomial| |#1| |#2|) $) 41) (($ (|LyndonWord| |#1|)) 25)) (|coefficients| (((|List| |#2|) $) NIL)) (|coefficient| ((|#2| $ (|LyndonWord| |#1|)) NIL)) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) 43)) (|Zero| (($) 23 T CONST)) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) 60)) (|LiePoly| (($ (|LyndonWord| |#1|)) 14)) (= (((|Boolean|) $ $) 44)) (/ (($ $ |#2|) NIL (|has| |#2| (|Field|)))) (- (($ $) 66) (($ $ $) NIL)) (+ (($ $ $) 29)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ |#2| $) 28) (($ $ |#2|) NIL) (($ |#2| (|LyndonWord| |#1|)) NIL))) 
(((|LiePolynomial| |#1| |#2|) (|Join| (|FreeLieAlgebra| |#1| |#2|) (|FreeModuleCat| |#2| (|LyndonWord| |#1|)) (CATEGORY |domain| (SIGNATURE |LiePolyIfCan| ((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|))) (SIGNATURE |construct| ($ (|LyndonWord| |#1|) (|LyndonWord| |#1|))) (SIGNATURE |construct| ($ (|LyndonWord| |#1|) $)) (SIGNATURE |construct| ($ $ (|LyndonWord| |#1|))))) (|OrderedSet|) (|CommutativeRing|)) (T |LiePolynomial|)) 
((|LiePolyIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|XDistributedPolynomial| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *1 (|LiePolynomial| *3 *4)))) (|construct| (*1 *1 *2 *2) (AND (|isDomain| *2 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|LiePolynomial| *3 *4)) (|ofCategory| *4 (|CommutativeRing|)))) (|construct| (*1 *1 *2 *1) (AND (|isDomain| *2 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|LiePolynomial| *3 *4)) (|ofCategory| *4 (|CommutativeRing|)))) (|construct| (*1 *1 *1 *2) (AND (|isDomain| *2 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|LiePolynomial| *3 *4)) (|ofCategory| *4 (|CommutativeRing|))))) 
(|Join| (|FreeLieAlgebra| |#1| |#2|) (|FreeModuleCat| |#2| (|LyndonWord| |#1|)) (CATEGORY |domain| (SIGNATURE |LiePolyIfCan| ((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|))) (SIGNATURE |construct| ($ (|LyndonWord| |#1|) (|LyndonWord| |#1|))) (SIGNATURE |construct| ($ (|LyndonWord| |#1|) $)) (SIGNATURE |construct| ($ $ (|LyndonWord| |#1|))))) 
((|sorted?| (((|Boolean|) $) NIL) (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) 49)) (|sort!| (($ $) NIL) (($ (|Mapping| (|Boolean|) |#2| |#2|) $) 11)) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) 27)) (|reverse!| (($ $) 55)) (|removeDuplicates!| (($ $) 62)) (|remove!| (($ |#2| $) NIL) (($ (|Mapping| (|Boolean|) |#2|) $) 36)) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $) 21) ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) 50) ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) 52)) (|position| (((|Integer|) |#2| $ (|Integer|)) 60) (((|Integer|) |#2| $) NIL) (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) 46)) (|new| (($ (|NonNegativeInteger|) |#2|) 53)) (|merge!| (($ $ $) NIL) (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) 29)) (|merge| (($ $ $) NIL) (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) 24)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL) (($ (|Mapping| |#2| |#2| |#2|) $ $) 54)) (|list| (($ |#2|) 14)) (|insert!| (($ $ $ (|Integer|)) 35) (($ |#2| $ (|Integer|)) 33)) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) 45)) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) 43) (($ $ (|Integer|)) 37)) (|copyInto!| (($ $ $ (|Integer|)) 59)) (|copy| (($ $) 57)) (< (((|Boolean|) $ $) 64))) 
(((|ListAggregate&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |list| (|#1| |#2|)) (SIGNATURE |delete!| (|#1| |#1| (|Integer|))) (SIGNATURE |delete!| (|#1| |#1| (|UniversalSegment| (|Integer|)))) (SIGNATURE |remove!| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |insert!| (|#1| |#2| |#1| (|Integer|))) (SIGNATURE |insert!| (|#1| |#1| |#1| (|Integer|))) (SIGNATURE |merge!| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1| |#1|)) (SIGNATURE |select!| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |remove!| (|#1| |#2| |#1|)) (SIGNATURE |removeDuplicates!| (|#1| |#1|)) (SIGNATURE |merge!| (|#1| |#1| |#1|)) (SIGNATURE |merge| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1| |#1|)) (SIGNATURE |sorted?| ((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) |#1|)) (SIGNATURE |position| ((|Integer|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |position| ((|Integer|) |#2| |#1|)) (SIGNATURE |position| ((|Integer|) |#2| |#1| (|Integer|))) (SIGNATURE |merge| (|#1| |#1| |#1|)) (SIGNATURE |sorted?| ((|Boolean|) |#1|)) (SIGNATURE |copyInto!| (|#1| |#1| |#1| (|Integer|))) (SIGNATURE |reverse!| (|#1| |#1|)) (SIGNATURE |sort!| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1|)) (SIGNATURE |sort!| (|#1| |#1|)) (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2| |#2|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1|)) (SIGNATURE |find| ((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |new| (|#1| (|NonNegativeInteger|) |#2|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2| |#2|) |#1| |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |copy| (|#1| |#1|))) (|ListAggregate| |#2|) (|Type|)) (T |ListAggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |list| (|#1| |#2|)) (SIGNATURE |delete!| (|#1| |#1| (|Integer|))) (SIGNATURE |delete!| (|#1| |#1| (|UniversalSegment| (|Integer|)))) (SIGNATURE |remove!| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |insert!| (|#1| |#2| |#1| (|Integer|))) (SIGNATURE |insert!| (|#1| |#1| |#1| (|Integer|))) (SIGNATURE |merge!| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1| |#1|)) (SIGNATURE |select!| (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |remove!| (|#1| |#2| |#1|)) (SIGNATURE |removeDuplicates!| (|#1| |#1|)) (SIGNATURE |merge!| (|#1| |#1| |#1|)) (SIGNATURE |merge| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1| |#1|)) (SIGNATURE |sorted?| ((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) |#1|)) (SIGNATURE |position| ((|Integer|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |position| ((|Integer|) |#2| |#1|)) (SIGNATURE |position| ((|Integer|) |#2| |#1| (|Integer|))) (SIGNATURE |merge| (|#1| |#1| |#1|)) (SIGNATURE |sorted?| ((|Boolean|) |#1|)) (SIGNATURE |copyInto!| (|#1| |#1| |#1| (|Integer|))) (SIGNATURE |reverse!| (|#1| |#1|)) (SIGNATURE |sort!| (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1|)) (SIGNATURE |sort!| (|#1| |#1|)) (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2| |#2|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1|)) (SIGNATURE |find| ((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |new| (|#1| (|NonNegativeInteger|) |#2|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2| |#2|) |#1| |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |copy| (|#1| |#1|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) 45)) (|third| ((|#1| $) 62)) (|tail| (($ $) 64)) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) 94 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|split!| (($ $ (|Integer|)) 49 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) $) 136 (|has| |#1| (|OrderedSet|))) (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) 130)) (|sort!| (($ $) 140 (AND (|has| |#1| (|OrderedSet|)) (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $) 139 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sort| (($ $) 135 (|has| |#1| (|OrderedSet|))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $) 129)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setvalue!| ((|#1| $ |#1|) 36 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setrest!| (($ $ $) 53 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setlast!| ((|#1| $ |#1|) 51 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setfirst!| ((|#1| $ |#1|) 55 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ "first" |#1|) 54 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "rest" $) 52 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ "last" |#1|) 50 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) 114 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|Integer|) |#1|) 83 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) 123)) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 99 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|second| ((|#1| $) 63)) (|sample| (($) 7 T CONST)) (|reverse!| (($ $) 138 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) 128)) (|rest| (($ $) 70) (($ $ (|NonNegativeInteger|)) 68)) (|removeDuplicates!| (($ $) 125 (|has| |#1| (|SetCategory|)))) (|removeDuplicates| (($ $) 96 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove!| (($ |#1| $) 124 (|has| |#1| (|SetCategory|))) (($ (|Mapping| (|Boolean|) |#1|) $) 119)) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) 100 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ |#1| $) 97 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $) 102 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 101 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 98 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|qsetelt!| ((|#1| $ (|Integer|) |#1|) 82 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#1| $ (|Integer|)) 84)) (|possiblyInfinite?| (((|Boolean|) $) 80)) (|position| (((|Integer|) |#1| $ (|Integer|)) 133 (|has| |#1| (|SetCategory|))) (((|Integer|) |#1| $) 132 (|has| |#1| (|SetCategory|))) (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) 131)) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) 47)) (|node?| (((|Boolean|) $ $) 39 (|has| |#1| (|SetCategory|)))) (|new| (($ (|NonNegativeInteger|) |#1|) 105)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|minIndex| (((|Integer|) $) 92 (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) 141 (|has| |#1| (|OrderedSet|)))) (|merge!| (($ $ $) 126 (|has| |#1| (|OrderedSet|))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) 122)) (|merge| (($ $ $) 134 (|has| |#1| (|OrderedSet|))) (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) 127)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|maxIndex| (((|Integer|) $) 91 (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) 142 (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35) (($ (|Mapping| |#1| |#1| |#1|) $ $) 108)) (|list| (($ |#1|) 116)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|leaves| (((|List| |#1|) $) 42)) (|leaf?| (((|Boolean|) $) 46)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|last| ((|#1| $) 67) (($ $ (|NonNegativeInteger|)) 65)) (|insert!| (($ $ $ (|Integer|)) 121) (($ |#1| $ (|Integer|)) 120)) (|insert| (($ $ $ (|Integer|)) 113) (($ |#1| $ (|Integer|)) 112)) (|indices| (((|List| (|Integer|)) $) 89)) (|index?| (((|Boolean|) (|Integer|) $) 88)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|first| ((|#1| $) 73) (($ $ (|NonNegativeInteger|)) 71)) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) 103)) (|fill!| (($ $ |#1|) 93 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|explicitlyFinite?| (((|Boolean|) $) 81)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|entry?| (((|Boolean|) |#1| $) 90 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|entries| (((|List| |#1|) $) 87)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| ((|#1| $ "value") 44) ((|#1| $ "first") 72) (($ $ "rest") 69) ((|#1| $ "last") 66) (($ $ (|UniversalSegment| (|Integer|))) 109) ((|#1| $ (|Integer|)) 86) ((|#1| $ (|Integer|) |#1|) 85)) (|distance| (((|Integer|) $ $) 41)) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) 118) (($ $ (|Integer|)) 117)) (|delete| (($ $ (|UniversalSegment| (|Integer|))) 111) (($ $ (|Integer|)) 110)) (|cyclic?| (((|Boolean|) $) 43)) (|cycleTail| (($ $) 59)) (|cycleSplit!| (($ $) 56 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|cycleLength| (((|NonNegativeInteger|) $) 60)) (|cycleEntry| (($ $) 61)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copyInto!| (($ $ $ (|Integer|)) 137 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) 13)) (|convert| (((|InputForm|) $) 95 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 104)) (|concat!| (($ $ $) 58) (($ $ |#1|) 57)) (|concat| (($ $ $) 75) (($ |#1| $) 74) (($ (|List| $)) 107) (($ $ |#1|) 106)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|children| (((|List| $) $) 48)) (|child?| (((|Boolean|) $ $) 40 (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (>= (((|Boolean|) $ $) 144 (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) 145 (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (<= (((|Boolean|) $ $) 143 (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) 146 (|has| |#1| (|OrderedSet|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|ListAggregate| |#1|) (|Category|) (|Type|)) (T |ListAggregate|)) 
((|list| (*1 *1 *2) (AND (|ofCategory| *1 (|ListAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|StreamAggregate| |t#1|) (|FiniteLinearAggregate| |t#1|) (|ExtensibleLinearAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |list| ($ |t#1|)))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| (|Integer|) |#1|) . T) ((|EltableAggregate| (|Integer|) |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|ExtensibleLinearAggregate| |#1|) . T) ((|FiniteLinearAggregate| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| (|Integer|) |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|LinearAggregate| |#1|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|StreamAggregate| |#1|) . T) ((|Type|) . T) ((|UnaryRecursiveAggregate| |#1|) . T)) 
((|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) 21) (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) 20) (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) 16) (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) 13)) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) 29)) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) 23)) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) 26))) 
(((|LinearSystemMatrixPackage1| |#1|) (CATEGORY |package| (SIGNATURE |solve| ((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |solve| ((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|))) (SIGNATURE |solve| ((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|)))) (SIGNATURE |solve| ((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|)))) (SIGNATURE |particularSolution| ((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |hasSolution?| ((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |rank| ((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)))) (|Field|)) (T |LinearSystemMatrixPackage1|)) 
((|rank| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Matrix| *5)) (|isDomain| *4 (|Vector| *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|LinearSystemMatrixPackage1| *5)))) (|hasSolution?| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Matrix| *5)) (|isDomain| *4 (|Vector| *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LinearSystemMatrixPackage1| *5)))) (|particularSolution| (*1 *2 *3 *2) (|partial| AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|Matrix| *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *1 (|LinearSystemMatrixPackage1| *4)))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|List| *5))) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|List| (|Record| (|:| |particular| (|Union| (|Vector| *5) "failed")) (|:| |basis| (|List| (|Vector| *5)))))) (|isDomain| *1 (|LinearSystemMatrixPackage1| *5)) (|isDomain| *4 (|List| (|Vector| *5))))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Matrix| *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|List| (|Record| (|:| |particular| (|Union| (|Vector| *5) "failed")) (|:| |basis| (|List| (|Vector| *5)))))) (|isDomain| *1 (|LinearSystemMatrixPackage1| *5)) (|isDomain| *4 (|List| (|Vector| *5))))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|List| *5))) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Record| (|:| |particular| (|Union| (|Vector| *5) "failed")) (|:| |basis| (|List| (|Vector| *5))))) (|isDomain| *1 (|LinearSystemMatrixPackage1| *5)) (|isDomain| *4 (|Vector| *5)))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Matrix| *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Record| (|:| |particular| (|Union| (|Vector| *5) "failed")) (|:| |basis| (|List| (|Vector| *5))))) (|isDomain| *1 (|LinearSystemMatrixPackage1| *5)) (|isDomain| *4 (|Vector| *5))))) 
(CATEGORY |package| (SIGNATURE |solve| ((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |solve| ((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|))) (SIGNATURE |solve| ((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|)))) (SIGNATURE |solve| ((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|)))) (SIGNATURE |particularSolution| ((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |hasSolution?| ((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |rank| ((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)))) 
((|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) 47) (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) 45)) (|rank| (((|NonNegativeInteger|) |#4| |#3|) 17)) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) 20)) (|hasSolution?| (((|Boolean|) |#4| |#3|) 13))) 
(((|LinearSystemMatrixPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |solve| ((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|)) (SIGNATURE |solve| ((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|))) (SIGNATURE |particularSolution| ((|Union| |#3| "failed") |#4| |#3|)) (SIGNATURE |hasSolution?| ((|Boolean|) |#4| |#3|)) (SIGNATURE |rank| ((|NonNegativeInteger|) |#4| |#3|))) (|Field|) (|Join| (|FiniteLinearAggregate| |#1|) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|))) (|Join| (|FiniteLinearAggregate| |#1|) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|))) (|MatrixCategory| |#1| |#2| |#3|)) (T |LinearSystemMatrixPackage|)) 
((|rank| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|Join| (|FiniteLinearAggregate| *5) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|)))) (|ofCategory| *4 (|Join| (|FiniteLinearAggregate| *5) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|)))) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|LinearSystemMatrixPackage| *5 *6 *4 *3)) (|ofCategory| *3 (|MatrixCategory| *5 *6 *4)))) (|hasSolution?| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|Join| (|FiniteLinearAggregate| *5) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|)))) (|ofCategory| *4 (|Join| (|FiniteLinearAggregate| *5) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|)))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LinearSystemMatrixPackage| *5 *6 *4 *3)) (|ofCategory| *3 (|MatrixCategory| *5 *6 *4)))) (|particularSolution| (*1 *2 *3 *2) (|partial| AND (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|Join| (|FiniteLinearAggregate| *4) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|)))) (|ofCategory| *2 (|Join| (|FiniteLinearAggregate| *4) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|)))) (|isDomain| *1 (|LinearSystemMatrixPackage| *4 *5 *2 *3)) (|ofCategory| *3 (|MatrixCategory| *4 *5 *2)))) (|solve| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|Join| (|FiniteLinearAggregate| *5) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|)))) (|ofCategory| *7 (|Join| (|FiniteLinearAggregate| *5) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|)))) (|isDomain| *2 (|List| (|Record| (|:| |particular| (|Union| *7 "failed")) (|:| |basis| (|List| *7))))) (|isDomain| *1 (|LinearSystemMatrixPackage| *5 *6 *7 *3)) (|isDomain| *4 (|List| *7)) (|ofCategory| *3 (|MatrixCategory| *5 *6 *7)))) (|solve| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|Join| (|FiniteLinearAggregate| *5) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|)))) (|ofCategory| *4 (|Join| (|FiniteLinearAggregate| *5) (CATEGORY |package| (ATTRIBUTE |shallowlyMutable|)))) (|isDomain| *2 (|Record| (|:| |particular| (|Union| *4 "failed")) (|:| |basis| (|List| *4)))) (|isDomain| *1 (|LinearSystemMatrixPackage| *5 *6 *4 *3)) (|ofCategory| *3 (|MatrixCategory| *5 *6 *4))))) 
(CATEGORY |package| (SIGNATURE |solve| ((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|)) (SIGNATURE |solve| ((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|))) (SIGNATURE |particularSolution| ((|Union| |#3| "failed") |#4| |#3|)) (SIGNATURE |hasSolution?| ((|Boolean|) |#4| |#3|)) (SIGNATURE |rank| ((|NonNegativeInteger|) |#4| |#3|))) 
((|linSolve| (((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)) 44))) 
(((|LinearSystemPolynomialPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |linSolve| ((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)))) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |LinearSystemPolynomialPackage|)) 
((|linSolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|List| *7)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|PolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| *8)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| *8)))))) (|isDomain| *1 (|LinearSystemPolynomialPackage| *5 *6 *7 *8))))) 
(CATEGORY |package| (SIGNATURE |linSolve| ((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)))) 
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(|associatorDependence| (((|List| (|Vector| |#2|))) NIL (|has| |#2| (|IntegralDomain|)))) (|associator| (($ $ $ $) NIL)) (|associative?| (((|Boolean|)) NIL)) (|apply| (($ (|Matrix| |#2|) $) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|antisymmetric?| (((|Boolean|) $) NIL)) (|antiCommutator| (($ $ $) NIL)) (|antiCommutative?| (((|Boolean|)) NIL)) (|antiAssociative?| (((|Boolean|)) NIL)) (|alternative?| (((|Boolean|)) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($ $ (|Mapping| |#2| |#2|)) NIL) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|)) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|DifferentialRing|))) (($ $) NIL (|has| |#2| (|DifferentialRing|)))) (= (((|Boolean|) $ $) NIL)) (/ (($ $ |#2|) NIL (|has| |#2| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| |#2| (|Field|)))) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ |#2|) NIL) (($ |#2| $) NIL) (((|DirectProduct| |#1| |#2|) $ (|DirectProduct| |#1| |#2|)) NIL) (((|DirectProduct| |#1| |#2|) (|DirectProduct| |#1| |#2|) $) NIL)) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|LieSquareMatrix| |#1| |#2|) (|Join| (|SquareMatrixCategory| |#1| |#2| (|DirectProduct| |#1| |#2|) (|DirectProduct| |#1| |#2|)) (|CoercibleTo| (|Matrix| |#2|)) (|FramedNonAssociativeAlgebra| |#2|)) (|PositiveInteger|) (|CommutativeRing|)) (T |LieSquareMatrix|)) 
NIL 
(|Join| (|SquareMatrixCategory| |#1| |#2| (|DirectProduct| |#1| |#2|) (|DirectProduct| |#1| |#2|)) (|CoercibleTo| (|Matrix| |#2|)) (|FramedNonAssociativeAlgebra| |#2|)) 
((~= (((|Boolean|) $ $) NIL)) (|varList| (((|List| |#1|) $) NIL)) (|right| (($ $) 50)) (|retractable?| (((|Boolean|) $) NIL)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL)) (|retract| ((|#1| $) NIL)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) 22)) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) 14)) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) 23)) (|lexico| (((|Boolean|) $ $) 28)) (|length| (((|PositiveInteger|) $) 35)) (|left| (($ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) 16)) (|coerce| (((|OutputForm|) $) 41) (($ |#1|) 32) (((|OrderedFreeMonoid| |#1|) $) 37) (((|Magma| |#1|) $) 42)) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) 55)) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) 57)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 51)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 36))) 
(((|LyndonWord| |#1|) (|Join| (|OrderedSet|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |retractable?| ((|Boolean|) $)) (SIGNATURE |left| ($ $)) (SIGNATURE |right| ($ $)) (SIGNATURE |length| ((|PositiveInteger|) $)) (SIGNATURE |lexico| ((|Boolean|) $ $)) (SIGNATURE |coerce| ((|OrderedFreeMonoid| |#1|) $)) (SIGNATURE |coerce| ((|Magma| |#1|) $)) (SIGNATURE |factor| ((|List| $) (|OrderedFreeMonoid| |#1|))) (SIGNATURE |lyndon?| ((|Boolean|) (|OrderedFreeMonoid| |#1|))) (SIGNATURE |lyndon| ($ (|OrderedFreeMonoid| |#1|))) (SIGNATURE |lyndonIfCan| ((|Union| $ "failed") (|OrderedFreeMonoid| |#1|))) (SIGNATURE |varList| ((|List| |#1|) $)) (SIGNATURE |LyndonWordsList1| ((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|))) (SIGNATURE |LyndonWordsList| ((|List| $) (|List| |#1|) (|PositiveInteger|))))) (|OrderedSet|)) (T |LyndonWord|)) 
((|retractable?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|left| (*1 *1 *1) (AND (|isDomain| *1 (|LyndonWord| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|right| (*1 *1 *1) (AND (|isDomain| *1 (|LyndonWord| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|length| (*1 *2 *1) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|lexico| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|OrderedFreeMonoid| *3)) (|isDomain| *1 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Magma| *3)) (|isDomain| *1 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|factor| (*1 *2 *3) (AND (|isDomain| *3 (|OrderedFreeMonoid| *4)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|List| (|LyndonWord| *4))) (|isDomain| *1 (|LyndonWord| *4)))) (|lyndon?| (*1 *2 *3) (AND (|isDomain| *3 (|OrderedFreeMonoid| *4)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LyndonWord| *4)))) (|lyndon| (*1 *1 *2) (AND (|isDomain| *2 (|OrderedFreeMonoid| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|LyndonWord| *3)))) (|lyndonIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|OrderedFreeMonoid| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|LyndonWord| *3)))) (|varList| (*1 *2 *1) (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|LyndonWordsList1| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|OneDimensionalArray| (|List| (|LyndonWord| *5)))) (|isDomain| *1 (|LyndonWord| *5)))) (|LyndonWordsList| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| (|LyndonWord| *5))) (|isDomain| *1 (|LyndonWord| *5))))) 
(|Join| (|OrderedSet|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |retractable?| ((|Boolean|) $)) (SIGNATURE |left| ($ $)) (SIGNATURE |right| ($ $)) (SIGNATURE |length| ((|PositiveInteger|) $)) (SIGNATURE |lexico| ((|Boolean|) $ $)) (SIGNATURE |coerce| ((|OrderedFreeMonoid| |#1|) $)) (SIGNATURE |coerce| ((|Magma| |#1|) $)) (SIGNATURE |factor| ((|List| $) (|OrderedFreeMonoid| |#1|))) (SIGNATURE |lyndon?| ((|Boolean|) (|OrderedFreeMonoid| |#1|))) (SIGNATURE |lyndon| ($ (|OrderedFreeMonoid| |#1|))) (SIGNATURE |lyndonIfCan| ((|Union| $ "failed") (|OrderedFreeMonoid| |#1|))) (SIGNATURE |varList| ((|List| |#1|) $)) (SIGNATURE |LyndonWordsList1| ((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|))) (SIGNATURE |LyndonWordsList| ((|List| $) (|List| |#1|) (|PositiveInteger|))))) 
((|value| ((|#2| $) 76)) (|tail| (($ $) 96)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 26)) (|rest| (($ $) 85) (($ $ (|NonNegativeInteger|)) 88)) (|possiblyInfinite?| (((|Boolean|) $) 97)) (|nodes| (((|List| $) $) 72)) (|node?| (((|Boolean|) $ $) 71)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 24)) (|minIndex| (((|Integer|) $) 46)) (|maxIndex| (((|Integer|) $) 45)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 22)) (|leaf?| (((|Boolean|) $) 74)) (|last| ((|#2| $) 89) (($ $ (|NonNegativeInteger|)) 92)) (|insert| (($ $ $ (|Integer|)) 62) (($ |#2| $ (|Integer|)) 61)) (|indices| (((|List| (|Integer|)) $) 44)) (|index?| (((|Boolean|) (|Integer|) $) 42)) (|first| ((|#2| $) NIL) (($ $ (|NonNegativeInteger|)) 84)) (|extend| (($ $ (|Integer|)) 99)) (|explicitlyFinite?| (((|Boolean|) $) 98)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 32)) (|entries| (((|List| |#2|) $) 33)) (|elt| ((|#2| $ "value") NIL) ((|#2| $ "first") 83) (($ $ "rest") 87) ((|#2| $ "last") 95) (($ $ (|UniversalSegment| (|Integer|))) 58) ((|#2| $ (|Integer|)) 40) ((|#2| $ (|Integer|) |#2|) 41)) (|distance| (((|Integer|) $ $) 70)) (|delete| (($ $ (|UniversalSegment| (|Integer|))) 57) (($ $ (|Integer|)) 51)) (|cyclic?| (((|Boolean|) $) 66)) (|cycleTail| (($ $) 81)) (|cycleLength| (((|NonNegativeInteger|) $) 80)) (|cycleEntry| (($ $) 79)) (|construct| (($ (|List| |#2|)) 37)) (|complete| (($ $) 100)) (|children| (((|List| $) $) 69)) (|child?| (((|Boolean|) $ $) 68)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 31)) (= (((|Boolean|) $ $) 18)) (|#| (((|NonNegativeInteger|) $) 29))) 
(((|LazyStreamAggregate&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |complete| (|#1| |#1|)) (SIGNATURE |extend| (|#1| |#1| (|Integer|))) (SIGNATURE |possiblyInfinite?| ((|Boolean|) |#1|)) (SIGNATURE |explicitlyFinite?| ((|Boolean|) |#1|)) (SIGNATURE |elt| (|#2| |#1| (|Integer|) |#2|)) (SIGNATURE |elt| (|#2| |#1| (|Integer|))) (SIGNATURE |entries| ((|List| |#2|) |#1|)) (SIGNATURE |index?| ((|Boolean|) (|Integer|) |#1|)) (SIGNATURE |indices| ((|List| (|Integer|)) |#1|)) (SIGNATURE |maxIndex| ((|Integer|) |#1|)) (SIGNATURE |minIndex| ((|Integer|) |#1|)) (SIGNATURE |construct| (|#1| (|List| |#2|))) (SIGNATURE |elt| (|#1| |#1| (|UniversalSegment| (|Integer|)))) (SIGNATURE |delete| (|#1| |#1| (|Integer|))) (SIGNATURE |delete| (|#1| |#1| (|UniversalSegment| (|Integer|)))) (SIGNATURE |insert| (|#1| |#2| |#1| (|Integer|))) (SIGNATURE |insert| (|#1| |#1| |#1| (|Integer|))) (SIGNATURE |cycleTail| (|#1| |#1|)) (SIGNATURE |cycleLength| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |cycleEntry| (|#1| |#1|)) (SIGNATURE |tail| (|#1| |#1|)) (SIGNATURE |last| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |elt| (|#2| |#1| "last")) (SIGNATURE |last| (|#2| |#1|)) (SIGNATURE |rest| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |elt| (|#1| |#1| "rest")) (SIGNATURE |rest| (|#1| |#1|)) (SIGNATURE |first| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |elt| (|#2| |#1| "first")) (SIGNATURE |first| (|#2| |#1|)) (SIGNATURE |node?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |child?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |distance| ((|Integer|) |#1| |#1|)) (SIGNATURE |cyclic?| ((|Boolean|) |#1|)) (SIGNATURE |elt| (|#2| |#1| "value")) (SIGNATURE |value| (|#2| |#1|)) (SIGNATURE |leaf?| ((|Boolean|) |#1|)) (SIGNATURE |nodes| ((|List| |#1|) |#1|)) (SIGNATURE |children| ((|List| |#1|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|)) (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |size?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |less?| ((|Boolean|) |#1| (|NonNegativeInteger|)))) (|LazyStreamAggregate| |#2|) (|Type|)) (T |LazyStreamAggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |complete| (|#1| |#1|)) (SIGNATURE |extend| (|#1| |#1| (|Integer|))) (SIGNATURE |possiblyInfinite?| ((|Boolean|) |#1|)) (SIGNATURE |explicitlyFinite?| ((|Boolean|) |#1|)) (SIGNATURE |elt| (|#2| |#1| (|Integer|) |#2|)) (SIGNATURE |elt| (|#2| |#1| (|Integer|))) (SIGNATURE |entries| ((|List| |#2|) |#1|)) (SIGNATURE |index?| ((|Boolean|) (|Integer|) |#1|)) (SIGNATURE |indices| ((|List| (|Integer|)) |#1|)) (SIGNATURE |maxIndex| ((|Integer|) |#1|)) (SIGNATURE |minIndex| ((|Integer|) |#1|)) (SIGNATURE |construct| (|#1| (|List| |#2|))) (SIGNATURE |elt| (|#1| |#1| (|UniversalSegment| (|Integer|)))) (SIGNATURE |delete| (|#1| |#1| (|Integer|))) (SIGNATURE |delete| (|#1| |#1| (|UniversalSegment| (|Integer|)))) (SIGNATURE |insert| (|#1| |#2| |#1| (|Integer|))) (SIGNATURE |insert| (|#1| |#1| |#1| (|Integer|))) (SIGNATURE |cycleTail| (|#1| |#1|)) (SIGNATURE |cycleLength| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |cycleEntry| (|#1| |#1|)) (SIGNATURE |tail| (|#1| |#1|)) (SIGNATURE |last| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |elt| (|#2| |#1| "last")) (SIGNATURE |last| (|#2| |#1|)) (SIGNATURE |rest| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |elt| (|#1| |#1| "rest")) (SIGNATURE |rest| (|#1| |#1|)) (SIGNATURE |first| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |elt| (|#2| |#1| "first")) (SIGNATURE |first| (|#2| |#1|)) (SIGNATURE |node?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |child?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |distance| ((|Integer|) |#1| |#1|)) (SIGNATURE |cyclic?| ((|Boolean|) |#1|)) (SIGNATURE |elt| (|#2| |#1| "value")) (SIGNATURE |value| (|#2| |#1|)) (SIGNATURE |leaf?| ((|Boolean|) |#1|)) (SIGNATURE |nodes| ((|List| |#1|) |#1|)) (SIGNATURE |children| ((|List| |#1|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|)) (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |size?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |less?| ((|Boolean|) |#1| (|NonNegativeInteger|)))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) 45)) (|third| ((|#1| $) 62)) (|tail| (($ $) 64)) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) 94 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|split!| (($ $ (|Integer|)) 49 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setvalue!| ((|#1| $ |#1|) 36 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setrest!| (($ $ $) 53 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setlast!| ((|#1| $ |#1|) 51 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setfirst!| ((|#1| $ |#1|) 55 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ "first" |#1|) 54 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "rest" $) 52 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ "last" |#1|) 50 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) 114 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|Integer|) |#1|) 83 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 99)) (|second| ((|#1| $) 63)) (|sample| (($) 7 T CONST)) (|rst| (($ $) 118)) (|rest| (($ $) 70) (($ $ (|NonNegativeInteger|)) 68)) (|removeDuplicates| (($ $) 96 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove| (($ |#1| $) 97 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#1|) $) 100)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $) 102 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 101 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 98 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|qsetelt!| ((|#1| $ (|Integer|) |#1|) 82 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#1| $ (|Integer|)) 84)) (|possiblyInfinite?| (((|Boolean|) $) 80)) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) 117)) (|nodes| (((|List| $) $) 47)) (|node?| (((|Boolean|) $ $) 39 (|has| |#1| (|SetCategory|)))) (|new| (($ (|NonNegativeInteger|) |#1|) 105)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|minIndex| (((|Integer|) $) 92 (|has| (|Integer|) (|OrderedSet|)))) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|maxIndex| (((|Integer|) $) 91 (|has| (|Integer|) (|OrderedSet|)))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35) (($ (|Mapping| |#1| |#1| |#1|) $ $) 108)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|leaves| (((|List| |#1|) $) 42)) (|leaf?| (((|Boolean|) $) 46)) (|lazyEvaluate| (($ $) 120)) (|lazy?| (((|Boolean|) $) 121)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|last| ((|#1| $) 67) (($ $ (|NonNegativeInteger|)) 65)) (|insert| (($ $ $ (|Integer|)) 113) (($ |#1| $ (|Integer|)) 112)) (|indices| (((|List| (|Integer|)) $) 89)) (|index?| (((|Boolean|) (|Integer|) $) 88)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|frst| ((|#1| $) 119)) (|first| ((|#1| $) 73) (($ $ (|NonNegativeInteger|)) 71)) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) 103)) (|fill!| (($ $ |#1|) 93 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|extend| (($ $ (|Integer|)) 116)) (|explicitlyFinite?| (((|Boolean|) $) 81)) (|explicitlyEmpty?| (((|Boolean|) $) 122)) (|explicitEntries?| (((|Boolean|) $) 123)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|entry?| (((|Boolean|) |#1| $) 90 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|entries| (((|List| |#1|) $) 87)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| ((|#1| $ "value") 44) ((|#1| $ "first") 72) (($ $ "rest") 69) ((|#1| $ "last") 66) (($ $ (|UniversalSegment| (|Integer|))) 109) ((|#1| $ (|Integer|)) 86) ((|#1| $ (|Integer|) |#1|) 85)) (|distance| (((|Integer|) $ $) 41)) (|delete| (($ $ (|UniversalSegment| (|Integer|))) 111) (($ $ (|Integer|)) 110)) (|cyclic?| (((|Boolean|) $) 43)) (|cycleTail| (($ $) 59)) (|cycleSplit!| (($ $) 56 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|cycleLength| (((|NonNegativeInteger|) $) 60)) (|cycleEntry| (($ $) 61)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|convert| (((|InputForm|) $) 95 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 104)) (|concat!| (($ $ $) 58 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ |#1|) 57 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|concat| (($ $ $) 75) (($ |#1| $) 74) (($ (|List| $)) 107) (($ $ |#1|) 106)) (|complete| (($ $) 115)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|children| (((|List| $) $) 48)) (|child?| (((|Boolean|) $ $) 40 (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|LazyStreamAggregate| |#1|) (|Category|) (|Type|)) (T |LazyStreamAggregate|)) 
((|remove| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|select| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|explicitEntries?| (*1 *2 *1) (AND (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|explicitlyEmpty?| (*1 *2 *1) (AND (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|lazy?| (*1 *2 *1) (AND (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|lazyEvaluate| (*1 *1 *1) (AND (|ofCategory| *1 (|LazyStreamAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|frst| (*1 *2 *1) (AND (|ofCategory| *1 (|LazyStreamAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|rst| (*1 *1 *1) (AND (|ofCategory| *1 (|LazyStreamAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|numberOfComputedEntries| (*1 *2 *1) (AND (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|extend| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|complete| (*1 *1 *1) (AND (|ofCategory| *1 (|LazyStreamAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|StreamAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |remove| ($ (|Mapping| (|Boolean|) |t#1|) $)) (SIGNATURE |select| ($ (|Mapping| (|Boolean|) |t#1|) $)) (SIGNATURE |explicitEntries?| ((|Boolean|) $)) (SIGNATURE |explicitlyEmpty?| ((|Boolean|) $)) (SIGNATURE |lazy?| ((|Boolean|) $)) (SIGNATURE |lazyEvaluate| ($ $)) (SIGNATURE |frst| (|t#1| $)) (SIGNATURE |rst| ($ $)) (SIGNATURE |numberOfComputedEntries| ((|NonNegativeInteger|) $)) (SIGNATURE |extend| ($ $ (|Integer|))) (SIGNATURE |complete| ($ $)))) 
(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| (|Integer|) |#1|) . T) ((|EltableAggregate| (|Integer|) |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| (|Integer|) |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|LinearAggregate| |#1|) . T) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|StreamAggregate| |#1|) . T) ((|Type|) . T) ((|UnaryRecursiveAggregate| |#1|) . T)) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) 32 (|has| |#1| (|Ring|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) 27)) (|sample| (($) NIL T CONST)) (|plus| (($ $ $) 36 (|has| |#1| (|Ring|)))) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) 8)) (|matrixConcat3D| (($ (|Symbol|) $ $) 22)) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|identityMatrix| (($ (|NonNegativeInteger|)) 34 (|has| |#1| (|Ring|)))) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) 25)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) NIL)) (|construct| (($ (|List| (|List| (|List| |#1|)))) 43)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|))) (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) 15) (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) 12)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|ThreeDimensionalMatrix| |#1|) (|Join| (|HomogeneousAggregate| |#1|) (CATEGORY |domain| (IF (|has| |#1| (|Ring|)) (PROGN (SIGNATURE |zeroMatrix| ($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |identityMatrix| ($ (|NonNegativeInteger|))) (SIGNATURE |plus| ($ $ $))) |noBranch|) (SIGNATURE |construct| ($ (|List| (|List| (|List| |#1|))))) (SIGNATURE |elt| (|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |setelt!| (|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|)) (SIGNATURE |coerce| ($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))))) (SIGNATURE |coerce| ((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $)) (SIGNATURE |matrixConcat3D| ($ (|Symbol|) $ $)) (SIGNATURE |matrixDimensions| ((|Vector| (|NonNegativeInteger|)) $)))) (|SetCategory|)) (T |ThreeDimensionalMatrix|)) 
((|zeroMatrix| (*1 *1 *2 *2 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ThreeDimensionalMatrix| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|SetCategory|)))) (|identityMatrix| (*1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ThreeDimensionalMatrix| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|SetCategory|)))) (|plus| (*1 *1 *1 *1) (AND (|isDomain| *1 (|ThreeDimensionalMatrix| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|SetCategory|)))) (|construct| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|List| (|List| *3)))) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|ThreeDimensionalMatrix| *3)))) (|elt| (*1 *2 *1 *3 *3 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|ThreeDimensionalMatrix| *2)) (|ofCategory| *2 (|SetCategory|)))) (|setelt!| (*1 *2 *1 *3 *3 *3 *2) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|ThreeDimensionalMatrix| *2)) (|ofCategory| *2 (|SetCategory|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| *3)))) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|ThreeDimensionalMatrix| *3)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| *3)))) (|isDomain| *1 (|ThreeDimensionalMatrix| *3)) (|ofCategory| *3 (|SetCategory|)))) (|matrixConcat3D| (*1 *1 *2 *1 *1) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|ThreeDimensionalMatrix| *3)) (|ofCategory| *3 (|SetCategory|)))) (|matrixDimensions| (*1 *2 *1) (AND (|isDomain| *2 (|Vector| (|NonNegativeInteger|))) (|isDomain| *1 (|ThreeDimensionalMatrix| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(|Join| (|HomogeneousAggregate| |#1|) (CATEGORY |domain| (IF (|has| |#1| (|Ring|)) (PROGN (SIGNATURE |zeroMatrix| ($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |identityMatrix| ($ (|NonNegativeInteger|))) (SIGNATURE |plus| ($ $ $))) |noBranch|) (SIGNATURE |construct| ($ (|List| (|List| (|List| |#1|))))) (SIGNATURE |elt| (|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |setelt!| (|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|)) (SIGNATURE |coerce| ($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))))) (SIGNATURE |coerce| ((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $)) (SIGNATURE |matrixConcat3D| ($ (|Symbol|) $ $)) (SIGNATURE |matrixDimensions| ((|Vector| (|NonNegativeInteger|)) $)))) 
((|zero?| (((|Boolean|) |#1|) 5)) (|repack1| (((|Void|) |#1| (|U32Vector|) (|Integer|) |#2|) 8)) (|pseudoRem| ((|#1| |#1| |#1| |#2|) 1)) (|packModulus| (((|Union| |#2| "failed") (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Integer|)) 3)) (|packExps| ((|SortedExponentVector| (|Integer|) (|Integer|) |#2|) 7)) (|degree| (((|Integer|) |#1|) 6)) (|canonicalIfCan| (((|Union| |#1| "failed") |#1| |#2|) 2)) (|MPtoMPT| ((|#1| (|Polynomial| (|Integer|)) (|Symbol|) (|List| (|Symbol|)) |#2|) 4))) 
(((|ModularAlgebraicGcdOperations| |#1| |#2|) (|Category|) (|Type|) (|Type|)) (T |ModularAlgebraicGcdOperations|)) 
((|repack1| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *4 (|U32Vector|)) (|isDomain| *5 (|Integer|)) (|ofCategory| *1 (|ModularAlgebraicGcdOperations| *3 *6)) (|ofCategory| *3 (|Type|)) (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|Void|)))) (|packExps| (*1 *2 *3 *3 *4) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|ModularAlgebraicGcdOperations| *5 *4)) (|ofCategory| *5 (|Type|)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 |SortedExponentVector|))) (|degree| (*1 *2 *3) (AND (|ofCategory| *1 (|ModularAlgebraicGcdOperations| *3 *4)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Integer|)))) (|zero?| (*1 *2 *3) (AND (|ofCategory| *1 (|ModularAlgebraicGcdOperations| *3 *4)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|MPtoMPT| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *3 (|Polynomial| (|Integer|))) (|isDomain| *5 (|List| (|Symbol|))) (|ofCategory| *1 (|ModularAlgebraicGcdOperations| *2 *6)) (|ofCategory| *6 (|Type|)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *2 (|Type|)))) (|packModulus| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *3 (|List| (|Polynomial| (|Integer|)))) (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *5 (|Integer|)) (|ofCategory| *1 (|ModularAlgebraicGcdOperations| *6 *2)) (|ofCategory| *6 (|Type|)) (|ofCategory| *2 (|Type|)))) (|canonicalIfCan| (*1 *2 *2 *3) (|partial| AND (|ofCategory| *1 (|ModularAlgebraicGcdOperations| *2 *3)) (|ofCategory| *2 (|Type|)) (|ofCategory| *3 (|Type|)))) (|pseudoRem| (*1 *2 *2 *2 *3) (AND (|ofCategory| *1 (|ModularAlgebraicGcdOperations| *2 *3)) (|ofCategory| *2 (|Type|)) (|ofCategory| *3 (|Type|))))) 
(|Join| (CATEGORY |package| (SIGNATURE |pseudoRem| (|t#1| |t#1| |t#1| |t#2|)) (SIGNATURE |canonicalIfCan| ((|Union| |t#1| "failed") |t#1| |t#2|)) (SIGNATURE |packModulus| ((|Union| |t#2| "failed") (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Integer|))) (SIGNATURE |MPtoMPT| (|t#1| (|Polynomial| (|Integer|)) (|Symbol|) (|List| (|Symbol|)) |t#2|)) (SIGNATURE |zero?| ((|Boolean|) |t#1|)) (SIGNATURE |degree| ((|Integer|) |t#1|)) (SIGNATURE |packExps| (|SortedExponentVector| (|Integer|) (|Integer|) |t#2|)) (SIGNATURE |repack1| ((|Void|) |t#1| (|U32Vector|) (|Integer|) |t#2|)))) 
((~= (((|Boolean|) $ $) NIL)) (|varList| (((|List| |#1|) $) 14)) (|right| (($ $) 18)) (|retractable?| (((|Boolean|) $) 19)) (|retractIfCan| (((|Union| |#1| "failed") $) 22)) (|retract| ((|#1| $) 20)) (|rest| (($ $) 36)) (|mirror| (($ $) 24)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|lexico| (((|Boolean|) $ $) 41)) (|length| (((|PositiveInteger|) $) 38)) (|left| (($ $) 17)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|first| ((|#1| $) 35)) (|coerce| (((|OutputForm|) $) 31) (($ |#1|) 23) (((|OrderedFreeMonoid| |#1|) $) 27)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 12)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 40)) (* (($ $ $) 34))) 
(((|Magma| |#1|) (|Join| (|OrderedSet|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE * ($ $ $)) (SIGNATURE |coerce| ((|OrderedFreeMonoid| |#1|) $)) (SIGNATURE |first| (|#1| $)) (SIGNATURE |left| ($ $)) (SIGNATURE |length| ((|PositiveInteger|) $)) (SIGNATURE |lexico| ((|Boolean|) $ $)) (SIGNATURE |mirror| ($ $)) (SIGNATURE |rest| ($ $)) (SIGNATURE |retractable?| ((|Boolean|) $)) (SIGNATURE |right| ($ $)) (SIGNATURE |varList| ((|List| |#1|) $)))) (|OrderedSet|)) (T |Magma|)) 
((* (*1 *1 *1 *1) (AND (|isDomain| *1 (|Magma| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|OrderedFreeMonoid| *3)) (|isDomain| *1 (|Magma| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|first| (*1 *2 *1) (AND (|isDomain| *1 (|Magma| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|left| (*1 *1 *1) (AND (|isDomain| *1 (|Magma| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|length| (*1 *2 *1) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|Magma| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|lexico| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Magma| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|mirror| (*1 *1 *1) (AND (|isDomain| *1 (|Magma| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|rest| (*1 *1 *1) (AND (|isDomain| *1 (|Magma| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|retractable?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Magma| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|right| (*1 *1 *1) (AND (|isDomain| *1 (|Magma| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|varList| (*1 *2 *1) (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|Magma| *3)) (|ofCategory| *3 (|OrderedSet|))))) 
(|Join| (|OrderedSet|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE * ($ $ $)) (SIGNATURE |coerce| ((|OrderedFreeMonoid| |#1|) $)) (SIGNATURE |first| (|#1| $)) (SIGNATURE |left| ($ $)) (SIGNATURE |length| ((|PositiveInteger|) $)) (SIGNATURE |lexico| ((|Boolean|) $ $)) (SIGNATURE |mirror| ($ $)) (SIGNATURE |rest| ($ $)) (SIGNATURE |retractable?| ((|Boolean|) $)) (SIGNATURE |right| ($ $)) (SIGNATURE |varList| ((|List| |#1|) $)))) 
((|vertSplit| (((|List| |#4|) |#4| (|List| (|PositiveInteger|))) 72) (((|List| |#4|) |#4| (|PositiveInteger|)) 62)) (|vertConcat| ((|#4| (|List| |#4|)) 59)) (|subMatrix| ((|#4| |#4| (|Segment| (|PositiveInteger|)) (|Segment| (|PositiveInteger|))) 57) ((|#4| |#4| (|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) 54)) (|rows| ((|#4| |#4| (|Segment| (|PositiveInteger|))) 31) ((|#4| |#4| (|List| (|PositiveInteger|))) 30)) (|horizSplit| (((|List| |#4|) |#4| (|List| (|PositiveInteger|))) 74) (((|List| |#4|) |#4| (|PositiveInteger|)) 73)) (|horizConcat| ((|#4| (|List| |#4|)) 58)) (|element| ((|#4| |#4| (|PositiveInteger|) (|PositiveInteger|)) 20)) (|diagonalMatrix| ((|#4| |#4|) 45) ((|#4| |#4| (|Integer|)) 44)) (|columns| ((|#4| |#4| (|Segment| (|PositiveInteger|))) 37) ((|#4| |#4| (|List| (|PositiveInteger|))) 36)) (|blockSplit| (((|List| (|List| |#4|)) |#4| (|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) 78) (((|List| (|List| |#4|)) |#4| (|PositiveInteger|) (|List| (|PositiveInteger|))) 77) (((|List| (|List| |#4|)) |#4| (|List| (|PositiveInteger|)) (|PositiveInteger|)) 76) (((|List| (|List| |#4|)) |#4| (|PositiveInteger|) (|PositiveInteger|)) 75)) (|blockConcat| ((|#4| (|List| (|List| |#4|))) 53)) (|bandMatrix| ((|#4| |#4| (|Segment| (|Integer|))) 51) ((|#4| |#4| (|List| (|Integer|))) 48)) (|aRow| ((|#4| |#4| (|PositiveInteger|)) 24)) (|aColumn| ((|#4| |#4| (|PositiveInteger|)) 34))) 
(((|MatrixManipulation| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |element| (|#4| |#4| (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |aRow| (|#4| |#4| (|PositiveInteger|))) (SIGNATURE |rows| (|#4| |#4| (|List| (|PositiveInteger|)))) (SIGNATURE |rows| (|#4| |#4| (|Segment| (|PositiveInteger|)))) (SIGNATURE |aColumn| (|#4| |#4| (|PositiveInteger|))) (SIGNATURE |columns| (|#4| |#4| (|List| (|PositiveInteger|)))) (SIGNATURE |columns| (|#4| |#4| (|Segment| (|PositiveInteger|)))) (SIGNATURE |subMatrix| (|#4| |#4| (|List| (|PositiveInteger|)) (|List| (|PositiveInteger|)))) (SIGNATURE |subMatrix| (|#4| |#4| (|Segment| (|PositiveInteger|)) (|Segment| (|PositiveInteger|)))) (SIGNATURE |diagonalMatrix| (|#4| |#4| (|Integer|))) (SIGNATURE |diagonalMatrix| (|#4| |#4|)) (SIGNATURE |bandMatrix| (|#4| |#4| (|List| (|Integer|)))) (SIGNATURE |bandMatrix| (|#4| |#4| (|Segment| (|Integer|)))) (SIGNATURE |horizConcat| (|#4| (|List| |#4|))) (SIGNATURE |vertConcat| (|#4| (|List| |#4|))) (SIGNATURE |blockConcat| (|#4| (|List| (|List| |#4|)))) (SIGNATURE |vertSplit| ((|List| |#4|) |#4| (|PositiveInteger|))) (SIGNATURE |vertSplit| ((|List| |#4|) |#4| (|List| (|PositiveInteger|)))) (SIGNATURE |horizSplit| ((|List| |#4|) |#4| (|PositiveInteger|))) (SIGNATURE |horizSplit| ((|List| |#4|) |#4| (|List| (|PositiveInteger|)))) (SIGNATURE |blockSplit| ((|List| (|List| |#4|)) |#4| (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |blockSplit| ((|List| (|List| |#4|)) |#4| (|List| (|PositiveInteger|)) (|PositiveInteger|))) (SIGNATURE |blockSplit| ((|List| (|List| |#4|)) |#4| (|PositiveInteger|) (|List| (|PositiveInteger|)))) (SIGNATURE |blockSplit| ((|List| (|List| |#4|)) |#4| (|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))))) (|Field|) (|FiniteLinearAggregate| |#1|) (|FiniteLinearAggregate| |#1|) (|MatrixCategory| |#1| |#2| |#3|)) (T |MatrixManipulation|)) 
((|blockSplit| (*1 *2 *3 *4 *4) (AND (|isDomain| *4 (|List| (|PositiveInteger|))) (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|FiniteLinearAggregate| *5)) (|ofCategory| *7 (|FiniteLinearAggregate| *5)) (|isDomain| *2 (|List| (|List| *3))) (|isDomain| *1 (|MatrixManipulation| *5 *6 *7 *3)) (|ofCategory| *3 (|MatrixCategory| *5 *6 *7)))) (|blockSplit| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|List| (|PositiveInteger|))) (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *6 (|Field|)) (|ofCategory| *7 (|FiniteLinearAggregate| *6)) (|ofCategory| *8 (|FiniteLinearAggregate| *6)) (|isDomain| *2 (|List| (|List| *3))) (|isDomain| *1 (|MatrixManipulation| *6 *7 *8 *3)) (|ofCategory| *3 (|MatrixCategory| *6 *7 *8)))) (|blockSplit| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|List| (|PositiveInteger|))) (|isDomain| *5 (|PositiveInteger|)) (|ofCategory| *6 (|Field|)) (|ofCategory| *7 (|FiniteLinearAggregate| *6)) (|ofCategory| *8 (|FiniteLinearAggregate| *6)) (|isDomain| *2 (|List| (|List| *3))) (|isDomain| *1 (|MatrixManipulation| *6 *7 *8 *3)) (|ofCategory| *3 (|MatrixCategory| *6 *7 *8)))) (|blockSplit| (*1 *2 *3 *4 *4) (AND (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|FiniteLinearAggregate| *5)) (|ofCategory| *7 (|FiniteLinearAggregate| *5)) (|isDomain| *2 (|List| (|List| *3))) (|isDomain| *1 (|MatrixManipulation| *5 *6 *7 *3)) (|ofCategory| *3 (|MatrixCategory| *5 *6 *7)))) (|horizSplit| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| (|PositiveInteger|))) (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|FiniteLinearAggregate| *5)) (|ofCategory| *7 (|FiniteLinearAggregate| *5)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|MatrixManipulation| *5 *6 *7 *3)) (|ofCategory| *3 (|MatrixCategory| *5 *6 *7)))) (|horizSplit| (*1 *2 *3 *4) (AND (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|FiniteLinearAggregate| *5)) (|ofCategory| *7 (|FiniteLinearAggregate| *5)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|MatrixManipulation| *5 *6 *7 *3)) (|ofCategory| *3 (|MatrixCategory| *5 *6 *7)))) (|vertSplit| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| (|PositiveInteger|))) (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|FiniteLinearAggregate| *5)) (|ofCategory| *7 (|FiniteLinearAggregate| *5)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|MatrixManipulation| *5 *6 *7 *3)) (|ofCategory| *3 (|MatrixCategory| *5 *6 *7)))) (|vertSplit| (*1 *2 *3 *4) (AND (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|FiniteLinearAggregate| *5)) (|ofCategory| *7 (|FiniteLinearAggregate| *5)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|MatrixManipulation| *5 *6 *7 *3)) (|ofCategory| *3 (|MatrixCategory| *5 *6 *7)))) (|blockConcat| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|List| *2))) (|ofCategory| *4 (|Field|)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)) (|isDomain| *1 (|MatrixManipulation| *4 *5 *6 *2)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)))) (|vertConcat| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *4 (|Field|)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)) (|isDomain| *1 (|MatrixManipulation| *4 *5 *6 *2)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)))) (|horizConcat| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *4 (|Field|)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)) (|isDomain| *1 (|MatrixManipulation| *4 *5 *6 *2)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)))) (|bandMatrix| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Segment| (|Integer|))) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *1 (|MatrixManipulation| *4 *5 *6 *2)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)))) (|bandMatrix| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *1 (|MatrixManipulation| *4 *5 *6 *2)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)))) (|diagonalMatrix| (*1 *2 *2) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *1 (|MatrixManipulation| *3 *4 *5 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *4 *5)))) (|diagonalMatrix| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *1 (|MatrixManipulation| *4 *5 *6 *2)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)))) (|subMatrix| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 (|Segment| (|PositiveInteger|))) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *1 (|MatrixManipulation| *4 *5 *6 *2)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)))) (|subMatrix| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 (|List| (|PositiveInteger|))) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *1 (|MatrixManipulation| *4 *5 *6 *2)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)))) (|columns| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Segment| (|PositiveInteger|))) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *1 (|MatrixManipulation| *4 *5 *6 *2)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)))) (|columns| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| (|PositiveInteger|))) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *1 (|MatrixManipulation| *4 *5 *6 *2)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)))) (|aColumn| (*1 *2 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *1 (|MatrixManipulation| *4 *5 *6 *2)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)))) (|rows| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Segment| (|PositiveInteger|))) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *1 (|MatrixManipulation| *4 *5 *6 *2)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)))) (|rows| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| (|PositiveInteger|))) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *1 (|MatrixManipulation| *4 *5 *6 *2)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)))) (|aRow| (*1 *2 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *1 (|MatrixManipulation| *4 *5 *6 *2)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)))) (|element| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *1 (|MatrixManipulation| *4 *5 *6 *2)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6))))) 
(CATEGORY |package| (SIGNATURE |element| (|#4| |#4| (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |aRow| (|#4| |#4| (|PositiveInteger|))) (SIGNATURE |rows| (|#4| |#4| (|List| (|PositiveInteger|)))) (SIGNATURE |rows| (|#4| |#4| (|Segment| (|PositiveInteger|)))) (SIGNATURE |aColumn| (|#4| |#4| (|PositiveInteger|))) (SIGNATURE |columns| (|#4| |#4| (|List| (|PositiveInteger|)))) (SIGNATURE |columns| (|#4| |#4| (|Segment| (|PositiveInteger|)))) (SIGNATURE |subMatrix| (|#4| |#4| (|List| (|PositiveInteger|)) (|List| (|PositiveInteger|)))) (SIGNATURE |subMatrix| (|#4| |#4| (|Segment| (|PositiveInteger|)) (|Segment| (|PositiveInteger|)))) (SIGNATURE |diagonalMatrix| (|#4| |#4| (|Integer|))) (SIGNATURE |diagonalMatrix| (|#4| |#4|)) (SIGNATURE |bandMatrix| (|#4| |#4| (|List| (|Integer|)))) (SIGNATURE |bandMatrix| (|#4| |#4| (|Segment| (|Integer|)))) (SIGNATURE |horizConcat| (|#4| (|List| |#4|))) (SIGNATURE |vertConcat| (|#4| (|List| |#4|))) (SIGNATURE |blockConcat| (|#4| (|List| (|List| |#4|)))) (SIGNATURE |vertSplit| ((|List| |#4|) |#4| (|PositiveInteger|))) (SIGNATURE |vertSplit| ((|List| |#4|) |#4| (|List| (|PositiveInteger|)))) (SIGNATURE |horizSplit| ((|List| |#4|) |#4| (|PositiveInteger|))) (SIGNATURE |horizSplit| ((|List| |#4|) |#4| (|List| (|PositiveInteger|)))) (SIGNATURE |blockSplit| ((|List| (|List| |#4|)) |#4| (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |blockSplit| ((|List| (|List| |#4|)) |#4| (|List| (|PositiveInteger|)) (|PositiveInteger|))) (SIGNATURE |blockSplit| ((|List| (|List| |#4|)) |#4| (|PositiveInteger|) (|List| (|PositiveInteger|)))) (SIGNATURE |blockSplit| ((|List| (|List| |#4|)) |#4| (|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))))) 
((|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) 11)) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) 9))) 
(((|MappingPackageInternalHacks1| |#1|) (CATEGORY |package| (SIGNATURE |iter| (|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|)) (SIGNATURE |recur| (|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|))) (|SetCategory|)) (T |MappingPackageInternalHacks1|)) 
((|recur| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 (|NonNegativeInteger|) *2)) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *2 (|SetCategory|)) (|isDomain| *1 (|MappingPackageInternalHacks1| *2)))) (|iter| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *2)) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *2 (|SetCategory|)) (|isDomain| *1 (|MappingPackageInternalHacks1| *2))))) 
(CATEGORY |package| (SIGNATURE |iter| (|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|)) (SIGNATURE |recur| (|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|))) 
((|arg2| ((|#2| |#1| |#2|) 9)) (|arg1| ((|#1| |#1| |#2|) 8))) 
(((|MappingPackageInternalHacks2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |arg1| (|#1| |#1| |#2|)) (SIGNATURE |arg2| (|#2| |#1| |#2|))) (|SetCategory|) (|SetCategory|)) (T |MappingPackageInternalHacks2|)) 
((|arg2| (*1 *2 *3 *2) (AND (|isDomain| *1 (|MappingPackageInternalHacks2| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)))) (|arg1| (*1 *2 *2 *3) (AND (|isDomain| *1 (|MappingPackageInternalHacks2| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|))))) 
(CATEGORY |package| (SIGNATURE |arg1| (|#1| |#1| |#2|)) (SIGNATURE |arg2| (|#2| |#1| |#2|))) 
((|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) 11))) 
(((|MappingPackageInternalHacks3| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |comp| (|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|))) (|SetCategory|) (|SetCategory|) (|SetCategory|)) (T |MappingPackageInternalHacks3|)) 
((|comp| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *2 *6)) (|isDomain| *4 (|Mapping| *6 *5)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)) (|isDomain| *1 (|MappingPackageInternalHacks3| *5 *6 *2))))) 
(CATEGORY |package| (SIGNATURE |comp| (|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|))) 
((|recur| (((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)) 23)) (|nullary| (((|Mapping| |#1|) |#1|) 8)) (|id| ((|#1| |#1|) 16)) (|fixedPoint| (((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|)) 15) ((|#1| (|Mapping| |#1| |#1|)) 11)) (|coerce| (((|Mapping| |#1|) |#1|) 9)) (** (((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) 20))) 
(((|MappingPackage1| |#1|) (CATEGORY |package| (SIGNATURE |nullary| ((|Mapping| |#1|) |#1|)) (SIGNATURE |coerce| ((|Mapping| |#1|) |#1|)) (SIGNATURE |fixedPoint| (|#1| (|Mapping| |#1| |#1|))) (SIGNATURE |fixedPoint| ((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|))) (SIGNATURE |id| (|#1| |#1|)) (SIGNATURE ** ((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|))) (SIGNATURE |recur| ((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)))) (|SetCategory|)) (T |MappingPackage1|)) 
((|recur| (*1 *2 *2) (AND (|isDomain| *2 (|Mapping| *3 (|NonNegativeInteger|) *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|MappingPackage1| *3)))) (** (*1 *2 *2 *3) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *1 (|MappingPackage1| *4)))) (|id| (*1 *2 *2) (AND (|isDomain| *1 (|MappingPackage1| *2)) (|ofCategory| *2 (|SetCategory|)))) (|fixedPoint| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| (|List| *5) (|List| *5))) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|MappingPackage1| *5)) (|ofCategory| *5 (|SetCategory|)))) (|fixedPoint| (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| *2 *2)) (|isDomain| *1 (|MappingPackage1| *2)) (|ofCategory| *2 (|SetCategory|)))) (|coerce| (*1 *2 *3) (AND (|isDomain| *2 (|Mapping| *3)) (|isDomain| *1 (|MappingPackage1| *3)) (|ofCategory| *3 (|SetCategory|)))) (|nullary| (*1 *2 *3) (AND (|isDomain| *2 (|Mapping| *3)) (|isDomain| *1 (|MappingPackage1| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(CATEGORY |package| (SIGNATURE |nullary| ((|Mapping| |#1|) |#1|)) (SIGNATURE |coerce| ((|Mapping| |#1|) |#1|)) (SIGNATURE |fixedPoint| (|#1| (|Mapping| |#1| |#1|))) (SIGNATURE |fixedPoint| ((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|))) (SIGNATURE |id| (|#1| |#1|)) (SIGNATURE ** ((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|))) (SIGNATURE |recur| ((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)))) 
((|diag| (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) 16)) (|curry| (((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|) 13)) (|constant| (((|Mapping| |#2| |#1|) (|Mapping| |#2|)) 14)) (|const| (((|Mapping| |#2| |#1|) |#2|) 11))) 
(((|MappingPackage2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |const| ((|Mapping| |#2| |#1|) |#2|)) (SIGNATURE |curry| ((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|)) (SIGNATURE |constant| ((|Mapping| |#2| |#1|) (|Mapping| |#2|))) (SIGNATURE |diag| ((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)))) (|SetCategory|) (|SetCategory|)) (T |MappingPackage2|)) 
((|diag| (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| *5 *4 *4)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|isDomain| *2 (|Mapping| *5 *4)) (|isDomain| *1 (|MappingPackage2| *4 *5)))) (|constant| (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| *5)) (|ofCategory| *5 (|SetCategory|)) (|isDomain| *2 (|Mapping| *5 *4)) (|isDomain| *1 (|MappingPackage2| *4 *5)) (|ofCategory| *4 (|SetCategory|)))) (|curry| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *5 *4)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|isDomain| *2 (|Mapping| *5)) (|isDomain| *1 (|MappingPackage2| *4 *5)))) (|const| (*1 *2 *3) (AND (|isDomain| *2 (|Mapping| *3 *4)) (|isDomain| *1 (|MappingPackage2| *4 *3)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|))))) 
(CATEGORY |package| (SIGNATURE |const| ((|Mapping| |#2| |#1|) |#2|)) (SIGNATURE |curry| ((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|)) (SIGNATURE |constant| ((|Mapping| |#2| |#1|) (|Mapping| |#2|))) (SIGNATURE |diag| ((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)))) 
((|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) 17)) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) 11)) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) 13)) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) 14)) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) 15)) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) 21))) 
(((|MappingPackage3| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |curryRight| ((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|)) (SIGNATURE |curryLeft| ((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|)) (SIGNATURE |constantRight| ((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|))) (SIGNATURE |constantLeft| ((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|))) (SIGNATURE |twist| ((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|))) (SIGNATURE * ((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)))) (|SetCategory|) (|SetCategory|) (|SetCategory|)) (T |MappingPackage3|)) 
((* (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *7 *6)) (|isDomain| *4 (|Mapping| *6 *5)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Mapping| *7 *5)) (|isDomain| *1 (|MappingPackage3| *5 *6 *7)))) (|twist| (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| *6 *4 *5)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|isDomain| *2 (|Mapping| *6 *5 *4)) (|isDomain| *1 (|MappingPackage3| *4 *5 *6)))) (|constantLeft| (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|isDomain| *2 (|Mapping| *6 *4 *5)) (|isDomain| *1 (|MappingPackage3| *4 *5 *6)) (|ofCategory| *4 (|SetCategory|)))) (|constantRight| (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| *6 *4)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|isDomain| *2 (|Mapping| *6 *4 *5)) (|isDomain| *1 (|MappingPackage3| *4 *5 *6)) (|ofCategory| *5 (|SetCategory|)))) (|curryLeft| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *4 *5)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|isDomain| *2 (|Mapping| *6 *5)) (|isDomain| *1 (|MappingPackage3| *4 *5 *6)))) (|curryRight| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5 *4)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|isDomain| *2 (|Mapping| *6 *5)) (|isDomain| *1 (|MappingPackage3| *5 *4 *6))))) 
(CATEGORY |package| (SIGNATURE |curryRight| ((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|)) (SIGNATURE |curryLeft| ((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|)) (SIGNATURE |constantRight| ((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|))) (SIGNATURE |constantLeft| ((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|))) (SIGNATURE |twist| ((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|))) (SIGNATURE * ((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)))) 
((/ (((|Mapping| (|Expression| (|Integer|)) |#1|) (|Mapping| (|Expression| (|Integer|)) |#1|) (|Mapping| (|Expression| (|Integer|)) |#1|)) 18)) (- (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|)) 12)) (+ (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|)) 10)) (* (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|)) 14))) 
(((|MappingPackage4| |#1| |#2|) (CATEGORY |package| (SIGNATURE + ((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|))) (SIGNATURE - ((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|))) (SIGNATURE * ((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|))) (SIGNATURE / ((|Mapping| (|Expression| (|Integer|)) |#1|) (|Mapping| (|Expression| (|Integer|)) |#1|) (|Mapping| (|Expression| (|Integer|)) |#1|)))) (|SetCategory|) (|Ring|)) (T |MappingPackage4|)) 
((/ (*1 *2 *2 *2) (AND (|isDomain| *2 (|Mapping| (|Expression| (|Integer|)) *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|MappingPackage4| *3 *4)) (|ofCategory| *4 (|Ring|)))) (* (*1 *2 *2 *2) (AND (|isDomain| *2 (|Mapping| *4 *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|MappingPackage4| *3 *4)))) (- (*1 *2 *2 *2) (AND (|isDomain| *2 (|Mapping| *4 *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|MappingPackage4| *3 *4)))) (+ (*1 *2 *2 *2) (AND (|isDomain| *2 (|Mapping| *4 *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|MappingPackage4| *3 *4))))) 
(CATEGORY |package| (SIGNATURE + ((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|))) (SIGNATURE - ((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|))) (SIGNATURE * ((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|))) (SIGNATURE / ((|Mapping| (|Expression| (|Integer|)) |#1|) (|Mapping| (|Expression| (|Integer|)) |#1|) (|Mapping| (|Expression| (|Integer|)) |#1|)))) 
((|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) 39)) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) 37) ((|#8| (|Mapping| |#5| |#1|) |#4|) 31))) 
(((|MatrixCategoryFunctions2| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (CATEGORY |package| (SIGNATURE |map| (|#8| (|Mapping| |#5| |#1|) |#4|)) (SIGNATURE |map| ((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|)) (SIGNATURE |reduce| (|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|))) (|Ring|) (|FiniteLinearAggregate| |#1|) (|FiniteLinearAggregate| |#1|) (|MatrixCategory| |#1| |#2| |#3|) (|Ring|) (|FiniteLinearAggregate| |#5|) (|FiniteLinearAggregate| |#5|) (|MatrixCategory| |#5| |#6| |#7|)) (T |MatrixCategoryFunctions2|)) 
((|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *6 (|FiniteLinearAggregate| *5)) (|ofCategory| *7 (|FiniteLinearAggregate| *5)) (|ofCategory| *8 (|FiniteLinearAggregate| *2)) (|ofCategory| *9 (|FiniteLinearAggregate| *2)) (|isDomain| *1 (|MatrixCategoryFunctions2| *5 *6 *7 *4 *2 *8 *9 *10)) (|ofCategory| *4 (|MatrixCategory| *5 *6 *7)) (|ofCategory| *10 (|MatrixCategory| *2 *8 *9)))) (|map| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Mapping| (|Union| *8 "failed") *5)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *8 (|Ring|)) (|ofCategory| *6 (|FiniteLinearAggregate| *5)) (|ofCategory| *7 (|FiniteLinearAggregate| *5)) (|ofCategory| *2 (|MatrixCategory| *8 *9 *10)) (|isDomain| *1 (|MatrixCategoryFunctions2| *5 *6 *7 *4 *8 *9 *10 *2)) (|ofCategory| *4 (|MatrixCategory| *5 *6 *7)) (|ofCategory| *9 (|FiniteLinearAggregate| *8)) (|ofCategory| *10 (|FiniteLinearAggregate| *8)))) (|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *8 *5)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *8 (|Ring|)) (|ofCategory| *6 (|FiniteLinearAggregate| *5)) (|ofCategory| *7 (|FiniteLinearAggregate| *5)) (|ofCategory| *2 (|MatrixCategory| *8 *9 *10)) (|isDomain| *1 (|MatrixCategoryFunctions2| *5 *6 *7 *4 *8 *9 *10 *2)) (|ofCategory| *4 (|MatrixCategory| *5 *6 *7)) (|ofCategory| *9 (|FiniteLinearAggregate| *8)) (|ofCategory| *10 (|FiniteLinearAggregate| *8))))) 
(CATEGORY |package| (SIGNATURE |map| (|#8| (|Mapping| |#5| |#1|) |#4|)) (SIGNATURE |map| ((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|)) (SIGNATURE |reduce| (|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|))) 
((|zero?| (((|Boolean|) $) 30)) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) 32)) (|vertConcat| (($ $ $) 57)) (|transpose| (($ |#3|) 53) (($ $) 54)) (|symmetric?| (((|Boolean|) $) 26)) (|swapRows!| (($ $ (|Integer|) (|Integer|)) 59)) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) 60)) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) 64)) (|squareTop| (($ $) 55)) (|square?| (((|Boolean|) $) 14)) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) 65)) (|setelt| ((|#2| $ (|Integer|) (|Integer|) |#2|) NIL) (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) 63)) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) 39)) (|pfaffian| ((|#2| $) 108)) (|matrix| (($ (|List| (|List| |#2|))) 35) (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) 37)) (|listOfLists| (((|List| (|List| |#2|)) $) 58)) (|horizConcat| (($ $ $) 56)) (|exquo| (((|Union| $ "failed") $ |#2|) 111)) (|elt| ((|#2| $ (|Integer|) (|Integer|)) NIL) ((|#2| $ (|Integer|) (|Integer|) |#2|) NIL) (($ $ (|List| (|Integer|)) (|List| (|Integer|))) 62)) (|diagonalMatrix| (($ (|List| |#2|)) 41) (($ (|List| $)) 43)) (|diagonal?| (((|Boolean|) $) 23)) (|columnSpace| (((|List| |#4|) $) 94)) (|coerce| (((|OutputForm|) $) NIL) (($ |#4|) 48)) (|antisymmetric?| (((|Boolean|) $) 28)) (/ (($ $ |#2|) 113)) (- (($ $ $) 69) (($ $) 72)) (+ (($ $ $) 67)) (** (($ $ (|NonNegativeInteger|)) 81) (($ $ (|Integer|)) 116)) (* (($ $ $) 78) (($ |#2| $) 74) (($ $ |#2|) 75) (($ (|Integer|) $) 77) ((|#4| $ |#4|) 85) ((|#3| |#3| $) 89))) 
(((|MatrixCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE ** (|#1| |#1| (|Integer|))) (SIGNATURE |pfaffian| (|#2| |#1|)) (SIGNATURE |columnSpace| ((|List| |#4|) |#1|)) (SIGNATURE / (|#1| |#1| |#2|)) (SIGNATURE |exquo| ((|Union| |#1| "failed") |#1| |#2|)) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE * (|#3| |#3| |#1|)) (SIGNATURE * (|#4| |#1| |#4|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|)) (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE + (|#1| |#1| |#1|)) (SIGNATURE |setsubMatrix!| (|#1| |#1| (|Integer|) (|Integer|) |#1|)) (SIGNATURE |subMatrix| (|#1| |#1| (|Integer|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |swapColumns!| (|#1| |#1| (|Integer|) (|Integer|))) (SIGNATURE |swapRows!| (|#1| |#1| (|Integer|) (|Integer|))) (SIGNATURE |setelt| (|#1| |#1| (|List| (|Integer|)) (|List| (|Integer|)) |#1|)) (SIGNATURE |elt| (|#1| |#1| (|List| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |listOfLists| ((|List| (|List| |#2|)) |#1|)) (SIGNATURE |vertConcat| (|#1| |#1| |#1|)) (SIGNATURE |horizConcat| (|#1| |#1| |#1|)) (SIGNATURE |squareTop| (|#1| |#1|)) (SIGNATURE |transpose| (|#1| |#1|)) (SIGNATURE |transpose| (|#1| |#3|)) (SIGNATURE |coerce| (|#1| |#4|)) (SIGNATURE |diagonalMatrix| (|#1| (|List| |#1|))) (SIGNATURE |diagonalMatrix| (|#1| (|List| |#2|))) (SIGNATURE |scalarMatrix| (|#1| (|NonNegativeInteger|) |#2|)) (SIGNATURE |matrix| (|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|)))) (SIGNATURE |matrix| (|#1| (|List| (|List| |#2|)))) (SIGNATURE |zero| (|#1| (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |zero?| ((|Boolean|) |#1|)) (SIGNATURE |antisymmetric?| ((|Boolean|) |#1|)) (SIGNATURE |symmetric?| ((|Boolean|) |#1|)) (SIGNATURE |diagonal?| ((|Boolean|) |#1|)) (SIGNATURE |square?| ((|Boolean|) |#1|)) (SIGNATURE |setelt| (|#2| |#1| (|Integer|) (|Integer|) |#2|)) (SIGNATURE |elt| (|#2| |#1| (|Integer|) (|Integer|) |#2|)) (SIGNATURE |elt| (|#2| |#1| (|Integer|) (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|MatrixCategory| |#2| |#3| |#4|) (|Ring|) (|FiniteLinearAggregate| |#2|) (|FiniteLinearAggregate| |#2|)) (T |MatrixCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE ** (|#1| |#1| (|Integer|))) (SIGNATURE |pfaffian| (|#2| |#1|)) (SIGNATURE |columnSpace| ((|List| |#4|) |#1|)) (SIGNATURE / (|#1| |#1| |#2|)) (SIGNATURE |exquo| ((|Union| |#1| "failed") |#1| |#2|)) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE * (|#3| |#3| |#1|)) (SIGNATURE * (|#4| |#1| |#4|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|)) (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE + (|#1| |#1| |#1|)) (SIGNATURE |setsubMatrix!| (|#1| |#1| (|Integer|) (|Integer|) |#1|)) (SIGNATURE |subMatrix| (|#1| |#1| (|Integer|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |swapColumns!| (|#1| |#1| (|Integer|) (|Integer|))) (SIGNATURE |swapRows!| (|#1| |#1| (|Integer|) (|Integer|))) (SIGNATURE |setelt| (|#1| |#1| (|List| (|Integer|)) (|List| (|Integer|)) |#1|)) (SIGNATURE |elt| (|#1| |#1| (|List| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |listOfLists| ((|List| (|List| |#2|)) |#1|)) (SIGNATURE |vertConcat| (|#1| |#1| |#1|)) (SIGNATURE |horizConcat| (|#1| |#1| |#1|)) (SIGNATURE |squareTop| (|#1| |#1|)) (SIGNATURE |transpose| (|#1| |#1|)) (SIGNATURE |transpose| (|#1| |#3|)) (SIGNATURE |coerce| (|#1| |#4|)) (SIGNATURE |diagonalMatrix| (|#1| (|List| |#1|))) (SIGNATURE |diagonalMatrix| (|#1| (|List| |#2|))) (SIGNATURE |scalarMatrix| (|#1| (|NonNegativeInteger|) |#2|)) (SIGNATURE |matrix| (|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|)))) (SIGNATURE |matrix| (|#1| (|List| (|List| |#2|)))) (SIGNATURE |zero| (|#1| (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |zero?| ((|Boolean|) |#1|)) (SIGNATURE |antisymmetric?| ((|Boolean|) |#1|)) (SIGNATURE |symmetric?| ((|Boolean|) |#1|)) (SIGNATURE |diagonal?| ((|Boolean|) |#1|)) (SIGNATURE |square?| ((|Boolean|) |#1|)) (SIGNATURE |setelt| (|#2| |#1| (|Integer|) (|Integer|) |#2|)) (SIGNATURE |elt| (|#2| |#1| (|Integer|) (|Integer|) |#2|)) (SIGNATURE |elt| (|#2| |#1| (|Integer|) (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|zero?| (((|Boolean|) $) 96)) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) 95)) (|vertConcat| (($ $ $) 84)) (|transpose| (($ |#2|) 88) (($ $) 87)) (|symmetric?| (((|Boolean|) $) 98)) (|swapRows!| (($ $ (|Integer|) (|Integer|)) 80)) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) 79)) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) 78)) (|squareTop| (($ $) 86)) (|square?| (((|Boolean|) $) 100)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) 77)) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) 41) (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) 81)) (|setRow!| (($ $ (|Integer|) |#2|) 39)) (|setColumn!| (($ $ (|Integer|) |#3|) 38)) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) 92)) (|sample| (($) 7 T CONST)) (|rowEchelon| (($ $) 64 (|has| |#1| (|EuclideanDomain|)))) (|row| ((|#2| $ (|Integer|)) 43)) (|rank| (((|NonNegativeInteger|) $) 62 (|has| |#1| (|IntegralDomain|)))) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) 40)) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) 45)) (|pfaffian| ((|#1| $) 57 (|has| |#1| (|CommutativeRing|)))) (|parts| (((|List| |#1|) $) 30)) (|nullity| (((|NonNegativeInteger|) $) 61 (|has| |#1| (|IntegralDomain|)))) (|nullSpace| (((|List| |#3|) $) 60 (|has| |#1| (|IntegralDomain|)))) (|nrows| (((|NonNegativeInteger|) $) 48)) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) 54)) (|ncols| (((|NonNegativeInteger|) $) 47)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|minordet| ((|#1| $) 58 (|has| |#1| (ATTRIBUTE (|commutative| "*"))))) (|minRowIndex| (((|Integer|) $) 52)) (|minColIndex| (((|Integer|) $) 50)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|maxRowIndex| (((|Integer|) $) 51)) (|maxColIndex| (((|Integer|) $) 49)) (|matrix| (($ (|List| (|List| |#1|))) 94) (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) 93)) (|map!| (($ (|Mapping| |#1| |#1|) $) 34)) (|map| (($ (|Mapping| |#1| |#1|) $) 35) (($ (|Mapping| |#1| |#1| |#1|) $ $) 37) (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) 36)) (|listOfLists| (((|List| (|List| |#1|)) $) 83)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|inverse| (((|Union| $ "failed") $) 56 (|has| |#1| (|Field|)))) (|horizConcat| (($ $ $) 85)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|fill!| (($ $ |#1|) 53)) (|exquo| (((|Union| $ "failed") $ |#1|) 66 (|has| |#1| (|IntegralDomain|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| ((|#1| $ (|Integer|) (|Integer|)) 46) ((|#1| $ (|Integer|) (|Integer|) |#1|) 44) (($ $ (|List| (|Integer|)) (|List| (|Integer|))) 82)) (|diagonalMatrix| (($ (|List| |#1|)) 91) (($ (|List| $)) 90)) (|diagonal?| (((|Boolean|) $) 99)) (|determinant| ((|#1| $) 59 (|has| |#1| (ATTRIBUTE (|commutative| "*"))))) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|columnSpace| (((|List| |#3|) $) 63 (|has| |#1| (|EuclideanDomain|)))) (|column| ((|#3| $ (|Integer|)) 42)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|))) (($ |#3|) 89)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|antisymmetric?| (((|Boolean|) $) 97)) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (/ (($ $ |#1|) 65 (|has| |#1| (|Field|)))) (- (($ $ $) 75) (($ $) 74)) (+ (($ $ $) 76)) (** (($ $ (|NonNegativeInteger|)) 67) (($ $ (|Integer|)) 55 (|has| |#1| (|Field|)))) (* (($ $ $) 73) (($ |#1| $) 72) (($ $ |#1|) 71) (($ (|Integer|) $) 70) ((|#3| $ |#3|) 69) ((|#2| |#2| $) 68)) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|MatrixCategory| |#1| |#2| |#3|) (|Category|) (|Ring|) (|FiniteLinearAggregate| |t#1|) (|FiniteLinearAggregate| |t#1|)) (T |MatrixCategory|)) 
((|square?| (*1 *2 *1) (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|Boolean|)))) (|diagonal?| (*1 *2 *1) (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|Boolean|)))) (|symmetric?| (*1 *2 *1) (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|Boolean|)))) (|antisymmetric?| (*1 *2 *1) (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|Boolean|)))) (|zero?| (*1 *2 *1) (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|Boolean|)))) (|zero| (*1 *1 *2 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)))) (|matrix| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)))) (|matrix| (*1 *1 *2 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *3 (|Mapping| *4 (|Integer|) (|Integer|))) (|ofCategory| *4 (|Ring|)) (|ofCategory| *1 (|MatrixCategory| *4 *5 *6)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)))) (|scalarMatrix| (*1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)))) (|diagonalMatrix| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)))) (|diagonalMatrix| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)))) (|coerce| (*1 *1 *2) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *2 (|FiniteLinearAggregate| *3)))) (|transpose| (*1 *1 *2) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|MatrixCategory| *3 *2 *4)) (|ofCategory| *2 (|FiniteLinearAggregate| *3)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)))) (|transpose| (*1 *1 *1) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)))) (|squareTop| (*1 *1 *1) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)))) (|horizConcat| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)))) (|vertConcat| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)))) (|listOfLists| (*1 *2 *1) (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|List| (|List| *3))))) (|elt| (*1 *1 *1 *2 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)))) (|setelt| (*1 *1 *1 *2 *2 *1) (AND (|isDomain| *2 (|List| (|Integer|))) (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)))) (|swapRows!| (*1 *1 *1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)))) (|swapColumns!| (*1 *1 *1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)))) (|subMatrix| (*1 *1 *1 *2 *2 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)))) (|setsubMatrix!| (*1 *1 *1 *2 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)))) (+ (*1 *1 *1 *1) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)))) (- (*1 *1 *1 *1) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)))) (- (*1 *1 *1) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)))) (* (*1 *1 *1 *1) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)))) (* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)))) (* (*1 *1 *1 *2) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)))) (* (*1 *1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)))) (* (*1 *2 *1 *2) (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *2 (|FiniteLinearAggregate| *3)))) (* (*1 *2 *2 *1) (AND (|ofCategory| *1 (|MatrixCategory| *3 *2 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|FiniteLinearAggregate| *3)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)))) (** (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)))) (|exquo| (*1 *1 *1 *2) (|partial| AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (/ (*1 *1 *1 *2) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|Field|)))) (|rowEchelon| (*1 *1 *1) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|EuclideanDomain|)))) (|columnSpace| (*1 *2 *1) (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|EuclideanDomain|)) (|isDomain| *2 (|List| *5)))) (|rank| (*1 *2 *1) (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|nullity| (*1 *2 *1) (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|nullSpace| (*1 *2 *1) (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *5)))) (|determinant| (*1 *2 *1) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)) (|has| *2 (ATTRIBUTE (|commutative| "*"))) (|ofCategory| *2 (|Ring|)))) (|minordet| (*1 *2 *1) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)) (|has| *2 (ATTRIBUTE (|commutative| "*"))) (|ofCategory| *2 (|Ring|)))) (|pfaffian| (*1 *2 *1) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|CommutativeRing|)))) (|inverse| (*1 *1 *1) (|partial| AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|Field|)))) (** (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Field|))))) 
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(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|TwoDimensionalArrayCategory| |#1| |#2| |#3|) . T) ((|Type|) . T)) 
((|rowEchelon| ((|#4| |#4|) 67 (|has| |#1| (|EuclideanDomain|)))) (|rank| (((|NonNegativeInteger|) |#4|) 69 (|has| |#1| (|IntegralDomain|)))) (|nullity| (((|NonNegativeInteger|) |#4|) 71 (|has| |#1| (|IntegralDomain|)))) (|nullSpace| (((|List| |#3|) |#4|) 78 (|has| |#1| (|IntegralDomain|)))) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) 95 (|has| |#1| (|EuclideanDomain|)))) (|minordet| ((|#1| |#4|) 33)) (|invertIfCan| (((|Union| |#4| "failed") |#4|) 61 (|has| |#1| (|IntegralDomain|)))) (|inverse| (((|Union| |#4| "failed") |#4|) 75 (|has| |#1| (|Field|)))) (|fractionFreeGauss!| ((|#4| |#4|) 54 (|has| |#1| (|IntegralDomain|)))) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) 41)) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) 36)) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) 46)) (|determinant| ((|#1| |#4|) 73)) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) 57 (|has| |#1| (|IntegralDomain|))))) 
(((|MatrixLinearAlgebraFunctions| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |determinant| (|#1| |#4|)) (SIGNATURE |minordet| (|#1| |#4|)) (SIGNATURE |elRow1!| (|#4| |#4| (|Integer|) (|Integer|))) (SIGNATURE |elRow2!| (|#4| |#4| |#1| (|Integer|) (|Integer|))) (SIGNATURE |elColumn2!| (|#4| |#4| |#1| (|Integer|) (|Integer|))) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |rank| ((|NonNegativeInteger|) |#4|)) (SIGNATURE |nullity| ((|NonNegativeInteger|) |#4|)) (SIGNATURE |nullSpace| ((|List| |#3|) |#4|)) (SIGNATURE |fractionFreeGauss!| (|#4| |#4|)) (SIGNATURE |invertIfCan| ((|Union| |#4| "failed") |#4|)) (SIGNATURE |adjoint| ((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|))) |noBranch|) (IF (|has| |#1| (|EuclideanDomain|)) (PROGN (SIGNATURE |rowEchelon| (|#4| |#4|)) (SIGNATURE |normalizedDivide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|))) |noBranch|) (IF (|has| |#1| (|Field|)) (SIGNATURE |inverse| ((|Union| |#4| "failed") |#4|)) |noBranch|)) (|CommutativeRing|) (|FiniteLinearAggregate| |#1|) (|FiniteLinearAggregate| |#1|) (|MatrixCategory| |#1| |#2| |#3|)) (T |MatrixLinearAlgebraFunctions|)) 
((|inverse| (*1 *2 *2) (|partial| AND (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *3 *4 *5 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *4 *5)))) (|normalizedDivide| (*1 *2 *3 *3) (AND (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *3 *4 *5 *6)) (|ofCategory| *6 (|MatrixCategory| *3 *4 *5)))) (|rowEchelon| (*1 *2 *2) (AND (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *3 *4 *5 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *4 *5)))) (|adjoint| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *2 (|Record| (|:| |adjMat| *3) (|:| |detMat| *4))) (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *4 *5 *6 *3)) (|ofCategory| *3 (|MatrixCategory| *4 *5 *6)))) (|invertIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *3 *4 *5 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *4 *5)))) (|fractionFreeGauss!| (*1 *2 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *3 *4 *5 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *4 *5)))) (|nullSpace| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *2 (|List| *6)) (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *4 *5 *6 *3)) (|ofCategory| *3 (|MatrixCategory| *4 *5 *6)))) (|nullity| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *4 *5 *6 *3)) (|ofCategory| *3 (|MatrixCategory| *4 *5 *6)))) (|rank| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *4 *5 *6 *3)) (|ofCategory| *3 (|MatrixCategory| *4 *5 *6)))) (|elColumn2!| (*1 *2 *2 *3 *4 *4) (AND (|isDomain| *4 (|Integer|)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|ofCategory| *6 (|FiniteLinearAggregate| *3)) (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *3 *5 *6 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *5 *6)))) (|elRow2!| (*1 *2 *2 *3 *4 *4) (AND (|isDomain| *4 (|Integer|)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|ofCategory| *6 (|FiniteLinearAggregate| *3)) (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *3 *5 *6 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *5 *6)))) (|elRow1!| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *4 *5 *6 *2)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)))) (|minordet| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteLinearAggregate| *2)) (|ofCategory| *5 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *2 *4 *5 *3)) (|ofCategory| *3 (|MatrixCategory| *2 *4 *5)))) (|determinant| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteLinearAggregate| *2)) (|ofCategory| *5 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *2 *4 *5 *3)) (|ofCategory| *3 (|MatrixCategory| *2 *4 *5))))) 
(CATEGORY |package| (SIGNATURE |determinant| (|#1| |#4|)) (SIGNATURE |minordet| (|#1| |#4|)) (SIGNATURE |elRow1!| (|#4| |#4| (|Integer|) (|Integer|))) (SIGNATURE |elRow2!| (|#4| |#4| |#1| (|Integer|) (|Integer|))) (SIGNATURE |elColumn2!| (|#4| |#4| |#1| (|Integer|) (|Integer|))) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |rank| ((|NonNegativeInteger|) |#4|)) (SIGNATURE |nullity| ((|NonNegativeInteger|) |#4|)) (SIGNATURE |nullSpace| ((|List| |#3|) |#4|)) (SIGNATURE |fractionFreeGauss!| (|#4| |#4|)) (SIGNATURE |invertIfCan| ((|Union| |#4| "failed") |#4|)) (SIGNATURE |adjoint| ((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|))) |noBranch|) (IF (|has| |#1| (|EuclideanDomain|)) (PROGN (SIGNATURE |rowEchelon| (|#4| |#4|)) (SIGNATURE |normalizedDivide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|))) |noBranch|) (IF (|has| |#1| (|Field|)) (SIGNATURE |inverse| ((|Union| |#4| "failed") |#4|)) |noBranch|)) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|zero?| (((|Boolean|) $) NIL)) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) 45)) (|vertConcat| (($ $ $) NIL)) (|transpose| (($ (|Vector| |#1|)) NIL) (($ $) NIL)) (|symmetric?| (((|Boolean|) $) NIL)) (|swapRows!| (($ $ (|Integer|) (|Integer|)) 12)) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) NIL)) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) NIL)) (|squareTop| (($ $) NIL)) (|square?| (((|Boolean|) $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) NIL)) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) NIL) (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) NIL)) (|setRow!| (($ $ (|Integer|) (|Vector| |#1|)) NIL)) (|setColumn!| (($ $ (|Integer|) (|Vector| |#1|)) NIL)) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) 22)) (|sample| (($) NIL T CONST)) (|rowEchelon| (($ $) 30 (|has| |#1| (|EuclideanDomain|)))) (|row| (((|Vector| |#1|) $ (|Integer|)) NIL)) (|rank| (((|NonNegativeInteger|) $) 32 (|has| |#1| (|IntegralDomain|)))) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) 50)) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) NIL)) (|pfaffian| ((|#1| $) NIL (|has| |#1| (|CommutativeRing|)))) (|parts| (((|List| |#1|) $) NIL)) (|nullity| (((|NonNegativeInteger|) $) 34 (|has| |#1| (|IntegralDomain|)))) (|nullSpace| (((|List| (|Vector| |#1|)) $) 37 (|has| |#1| (|IntegralDomain|)))) (|nrows| (((|NonNegativeInteger|) $) 20)) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) NIL)) (|ncols| (((|NonNegativeInteger|) $) 21)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minordet| ((|#1| $) 28 (|has| |#1| (ATTRIBUTE (|commutative| "*"))))) (|minRowIndex| (((|Integer|) $) 9)) (|minColIndex| (((|Integer|) $) 10)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|maxRowIndex| (((|Integer|) $) 11)) (|maxColIndex| (((|Integer|) $) 46)) (|matrix| (($ (|List| (|List| |#1|))) NIL) (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) NIL)) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) NIL)) (|listOfLists| (((|List| (|List| |#1|)) $) 58)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|inverse| (((|Union| $ "failed") $) 41 (|has| |#1| (|Field|)))) (|horizConcat| (($ $ $) NIL)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|fill!| (($ $ |#1|) NIL)) (|exquo| (((|Union| $ "failed") $ |#1|) NIL (|has| |#1| (|IntegralDomain|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#1| $ (|Integer|) (|Integer|)) NIL) ((|#1| $ (|Integer|) (|Integer|) |#1|) NIL) (($ $ (|List| (|Integer|)) (|List| (|Integer|))) NIL)) (|diagonalMatrix| (($ (|List| |#1|)) NIL) (($ (|List| $)) NIL) (($ (|Vector| |#1|)) 51)) (|diagonal?| (((|Boolean|) $) NIL)) (|determinant| ((|#1| $) 26 (|has| |#1| (ATTRIBUTE (|commutative| "*"))))) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) 62 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|columnSpace| (((|List| (|Vector| |#1|)) $) NIL (|has| |#1| (|EuclideanDomain|)))) (|column| (((|Vector| |#1|) $ (|Integer|)) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|))) (($ (|Vector| |#1|)) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|antisymmetric?| (((|Boolean|) $) NIL)) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (/ (($ $ |#1|) NIL (|has| |#1| (|Field|)))) (- (($ $ $) NIL) (($ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|NonNegativeInteger|)) 23) (($ $ (|Integer|)) 44 (|has| |#1| (|Field|)))) (* (($ $ $) 13) (($ |#1| $) NIL) (($ $ |#1|) NIL) (($ (|Integer|) $) NIL) (((|Vector| |#1|) $ (|Vector| |#1|)) NIL) (((|Vector| |#1|) (|Vector| |#1|) $) NIL)) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|Matrix| |#1|) (|Join| (|MatrixCategory| |#1| (|Vector| |#1|) (|Vector| |#1|)) (CATEGORY |domain| (SIGNATURE |diagonalMatrix| ($ (|Vector| |#1|))) (IF (|has| |#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |noBranch|) (IF (|has| |#1| (|Field|)) (SIGNATURE |inverse| ((|Union| $ "failed") $)) |noBranch|))) (|Ring|)) (T |Matrix|)) 
((|inverse| (*1 *1 *1) (|partial| AND (|isDomain| *1 (|Matrix| *2)) (|ofCategory| *2 (|Field|)) (|ofCategory| *2 (|Ring|)))) (|diagonalMatrix| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|Matrix| *3))))) 
(|Join| (|MatrixCategory| |#1| (|Vector| |#1|) (|Vector| |#1|)) (CATEGORY |domain| (SIGNATURE |diagonalMatrix| ($ (|Vector| |#1|))) (IF (|has| |#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |noBranch|) (IF (|has| |#1| (|Field|)) (SIGNATURE |inverse| ((|Union| $ "failed") $)) |noBranch|))) 
((|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) 25)) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) 21)) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) 26)) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) 14)) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) 18) (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) 16)) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) 20)) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) 12)) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) 30))) 
(((|StorageEfficientMatrixOperations| |#1|) (CATEGORY |package| (SIGNATURE |copy!| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |plus!| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |minus!| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |minus!| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |leftScalarTimes!| ((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|))) (SIGNATURE |rightScalarTimes!| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|)) (SIGNATURE |times!| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |power!| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|))) (SIGNATURE ** ((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)))) (|Ring|)) (T |StorageEfficientMatrixOperations|)) 
((** (*1 *2 *2 *3) (AND (|isDomain| *2 (|Matrix| *4)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|StorageEfficientMatrixOperations| *4)))) (|power!| (*1 *2 *2 *2 *2 *2 *3) (AND (|isDomain| *2 (|Matrix| *4)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|StorageEfficientMatrixOperations| *4)))) (|times!| (*1 *2 *2 *2 *2) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|StorageEfficientMatrixOperations| *3)))) (|rightScalarTimes!| (*1 *2 *2 *2 *3) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|StorageEfficientMatrixOperations| *3)))) (|leftScalarTimes!| (*1 *2 *2 *3 *2) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|StorageEfficientMatrixOperations| *3)))) (|minus!| (*1 *2 *2 *2 *2) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|StorageEfficientMatrixOperations| *3)))) (|minus!| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|StorageEfficientMatrixOperations| *3)))) (|plus!| (*1 *2 *2 *2 *2) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|StorageEfficientMatrixOperations| *3)))) (|copy!| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|StorageEfficientMatrixOperations| *3))))) 
(CATEGORY |package| (SIGNATURE |copy!| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |plus!| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |minus!| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |minus!| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |leftScalarTimes!| ((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|))) (SIGNATURE |rightScalarTimes!| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|)) (SIGNATURE |times!| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |power!| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|))) (SIGNATURE ** ((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)))) 
((|laplacian| ((|#2| |#2| |#4|) 25)) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) 31)) (|hessian| (((|Matrix| |#2|) |#2| |#4|) 30)) (|gradient| (((|Vector| |#2|) |#2| |#4|) 16)) (|divergence| ((|#2| |#3| |#4|) 24)) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) 38)) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) 37))) 
(((|MultiVariableCalculusFunctions| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |gradient| ((|Vector| |#2|) |#2| |#4|)) (SIGNATURE |divergence| (|#2| |#3| |#4|)) (SIGNATURE |laplacian| (|#2| |#2| |#4|)) (SIGNATURE |hessian| ((|Matrix| |#2|) |#2| |#4|)) (SIGNATURE |bandedHessian| ((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|))) (SIGNATURE |jacobian| ((|Matrix| |#2|) |#3| |#4|)) (SIGNATURE |bandedJacobian| ((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)))) (|SetCategory|) (|PartialDifferentialRing| |#1|) (|FiniteLinearAggregate| |#2|) (|Join| (|FiniteLinearAggregate| |#1|) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|)))) (T |MultiVariableCalculusFunctions|)) 
((|bandedJacobian| (*1 *2 *3 *4 *5 *5) (AND (|isDomain| *5 (|NonNegativeInteger|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *7 (|PartialDifferentialRing| *6)) (|isDomain| *2 (|Matrix| *7)) (|isDomain| *1 (|MultiVariableCalculusFunctions| *6 *7 *3 *4)) (|ofCategory| *3 (|FiniteLinearAggregate| *7)) (|ofCategory| *4 (|Join| (|FiniteLinearAggregate| *6) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|)))))) (|jacobian| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|PartialDifferentialRing| *5)) (|isDomain| *2 (|Matrix| *6)) (|isDomain| *1 (|MultiVariableCalculusFunctions| *5 *6 *3 *4)) (|ofCategory| *3 (|FiniteLinearAggregate| *6)) (|ofCategory| *4 (|Join| (|FiniteLinearAggregate| *5) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|)))))) (|bandedHessian| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|NonNegativeInteger|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *3 (|PartialDifferentialRing| *6)) (|isDomain| *2 (|Matrix| *3)) (|isDomain| *1 (|MultiVariableCalculusFunctions| *6 *3 *7 *4)) (|ofCategory| *7 (|FiniteLinearAggregate| *3)) (|ofCategory| *4 (|Join| (|FiniteLinearAggregate| *6) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|)))))) (|hessian| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *3 (|PartialDifferentialRing| *5)) (|isDomain| *2 (|Matrix| *3)) (|isDomain| *1 (|MultiVariableCalculusFunctions| *5 *3 *6 *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *3)) (|ofCategory| *4 (|Join| (|FiniteLinearAggregate| *5) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|)))))) (|laplacian| (*1 *2 *2 *3) (AND (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *2 (|PartialDifferentialRing| *4)) (|isDomain| *1 (|MultiVariableCalculusFunctions| *4 *2 *5 *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *2)) (|ofCategory| *3 (|Join| (|FiniteLinearAggregate| *4) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|)))))) (|divergence| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *2 (|PartialDifferentialRing| *5)) (|isDomain| *1 (|MultiVariableCalculusFunctions| *5 *2 *3 *4)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|Join| (|FiniteLinearAggregate| *5) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|)))))) (|gradient| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *3 (|PartialDifferentialRing| *5)) (|isDomain| *2 (|Vector| *3)) (|isDomain| *1 (|MultiVariableCalculusFunctions| *5 *3 *6 *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *3)) (|ofCategory| *4 (|Join| (|FiniteLinearAggregate| *5) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|))))))) 
(CATEGORY |package| (SIGNATURE |gradient| ((|Vector| |#2|) |#2| |#4|)) (SIGNATURE |divergence| (|#2| |#3| |#4|)) (SIGNATURE |laplacian| (|#2| |#2| |#4|)) (SIGNATURE |hessian| ((|Matrix| |#2|) |#2| |#4|)) (SIGNATURE |bandedHessian| ((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|))) (SIGNATURE |jacobian| ((|Matrix| |#2|) |#3| |#4|)) (SIGNATURE |bandedJacobian| ((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)))) 
((|splitDenominator| (((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)) 18)) (|commonDenominator| ((|#1| (|Matrix| |#2|)) 9)) (|clearDenominator| (((|Matrix| |#1|) (|Matrix| |#2|)) 16))) 
(((|MatrixCommonDenominator| |#1| |#2|) (CATEGORY |package| (SIGNATURE |commonDenominator| (|#1| (|Matrix| |#2|))) (SIGNATURE |clearDenominator| ((|Matrix| |#1|) (|Matrix| |#2|))) (SIGNATURE |splitDenominator| ((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)))) (|IntegralDomain|) (|QuotientFieldCategory| |#1|)) (T |MatrixCommonDenominator|)) 
((|splitDenominator| (*1 *2 *3) (AND (|isDomain| *3 (|Matrix| *5)) (|ofCategory| *5 (|QuotientFieldCategory| *4)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |num| (|Matrix| *4)) (|:| |den| *4))) (|isDomain| *1 (|MatrixCommonDenominator| *4 *5)))) (|clearDenominator| (*1 *2 *3) (AND (|isDomain| *3 (|Matrix| *5)) (|ofCategory| *5 (|QuotientFieldCategory| *4)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|MatrixCommonDenominator| *4 *5)))) (|commonDenominator| (*1 *2 *3) (AND (|isDomain| *3 (|Matrix| *4)) (|ofCategory| *4 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|isDomain| *1 (|MatrixCommonDenominator| *2 *4))))) 
(CATEGORY |package| (SIGNATURE |commonDenominator| (|#1| (|Matrix| |#2|))) (SIGNATURE |clearDenominator| ((|Matrix| |#1|) (|Matrix| |#2|))) (SIGNATURE |splitDenominator| ((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|traceMatrix| (((|Matrix| (|MachineFloat|))) NIL) (((|Matrix| (|MachineFloat|)) (|Vector| $)) NIL)) (|trace| (((|MachineFloat|) $) NIL)) (|tanh| (($ $) NIL (|has| (|MachineFloat|) (|TranscendentalFunctionCategory|)))) (|tan| (($ $) NIL (|has| (|MachineFloat|) (|TranscendentalFunctionCategory|)))) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) NIL (|has| (|MachineFloat|) (|FiniteFieldCategory|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (AND (|has| (|MachineFloat|) (|EuclideanDomain|)) (|has| (|MachineFloat|) (|PolynomialFactorizationExplicit|))))) (|squareFreePart| (($ $) NIL (OR (AND (|has| 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(|nextItem| (((|Union| $ "failed") $) NIL (|has| (|MachineFloat|) (|FiniteFieldCategory|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| (|MachineFloat|) (|EuclideanDomain|)))) (|minimalPolynomial| (((|SparseUnivariatePolynomial| (|MachineFloat|)) $) NIL (|has| (|MachineFloat|) (|Field|)))) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|map| (($ (|Mapping| (|MachineFloat|) (|MachineFloat|)) $) NIL)) (|lookup| (((|PositiveInteger|) $) NIL (|has| (|MachineFloat|) (|Finite|)))) (|log| (($ $) NIL (|has| (|MachineFloat|) (|TranscendentalFunctionCategory|)))) (|lift| (((|SparseUnivariatePolynomial| (|MachineFloat|)) $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| (|MachineFloat|) (|EuclideanDomain|)))) (|lcm| (($ (|List| $)) NIL (|has| (|MachineFloat|) (|EuclideanDomain|))) (($ $ $) NIL (|has| (|MachineFloat|) (|EuclideanDomain|)))) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL (|has| (|MachineFloat|) 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(((|MachineComplex|) (|Join| (|FortranMachineTypeCategory|) (|ComplexCategory| (|MachineFloat|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Complex| (|Float|)))) (SIGNATURE |coerce| ($ (|Complex| (|Integer|)))) (SIGNATURE |coerce| ($ (|Complex| (|MachineFloat|)))) (SIGNATURE |coerce| ($ (|Complex| (|MachineInteger|)))) (SIGNATURE |coerce| ((|Complex| (|Float|)) $))))) (T |MachineComplex|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|MachineComplex|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Complex| (|Integer|))) (|isDomain| *1 (|MachineComplex|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Complex| (|MachineFloat|))) (|isDomain| *1 (|MachineComplex|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Complex| (|MachineInteger|))) (|isDomain| *1 (|MachineComplex|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|MachineComplex|))))) 
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((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) 42 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 52 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) 7 T CONST)) (|removeDuplicates!| (($ $) 58)) (|removeDuplicates| (($ $) 55 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove!| (($ |#1| $) 44 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) |#1|) $) 43 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remove| (($ |#1| $) 54 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#1|) $) 51 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 53 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 50 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 49 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|inspect| ((|#1| $) 36)) (|insert!| (($ |#1| $) 37) (($ |#1| $ (|NonNegativeInteger|)) 59)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) 48)) (|extract!| ((|#1| $) 38)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) 57)) (|dictionary| (($) 46) (($ (|List| |#1|)) 45)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|convert| (((|InputForm|) $) 56 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 47)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|bag| (($ (|List| |#1|)) 39)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|MultiDictionary| |#1|) (|Category|) (|SetCategory|)) (T |MultiDictionary|)) 
((|insert!| (*1 *1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|MultiDictionary| *2)) (|ofCategory| *2 (|SetCategory|)))) (|removeDuplicates!| (*1 *1 *1) (AND (|ofCategory| *1 (|MultiDictionary| *2)) (|ofCategory| *2 (|SetCategory|)))) (|duplicates| (*1 *2 *1) (AND (|ofCategory| *1 (|MultiDictionary| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|List| (|Record| (|:| |entry| *3) (|:| |count| (|NonNegativeInteger|)))))))) 
(|Join| (|DictionaryOperations| |t#1|) (CATEGORY |domain| (SIGNATURE |insert!| ($ |t#1| $ (|NonNegativeInteger|))) (SIGNATURE |removeDuplicates!| ($ $)) (SIGNATURE |duplicates| ((|List| (|Record| (|:| |entry| |t#1|) (|:| |count| (|NonNegativeInteger|)))) $)))) 
(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) 46)) (|linears| ((|#1| |#1| (|Integer|)) 45)) (|gcd| ((|#1| |#1| |#1| (|Integer|)) 35)) (|factor| (((|List| |#1|) |#1| (|Integer|)) 38)) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) 32)) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) 44))) 
(((|ModularDistinctDegreeFactorizer| |#1|) (CATEGORY |package| (SIGNATURE |gcd| (|#1| |#1| |#1| (|Integer|))) (SIGNATURE |linears| (|#1| |#1| (|Integer|))) (SIGNATURE |factor| ((|List| |#1|) |#1| (|Integer|))) (SIGNATURE |ddFact| ((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|))) (SIGNATURE |separateFactors| ((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|))) (SIGNATURE |exptMod| (|#1| |#1| (|Integer|) |#1| (|Integer|)))) (|UnivariatePolynomialCategory| (|Integer|))) (T |ModularDistinctDegreeFactorizer|)) 
((|exptMod| (*1 *2 *2 *3 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|ModularDistinctDegreeFactorizer| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|separateFactors| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Record| (|:| |factor| *5) (|:| |degree| (|Integer|))))) (|isDomain| *4 (|Integer|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|ModularDistinctDegreeFactorizer| *5)))) (|ddFact| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|List| (|Record| (|:| |factor| *3) (|:| |degree| *4)))) (|isDomain| *1 (|ModularDistinctDegreeFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|factor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|ModularDistinctDegreeFactorizer| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|linears| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|ModularDistinctDegreeFactorizer| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|gcd| (*1 *2 *2 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|ModularDistinctDegreeFactorizer| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(CATEGORY |package| (SIGNATURE |gcd| (|#1| |#1| |#1| (|Integer|))) (SIGNATURE |linears| (|#1| |#1| (|Integer|))) (SIGNATURE |factor| ((|List| |#1|) |#1| (|Integer|))) (SIGNATURE |ddFact| ((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|))) (SIGNATURE |separateFactors| ((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|))) (SIGNATURE |exptMod| (|#1| |#1| (|Integer|) |#1| (|Integer|)))) 
((|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) 17)) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) 38) (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) 40) (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) 42)) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) NIL)) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) 43))) 
(((|MeshCreationRoutinesForThreeDimensions|) (CATEGORY |package| (SIGNATURE |meshPar2Var| ((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|)))) (SIGNATURE |meshPar2Var| ((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|)))) (SIGNATURE |meshPar2Var| ((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|)))) (SIGNATURE |meshFun2Var| ((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|)))) (SIGNATURE |meshPar1Var| ((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|)))) (SIGNATURE |ptFunc| ((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)))))) (T |MeshCreationRoutinesForThreeDimensions|)) 
((|ptFunc| (*1 *2 *3 *3 *3 *4) (AND (|isDomain| *3 (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|isDomain| *4 (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|isDomain| *2 (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|))) (|isDomain| *1 (|MeshCreationRoutinesForThreeDimensions|)))) (|meshPar1Var| (*1 *2 *3 *3 *3 *4 *5 *6) (AND (|isDomain| *3 (|Expression| (|Integer|))) (|isDomain| *4 (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|isDomain| *5 (|Segment| (|DoubleFloat|))) (|isDomain| *6 (|List| (|DrawOption|))) (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|))) (|isDomain| *1 (|MeshCreationRoutinesForThreeDimensions|)))) (|meshFun2Var| (*1 *2 *3 *4 *5 *5 *6) (AND (|isDomain| *3 (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|isDomain| *4 (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined")) (|isDomain| *5 (|Segment| (|DoubleFloat|))) (|isDomain| *6 (|List| (|DrawOption|))) (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|))) (|isDomain| *1 (|MeshCreationRoutinesForThreeDimensions|)))) (|meshPar2Var| (*1 *2 *2 *3 *4 *4 *5) (AND (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|))) (|isDomain| *3 (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|))) (|isDomain| *4 (|Segment| (|DoubleFloat|))) (|isDomain| *5 (|List| (|DrawOption|))) (|isDomain| *1 (|MeshCreationRoutinesForThreeDimensions|)))) (|meshPar2Var| (*1 *2 *3 *4 *4 *5) (AND (|isDomain| *3 (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|))) (|isDomain| *4 (|Segment| (|DoubleFloat|))) (|isDomain| *5 (|List| (|DrawOption|))) (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|))) (|isDomain| *1 (|MeshCreationRoutinesForThreeDimensions|)))) (|meshPar2Var| (*1 *2 *3 *3 *3 *4 *5 *5 *6) (AND (|isDomain| *3 (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|isDomain| *4 (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined")) (|isDomain| *5 (|Segment| (|DoubleFloat|))) (|isDomain| *6 (|List| (|DrawOption|))) (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|))) (|isDomain| *1 (|MeshCreationRoutinesForThreeDimensions|))))) 
(CATEGORY |package| (SIGNATURE |meshPar2Var| ((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|)))) (SIGNATURE |meshPar2Var| ((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|)))) (SIGNATURE |meshPar2Var| ((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|)))) (SIGNATURE |meshFun2Var| ((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|)))) (SIGNATURE |meshPar1Var| ((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|)))) (SIGNATURE |ptFunc| ((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))))) 
((|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) 73) (((|Factored| |#4|) |#4|) 215))) 
(((|MultFiniteFactorize| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4|)) (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)))) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|FiniteFieldCategory|) (|PolynomialCategory| |#3| |#2| |#1|)) (T |MultFiniteFactorize|)) 
((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|FiniteFieldCategory|)) (|ofCategory| *7 (|PolynomialCategory| *6 *5 *4)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *7))) (|isDomain| *1 (|MultFiniteFactorize| *4 *5 *6 *7)) (|isDomain| *3 (|SparseUnivariatePolynomial| *7)))) (|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|FiniteFieldCategory|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|MultFiniteFactorize| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *6 *5 *4))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4|)) (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 84)) (|wholePart| (((|Integer|) $) 30)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|truncate| (($ $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sqrt| (($ $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sign| (((|Integer|) $) NIL)) (|sample| (($) NIL T CONST)) (|round| (($ $) NIL)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 73) (((|Union| (|Fraction| (|Integer|)) "failed") $) 26) (((|Union| (|Float|) "failed") $) 70)) (|retract| (((|Integer|) $) 75) (((|Fraction| (|Integer|)) $) 67) (((|Float|) $) 68)) (|rem| (($ $ $) 96)) (|recip| (((|Union| $ "failed") $) 87)) (|quo| (($ $ $) 95)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|precision| (((|PositiveInteger|)) 77) (((|PositiveInteger|) (|PositiveInteger|)) 76)) (|positive?| (((|Boolean|) $) NIL)) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL)) (|order| (((|Integer|) $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|nthRoot| (($ $ (|Integer|)) NIL)) (|norm| (($ $) NIL)) (|negative?| (((|Boolean|) $) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|minimumExponent| (((|Integer|) (|Integer|)) 81) (((|Integer|)) 82)) (|min| (($ $ $) NIL) (($) NIL (AND (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|))) (|not| (|has| $ (ATTRIBUTE |arbitraryPrecision|)))))) (|maximumExponent| (((|Integer|) (|Integer|)) 79) (((|Integer|)) 80)) (|max| (($ $ $) NIL) (($) NIL (AND (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|))) (|not| (|has| $ (ATTRIBUTE |arbitraryPrecision|)))))) (|mantissa| (((|Integer|) $) 16)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 91)) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |arbitraryPrecision|)))) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|fractionPart| (($ $) NIL)) (|floor| (($ $) NIL)) (|float| (($ (|Integer|) (|Integer|)) NIL) (($ (|Integer|) (|Integer|) (|PositiveInteger|)) NIL)) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) 92)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|exponent| (((|Integer|) $) 22)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 94)) (|digits| (((|PositiveInteger|)) NIL) (((|PositiveInteger|) (|PositiveInteger|)) NIL (|has| $ (ATTRIBUTE |arbitraryPrecision|)))) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |arbitraryPrecision|)))) (|convert| (((|Float|) $) NIL) (((|DoubleFloat|) $) NIL) (((|Pattern| (|Float|)) $) NIL)) (|coerce| (((|OutputForm|) $) 52) (($ (|Integer|)) 63) (($ $) NIL) (($ (|Fraction| (|Integer|))) 66) (($ (|Integer|)) 63) (($ (|Fraction| (|Integer|))) 66) (($ (|Float|)) 60) (((|Float|) $) 50) (($ (|MachineInteger|)) 55)) (|characteristic| (((|NonNegativeInteger|)) 103)) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) 44)) (|ceiling| (($ $) NIL)) (|bits| (((|PositiveInteger|)) NIL) (((|PositiveInteger|) (|PositiveInteger|)) NIL (|has| $ (ATTRIBUTE |arbitraryPrecision|)))) (|base| (((|PositiveInteger|)) 35) (((|PositiveInteger|) (|PositiveInteger|)) 78)) (|associates?| (((|Boolean|) $ $) NIL)) (|abs| (($ $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) 32 T CONST)) (|One| (($) 17 T CONST)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 83)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 101)) (/ (($ $ $) 65)) (- (($ $) 99) (($ $ $) 100)) (+ (($ $ $) 98)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL) (($ $ (|Fraction| (|Integer|))) 90)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 97) (($ $ $) 88) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL))) 
(((|MachineFloat|) (|Join| (|FloatingPointSystem|) (|FortranMachineTypeCategory|) (|Field|) (|RetractableTo| (|Float|)) (|RetractableTo| (|Fraction| (|Integer|))) (|CharacteristicZero|) (CATEGORY |domain| (SIGNATURE |precision| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |precision| ((|PositiveInteger|))) (SIGNATURE |base| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |base| ((|PositiveInteger|))) (SIGNATURE |maximumExponent| ((|Integer|) (|Integer|))) (SIGNATURE |maximumExponent| ((|Integer|))) (SIGNATURE |minimumExponent| ((|Integer|) (|Integer|))) (SIGNATURE |minimumExponent| ((|Integer|))) (SIGNATURE |coerce| ((|Float|) $)) (SIGNATURE |coerce| ($ (|MachineInteger|))) (SIGNATURE |mantissa| ((|Integer|) $)) (SIGNATURE |exponent| ((|Integer|) $)) (SIGNATURE |changeBase| ($ (|Integer|) (|Integer|) (|PositiveInteger|)))))) (T |MachineFloat|)) 
((|base| (*1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|MachineFloat|)))) (|exponent| (*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|MachineFloat|)))) (|mantissa| (*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|MachineFloat|)))) (|precision| (*1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|MachineFloat|)))) (|precision| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|MachineFloat|)))) (|base| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|MachineFloat|)))) (|maximumExponent| (*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|MachineFloat|)))) (|maximumExponent| (*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|MachineFloat|)))) (|minimumExponent| (*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|MachineFloat|)))) (|minimumExponent| (*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|MachineFloat|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|MachineFloat|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|MachineInteger|)) (|isDomain| *1 (|MachineFloat|)))) (|changeBase| (*1 *1 *2 *2 *3) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *1 (|MachineFloat|))))) 
(|Join| (|FloatingPointSystem|) (|FortranMachineTypeCategory|) (|Field|) (|RetractableTo| (|Float|)) (|RetractableTo| (|Fraction| (|Integer|))) (|CharacteristicZero|) (CATEGORY |domain| (SIGNATURE |precision| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |precision| ((|PositiveInteger|))) (SIGNATURE |base| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |base| ((|PositiveInteger|))) (SIGNATURE |maximumExponent| ((|Integer|) (|Integer|))) (SIGNATURE |maximumExponent| ((|Integer|))) (SIGNATURE |minimumExponent| ((|Integer|) (|Integer|))) (SIGNATURE |minimumExponent| ((|Integer|))) (SIGNATURE |coerce| ((|Float|) $)) (SIGNATURE |coerce| ($ (|MachineInteger|))) (SIGNATURE |mantissa| ((|Integer|) $)) (SIGNATURE |exponent| ((|Integer|) $)) (SIGNATURE |changeBase| ($ (|Integer|) (|Integer|) (|PositiveInteger|))))) 
((|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) 66)) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) 49)) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) 67)) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) 50)) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) 65))) 
(((|ModularHermitianRowReduction| |#1|) (CATEGORY |package| (SIGNATURE |rowEch| ((|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |rowEchelon| ((|Matrix| |#1|) (|Matrix| |#1|) |#1|)) (SIGNATURE |rowEchLocal| ((|Matrix| |#1|) (|Matrix| |#1|) |#1|)) (SIGNATURE |rowEchelonLocal| ((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|)) (SIGNATURE |normalizedDivide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|))) (|EuclideanDomain|)) (T |ModularHermitianRowReduction|)) 
((|normalizedDivide| (*1 *2 *3 *3) (AND (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) (|isDomain| *1 (|ModularHermitianRowReduction| *3)) (|ofCategory| *3 (|EuclideanDomain|)))) (|rowEchelonLocal| (*1 *2 *2 *3 *3) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|EuclideanDomain|)) (|isDomain| *1 (|ModularHermitianRowReduction| *3)))) (|rowEchLocal| (*1 *2 *2 *3) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|EuclideanDomain|)) (|isDomain| *1 (|ModularHermitianRowReduction| *3)))) (|rowEchelon| (*1 *2 *2 *3) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|EuclideanDomain|)) (|isDomain| *1 (|ModularHermitianRowReduction| *3)))) (|rowEch| (*1 *2 *2) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|EuclideanDomain|)) (|isDomain| *1 (|ModularHermitianRowReduction| *3))))) 
(CATEGORY |package| (SIGNATURE |rowEch| ((|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |rowEchelon| ((|Matrix| |#1|) (|Matrix| |#1|) |#1|)) (SIGNATURE |rowEchLocal| ((|Matrix| |#1|) (|Matrix| |#1|) |#1|)) (SIGNATURE |rowEchelonLocal| ((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|)) (SIGNATURE |normalizedDivide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|symmetricRemainder| (($ $ $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|submod| (($ $ $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sign| (((|Integer|) $) NIL)) (|shift| (($ $ $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 27)) (|retract| (((|Integer|) $) 25)) (|rem| (($ $ $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL)) (|rational?| (((|Boolean|) $) NIL)) (|rational| (((|Fraction| (|Integer|)) $) NIL)) (|random| (($ $) NIL) (($) NIL)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|powmod| (($ $ $ $) NIL)) (|positiveRemainder| (($ $ $) NIL)) (|positive?| (((|Boolean|) $) NIL)) (|permutation| (($ $ $) NIL)) (|patternMatch| (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL)) (|one?| (((|Boolean|) $) NIL)) (|odd?| (((|Boolean|) $) NIL)) (|nextItem| (((|Union| $ "failed") $) NIL)) (|negative?| (((|Boolean|) $) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|mulmod| (($ $ $ $) NIL)) (|min| (($ $ $) NIL)) (|maxint| (((|PositiveInteger|) (|PositiveInteger|)) 10) (((|PositiveInteger|)) 9)) (|max| (($ $ $) NIL)) (|mask| (($ $) NIL)) (|length| (($ $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ (|List| $)) NIL) (($ $ $) NIL)) (|latex| (((|String|) $) NIL)) (|invmod| (($ $ $) NIL)) (|init| (($) NIL T CONST)) (|inc| (($ $) NIL)) (|hash| (((|SingleInteger|) $) NIL) (($ $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ (|List| $)) NIL) (($ $ $) NIL)) (|factorial| (($ $) NIL)) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|even?| (((|Boolean|) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|differentiate| (($ $) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|dec| (($ $) NIL)) (|copy| (($ $) NIL)) (|convert| (((|DoubleFloat|) $) NIL) (((|Float|) $) NIL) (((|Pattern| (|Integer|)) $) NIL) (((|InputForm|) $) NIL) (((|Integer|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) 24) (($ $) NIL) (($ (|Integer|)) 24) (((|Expression| $) (|Expression| (|Integer|))) 18)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|bit?| (((|Boolean|) $ $) NIL)) (|binomial| (($ $ $) NIL)) (|base| (($) NIL)) (|associates?| (((|Boolean|) $ $) NIL)) (|addmod| (($ $ $ $) NIL)) (|abs| (($ $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($ $) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL))) 
(((|MachineInteger|) (|Join| (|FortranMachineTypeCategory|) (|IntegerNumberSystem|) (CATEGORY |domain| (SIGNATURE |maxint| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |maxint| ((|PositiveInteger|))) (SIGNATURE |coerce| ((|Expression| $) (|Expression| (|Integer|))))))) (T |MachineInteger|)) 
((|maxint| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|MachineInteger|)))) (|maxint| (*1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|MachineInteger|)))) (|coerce| (*1 *2 *3) (AND (|isDomain| *3 (|Expression| (|Integer|))) (|isDomain| *2 (|Expression| (|MachineInteger|))) (|isDomain| *1 (|MachineInteger|))))) 
(|Join| (|FortranMachineTypeCategory|) (|IntegerNumberSystem|) (CATEGORY |domain| (SIGNATURE |maxint| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |maxint| ((|PositiveInteger|))) (SIGNATURE |coerce| ((|Expression| $) (|Expression| (|Integer|)))))) 
((|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) 19)) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) 12))) 
(((|MakeBinaryCompiledFunction| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |binaryFunction| ((|Mapping| |#4| |#2| |#3|) (|Symbol|))) (SIGNATURE |compiledFunction| ((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)))) (|ConvertibleTo| (|InputForm|)) (|Type|) (|Type|) (|Type|)) (T |MakeBinaryCompiledFunction|)) 
((|compiledFunction| (*1 *2 *3 *4 *4) (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Mapping| *7 *5 *6)) (|isDomain| *1 (|MakeBinaryCompiledFunction| *3 *5 *6 *7)) (|ofCategory| *3 (|ConvertibleTo| (|InputForm|))) (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|)) (|ofCategory| *7 (|Type|)))) (|binaryFunction| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| *7 *5 *6)) (|isDomain| *1 (|MakeBinaryCompiledFunction| *4 *5 *6 *7)) (|ofCategory| *4 (|ConvertibleTo| (|InputForm|))) (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|)) (|ofCategory| *7 (|Type|))))) 
(CATEGORY |package| (SIGNATURE |binaryFunction| ((|Mapping| |#4| |#2| |#3|) (|Symbol|))) (SIGNATURE |compiledFunction| ((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)))) 
((~= (((|Boolean|) $ $) NIL)) (|setPosition| (((|Void|) $ (|NonNegativeInteger|)) 14)) (|position| (((|NonNegativeInteger|) $) 12)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 18) ((|#1| $) 15) (($ |#1|) 23)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 25)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 24))) 
(((|MakeCachableSet| |#1|) (|Join| (|CachableSet|) (|CoercibleTo| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#1|)))) (|SetCategory|)) (T |MakeCachableSet|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *1 (|MakeCachableSet| *2)) (|ofCategory| *2 (|SetCategory|))))) 
(|Join| (|CachableSet|) (|CoercibleTo| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#1|)))) 
((|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) 33) (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) 38))) 
(((|MakeFloatCompiledFunction| |#1|) (CATEGORY |package| (SIGNATURE |makeFloatFunction| ((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|))) (SIGNATURE |makeFloatFunction| ((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)))) (|ConvertibleTo| (|InputForm|))) (T |MakeFloatCompiledFunction|)) 
((|makeFloatFunction| (*1 *2 *3 *4 *4) (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|isDomain| *1 (|MakeFloatCompiledFunction| *3)) (|ofCategory| *3 (|ConvertibleTo| (|InputForm|))))) (|makeFloatFunction| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|isDomain| *1 (|MakeFloatCompiledFunction| *3)) (|ofCategory| *3 (|ConvertibleTo| (|InputForm|)))))) 
(CATEGORY |package| (SIGNATURE |makeFloatFunction| ((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|))) (SIGNATURE |makeFloatFunction| ((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)))) 
((|function| (((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))) 9) (((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|)) 12) (((|Symbol|) |#1| (|Symbol|) (|Symbol|)) 11) (((|Symbol|) |#1| (|Symbol|)) 10))) 
(((|MakeFunction| |#1|) (CATEGORY |package| (SIGNATURE |function| ((|Symbol|) |#1| (|Symbol|))) (SIGNATURE |function| ((|Symbol|) |#1| (|Symbol|) (|Symbol|))) (SIGNATURE |function| ((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|))) (SIGNATURE |function| ((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))))) (|ConvertibleTo| (|InputForm|))) (T |MakeFunction|)) 
((|function| (*1 *2 *3 *2 *4) (AND (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|MakeFunction| *3)) (|ofCategory| *3 (|ConvertibleTo| (|InputForm|))))) (|function| (*1 *2 *3 *2 *2 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|MakeFunction| *3)) (|ofCategory| *3 (|ConvertibleTo| (|InputForm|))))) (|function| (*1 *2 *3 *2 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|MakeFunction| *3)) (|ofCategory| *3 (|ConvertibleTo| (|InputForm|))))) (|function| (*1 *2 *3 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|MakeFunction| *3)) (|ofCategory| *3 (|ConvertibleTo| (|InputForm|)))))) 
(CATEGORY |package| (SIGNATURE |function| ((|Symbol|) |#1| (|Symbol|))) (SIGNATURE |function| ((|Symbol|) |#1| (|Symbol|) (|Symbol|))) (SIGNATURE |function| ((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|))) (SIGNATURE |function| ((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))))) 
((|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) 9))) 
(((|MakeRecord| |#1| |#2|) (CATEGORY |package| (SIGNATURE |makeRecord| ((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|))) (|Type|) (|Type|)) (T |MakeRecord|)) 
((|makeRecord| (*1 *2 *3 *4) (AND (|isDomain| *2 (|Record| (|:| |part1| *3) (|:| |part2| *4))) (|isDomain| *1 (|MakeRecord| *3 *4)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|Type|))))) 
(CATEGORY |package| (SIGNATURE |makeRecord| ((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|))) 
((|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) 11)) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) 21))) 
(((|MakeUnaryCompiledFunction| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |unaryFunction| ((|Mapping| |#3| |#2|) (|Symbol|))) (SIGNATURE |compiledFunction| ((|Mapping| |#3| |#2|) |#1| (|Symbol|)))) (|ConvertibleTo| (|InputForm|)) (|Type|) (|Type|)) (T |MakeUnaryCompiledFunction|)) 
((|compiledFunction| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Mapping| *6 *5)) (|isDomain| *1 (|MakeUnaryCompiledFunction| *3 *5 *6)) (|ofCategory| *3 (|ConvertibleTo| (|InputForm|))) (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|)))) (|unaryFunction| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| *6 *5)) (|isDomain| *1 (|MakeUnaryCompiledFunction| *4 *5 *6)) (|ofCategory| *4 (|ConvertibleTo| (|InputForm|))) (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|))))) 
(CATEGORY |package| (SIGNATURE |unaryFunction| ((|Mapping| |#3| |#2|) (|Symbol|))) (SIGNATURE |compiledFunction| ((|Mapping| |#3| |#2|) |#1| (|Symbol|)))) 
((|lifting1| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) 58)) (|lifting| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|) 71)) (|corrPoly| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) 32))) 
(((|MultivariateLifting| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |corrPoly| ((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|)) (SIGNATURE |lifting| ((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|)) (SIGNATURE |lifting1| ((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|EuclideanDomain|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |MultivariateLifting|)) 
((|lifting1| (*1 *2 *3 *4 *2 *5 *6 *7 *8 *9 *10) (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *13))) (|isDomain| *3 (|SparseUnivariatePolynomial| *13)) (|isDomain| *4 (|List| *12)) (|isDomain| *5 (|List| *10)) (|isDomain| *6 (|List| *13)) (|isDomain| *7 (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| *13))))) (|isDomain| *8 (|List| (|NonNegativeInteger|))) (|isDomain| *9 (|Vector| (|List| (|SparseUnivariatePolynomial| *10)))) (|ofCategory| *12 (|OrderedSet|)) (|ofCategory| *10 (|EuclideanDomain|)) (|ofCategory| *13 (|PolynomialCategory| *10 *11 *12)) (|ofCategory| *11 (|OrderedAbelianMonoidSup|)) (|isDomain| *1 (|MultivariateLifting| *11 *12 *10 *13)))) (|lifting| (*1 *2 *3 *4 *5 *6 *7 *8 *9) (|partial| AND (|isDomain| *4 (|List| *11)) (|isDomain| *5 (|List| (|SparseUnivariatePolynomial| *9))) (|isDomain| *6 (|List| *9)) (|isDomain| *7 (|List| *12)) (|isDomain| *8 (|List| (|NonNegativeInteger|))) (|ofCategory| *11 (|OrderedSet|)) (|ofCategory| *9 (|EuclideanDomain|)) (|ofCategory| *12 (|PolynomialCategory| *9 *10 *11)) (|ofCategory| *10 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *12))) (|isDomain| *1 (|MultivariateLifting| *10 *11 *9 *12)) (|isDomain| *3 (|SparseUnivariatePolynomial| *12)))) (|corrPoly| (*1 *2 *3 *4 *5 *6 *2 *7 *8) (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *11))) (|isDomain| *3 (|SparseUnivariatePolynomial| *11)) (|isDomain| *4 (|List| *10)) (|isDomain| *5 (|List| *8)) (|isDomain| *6 (|List| (|NonNegativeInteger|))) (|isDomain| *7 (|Vector| (|List| (|SparseUnivariatePolynomial| *8)))) (|ofCategory| *10 (|OrderedSet|)) (|ofCategory| *8 (|EuclideanDomain|)) (|ofCategory| *11 (|PolynomialCategory| *8 *9 *10)) (|ofCategory| *9 (|OrderedAbelianMonoidSup|)) (|isDomain| *1 (|MultivariateLifting| *9 *10 *8 *11))))) 
(CATEGORY |package| (SIGNATURE |corrPoly| ((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|)) (SIGNATURE |lifting| ((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|)) (SIGNATURE |lifting1| ((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|reductum| (($ $) 40)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|monomial| (($ |#1| (|NonNegativeInteger|)) 38)) (|minimumDegree| (((|NonNegativeInteger|) $) 42)) (|leadingCoefficient| ((|#1| $) 41)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|degree| (((|NonNegativeInteger|) $) 43)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ |#1|) 37 (|has| |#1| (|CommutativeRing|)))) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) 39)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 45) (($ |#1| $) 44))) 
(((|MonogenicLinearOperator| |#1|) (|Category|) (|Ring|)) (T |MonogenicLinearOperator|)) 
((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|MonogenicLinearOperator| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|minimumDegree| (*1 *2 *1) (AND (|ofCategory| *1 (|MonogenicLinearOperator| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *1 (|MonogenicLinearOperator| *2)) (|ofCategory| *2 (|Ring|)))) (|reductum| (*1 *1 *1) (AND (|ofCategory| *1 (|MonogenicLinearOperator| *2)) (|ofCategory| *2 (|Ring|)))) (|coefficient| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|MonogenicLinearOperator| *2)) (|ofCategory| *2 (|Ring|)))) (|monomial| (*1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|MonogenicLinearOperator| *2)) (|ofCategory| *2 (|Ring|))))) 
(|Join| (|Ring|) (|BiModule| |t#1| |t#1|) (CATEGORY |domain| (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |t#1|)) |noBranch|) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |minimumDegree| ((|NonNegativeInteger|) $)) (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |coefficient| (|t#1| $ (|NonNegativeInteger|))) (SIGNATURE |monomial| ($ |t#1| (|NonNegativeInteger|))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) 23))) 
(((|MultipleMap| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |map| (|#6| (|Mapping| |#4| |#1|) |#3|))) (|IntegralDomain|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|IntegralDomain|) (|UnivariatePolynomialCategory| |#4|) (|UnivariatePolynomialCategory| (|Fraction| |#5|))) (T |MultipleMap|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *7 *5)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *7 (|IntegralDomain|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Fraction| *8))) (|isDomain| *1 (|MultipleMap| *5 *6 *4 *7 *8 *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|ofCategory| *8 (|UnivariatePolynomialCategory| *7))))) 
(CATEGORY |package| (SIGNATURE |map| (|#6| (|Mapping| |#4| |#1|) |#3|))) 
((~= (((|Boolean|) $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|exprex| (((|String|) (|OutputForm|)) 31)) (|display| (((|Void|) (|String|)) 28)) (|coerceS| (((|String|) (|OutputForm|)) 24)) (|coerceL| (((|String|) (|OutputForm|)) 25)) (|coerce| (((|OutputForm|) $) NIL) (((|String|) (|OutputForm|)) 23)) (= (((|Boolean|) $ $) NIL))) 
(((|MathMLFormat|) (|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE |coerce| ((|String|) (|OutputForm|))) (SIGNATURE |coerceS| ((|String|) (|OutputForm|))) (SIGNATURE |coerceL| ((|String|) (|OutputForm|))) (SIGNATURE |exprex| ((|String|) (|OutputForm|))) (SIGNATURE |display| ((|Void|) (|String|)))))) (T |MathMLFormat|)) 
((|coerce| (*1 *2 *3) (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|String|)) (|isDomain| *1 (|MathMLFormat|)))) (|coerceS| (*1 *2 *3) (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|String|)) (|isDomain| *1 (|MathMLFormat|)))) (|coerceL| (*1 *2 *3) (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|String|)) (|isDomain| *1 (|MathMLFormat|)))) (|exprex| (*1 *2 *3) (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|String|)) (|isDomain| *1 (|MathMLFormat|)))) (|display| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|MathMLFormat|))))) 
(|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE |coerce| ((|String|) (|OutputForm|))) (SIGNATURE |coerceS| ((|String|) (|OutputForm|))) (SIGNATURE |coerceL| ((|String|) (|OutputForm|))) (SIGNATURE |exprex| ((|String|) (|OutputForm|))) (SIGNATURE |display| ((|Void|) (|String|))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sample| (($) NIL T CONST)) (|rem| (($ $ $) NIL)) (|reduce| (($ |#1| |#2|) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|modulus| ((|#2| $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|exQuo| (((|Union| $ "failed") $ $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) ((|#1| $) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|associates?| (((|Boolean|) $ $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (= (((|Boolean|) $ $) NIL)) (/ (($ $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL))) 
(((|ModularField| |#1| |#2| |#3| |#4| |#5|) (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |modulus| (|#2| $)) (SIGNATURE |coerce| (|#1| $)) (SIGNATURE |reduce| ($ |#1| |#2|)) (SIGNATURE |exQuo| ((|Union| $ "failed") $ $)))) (|CommutativeRing|) (|AbelianMonoid|) (|Mapping| |#1| |#1| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2|) (|Mapping| (|Union| |#1| "failed") |#1| |#1| |#2|)) (T |ModularField|)) 
((|modulus| (*1 *2 *1) (AND (|ofCategory| *2 (|AbelianMonoid|)) (|isDomain| *1 (|ModularField| *3 *2 *4 *5 *6)) (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|Mapping| *3 *3 *2)) (|ofType| *5 (|Mapping| (|Union| *2 "failed") *2 *2)) (|ofType| *6 (|Mapping| (|Union| *3 "failed") *3 *3 *2)))) (|coerce| (*1 *2 *1) (AND (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|ModularField| *2 *3 *4 *5 *6)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 (|Mapping| *2 *2 *3)) (|ofType| *5 (|Mapping| (|Union| *3 "failed") *3 *3)) (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2 *3)))) (|reduce| (*1 *1 *2 *3) (AND (|isDomain| *1 (|ModularField| *2 *3 *4 *5 *6)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 (|Mapping| *2 *2 *3)) (|ofType| *5 (|Mapping| (|Union| *3 "failed") *3 *3)) (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2 *3)))) (|exQuo| (*1 *1 *1 *1) (|partial| AND (|isDomain| *1 (|ModularField| *2 *3 *4 *5 *6)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 (|Mapping| *2 *2 *3)) (|ofType| *5 (|Mapping| (|Union| *3 "failed") *3 *3)) (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2 *3))))) 
(|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |modulus| (|#2| $)) (SIGNATURE |coerce| (|#1| $)) (SIGNATURE |reduce| ($ |#1| |#2|)) (SIGNATURE |exQuo| ((|Union| $ "failed") $ $)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 30)) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) NIL)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) NIL)) (|unvectorise| (($ (|Vector| |#1|)) NIL)) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) NIL)) (|univariate| (((|SparseUnivariatePolynomial| $) $ (|SingletonAsOrderedSet|)) NIL) (((|SparseUnivariatePolynomial| |#1|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|totalDegree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|List| (|SingletonAsOrderedSet|))) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|subResultantGcd| (($ $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL (|has| |#1| (|GcdDomain|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#1| (|GcdDomain|)))) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|sizeLess?| (((|Boolean|) $ $) NIL (|has| |#1| (|Field|)))) (|size| (((|NonNegativeInteger|)) 46 (|has| |#1| (|Finite|)))) (|shiftRight| (($ $ (|NonNegativeInteger|)) NIL)) (|shiftLeft| (($ $ (|NonNegativeInteger|)) NIL)) (|setPoly| ((|#2| |#2|) 43)) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) NIL (|has| |#1| (|GcdDomain|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|SingletonAsOrderedSet|) "failed") $) NIL)) (|retract| ((|#1| $) NIL) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|SingletonAsOrderedSet|) $) NIL)) (|resultant| (($ $ $ (|SingletonAsOrderedSet|)) NIL (|has| |#1| (|CommutativeRing|))) ((|#1| $ $) NIL (|has| |#1| (|CommutativeRing|)))) (|rem| (($ $ $) NIL (|has| |#1| (|Field|)))) (|reductum| (($ $) 33)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| |#1|) (|Matrix| $)) NIL)) (|reduce| (($ |#2|) 41)) (|recip| (((|Union| $ "failed") $) 84)) (|random| (($) 50 (|has| |#1| (|Finite|)))) (|quo| (($ $ $) NIL (|has| |#1| (|Field|)))) (|pseudoRemainder| (($ $ $) NIL)) (|pseudoQuotient| (($ $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL (|has| |#1| (|Field|)))) (|primitivePart| (($ $) NIL (|has| |#1| (|GcdDomain|))) (($ $ (|SingletonAsOrderedSet|)) NIL (|has| |#1| (|GcdDomain|)))) (|primitiveMonomials| (((|List| $) $) NIL)) (|prime?| (((|Boolean|) $) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|pow| (((|PrimitiveArray| $)) 78)) (|pomopo!| (($ $ |#1| (|NonNegativeInteger|) $) NIL)) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (AND (|has| (|SingletonAsOrderedSet|) (|PatternMatchable| (|Float|))) (|has| |#1| (|PatternMatchable| (|Float|))))) (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (AND (|has| (|SingletonAsOrderedSet|) (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Integer|)))))) (|order| (((|NonNegativeInteger|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|one?| (((|Boolean|) $) NIL)) (|numberOfMonomials| (((|NonNegativeInteger|) $) NIL)) (|nextItem| (((|Union| $ "failed") $) NIL (|has| |#1| (|StepThrough|)))) (|multivariate| (($ (|SparseUnivariatePolynomial| |#1|) (|SingletonAsOrderedSet|)) NIL) (($ (|SparseUnivariatePolynomial| $) (|SingletonAsOrderedSet|)) NIL)) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) (|monomials| (((|List| $) $) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monomial| (($ |#1| (|NonNegativeInteger|)) 76) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ (|SingletonAsOrderedSet|)) NIL) (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|modulus| ((|#2|) 44)) (|minimumDegree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|SingletonAsOrderedSet|)) NIL) (((|List| (|NonNegativeInteger|)) $ (|List| (|SingletonAsOrderedSet|))) NIL)) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|mapExponents| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) NIL)) (|mainVariable| (((|Union| (|SingletonAsOrderedSet|) "failed") $) NIL)) (|lookup| (((|PositiveInteger|) $) NIL (|has| |#1| (|Finite|)))) (|lift| ((|#2| $) 40)) (|leadingMonomial| (($ $) NIL)) (|leadingCoefficient| ((|#1| $) 28)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| |#1| (|GcdDomain|)))) (|lcm| (($ (|List| $)) NIL (|has| |#1| (|GcdDomain|))) (($ $ $) NIL (|has| |#1| (|GcdDomain|)))) (|latex| (((|String|) $) NIL)) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) NIL)) (|isTimes| (((|Union| (|List| $) "failed") $) NIL)) (|isPlus| (((|Union| (|List| $) "failed") $) NIL)) (|isExpt| (((|Union| (|Record| (|:| |var| (|SingletonAsOrderedSet|)) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) NIL)) (|integrate| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|init| (($) NIL (|has| |#1| (|StepThrough|)) CONST)) (|index| (($ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|hash| (((|SingleInteger|) $) NIL)) (|ground?| (((|Boolean|) $) NIL)) (|ground| ((|#1| $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|GcdDomain|)))) (|gcd| (($ (|List| $)) NIL (|has| |#1| (|GcdDomain|))) (($ $ $) NIL (|has| |#1| (|GcdDomain|)))) (|frobenius| (($ $) 77 (|has| |#1| (|FiniteFieldCategory|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL (|has| |#1| (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|exquo| (((|Union| $ "failed") $ |#1|) NIL (|has| |#1| (|IntegralDomain|))) (((|Union| $ "failed") $ $) 83 (|has| |#1| (|IntegralDomain|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) (|eval| (($ $ (|List| (|Equation| $))) NIL) (($ $ (|Equation| $)) NIL) (($ $ $ $) NIL) (($ $ (|List| $) (|List| $)) NIL) (($ $ (|SingletonAsOrderedSet|) |#1|) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| |#1|)) NIL) (($ $ (|SingletonAsOrderedSet|) $) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| $)) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|Field|)))) (|enumerate| (((|List| $)) NIL (|has| |#1| (|Finite|)))) (|elt| ((|#1| $ |#1|) NIL) (($ $ $) NIL) (((|Fraction| $) (|Fraction| $) (|Fraction| $)) NIL (|has| |#1| (|IntegralDomain|))) ((|#1| (|Fraction| $) |#1|) NIL (|has| |#1| (|Field|))) (((|Fraction| $) $ (|Fraction| $)) NIL (|has| |#1| (|IntegralDomain|)))) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 85 (|has| |#1| (|Field|)))) (|discriminant| (($ $ (|SingletonAsOrderedSet|)) NIL (|has| |#1| (|CommutativeRing|))) ((|#1| $) NIL (|has| 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(|convert| (((|Pattern| (|Float|)) $) NIL (AND (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))))) (((|Pattern| (|Integer|)) $) NIL (AND (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))))) (((|InputForm|) $) NIL (AND (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|InputForm|))) (|has| |#1| (|ConvertibleTo| (|InputForm|)))))) (|content| ((|#1| $) NIL (|has| |#1| (|GcdDomain|))) (($ $ (|SingletonAsOrderedSet|)) NIL (|has| |#1| (|GcdDomain|)))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))))) (|computePowers| (((|PrimitiveArray| $)) 35)) (|composite| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|IntegralDomain|))) (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) NIL (|has| |#1| (|IntegralDomain|)))) (|coerce| (((|OutputForm|) $) 60) (($ (|Integer|)) NIL) (($ |#1|) 57) (($ (|SingletonAsOrderedSet|)) NIL) (($ |#2|) 67) (($ (|Fraction| (|Integer|))) NIL (OR (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))))) (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|coefficients| (((|List| |#1|) $) NIL)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) 62) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|CommutativeRing|)))) (|associates?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 20 T CONST)) (|Vectorise| (((|Vector| |#1|) $) 74)) (|UnVectorise| (($ (|Vector| |#1|)) 49)) (|One| (($) 8 T CONST)) (D (($ $ (|SingletonAsOrderedSet|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|))) NIL) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL) (($ $ (|Symbol|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#1| |#1|)) NIL)) (|An| (((|Vector| |#1|) $) NIL)) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) 68)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (/ (($ $ |#1|) NIL (|has| |#1| (|Field|)))) (- (($ $) 71) (($ $ $) NIL)) (+ (($ $ $) 32)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 79)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 56) (($ $ $) 73) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ |#1| $) 54) (($ $ |#1|) NIL))) 
(((|ModMonic| |#1| |#2|) (|Join| (|UnivariatePolynomialCategory| |#1|) (CATEGORY |domain| (SIGNATURE |setPoly| (|#2| |#2|)) (SIGNATURE |modulus| (|#2|)) (SIGNATURE |reduce| ($ |#2|)) (SIGNATURE |lift| (|#2| $)) (SIGNATURE |coerce| ($ |#2|)) (SIGNATURE |Vectorise| ((|Vector| |#1|) $)) (SIGNATURE |UnVectorise| ($ (|Vector| |#1|))) (SIGNATURE |An| ((|Vector| |#1|) $)) (SIGNATURE |pow| ((|PrimitiveArray| $))) (SIGNATURE |computePowers| ((|PrimitiveArray| $))) (IF (|has| |#1| (|FiniteFieldCategory|)) (SIGNATURE |frobenius| ($ $)) |noBranch|) (IF (|has| |#1| (|Finite|)) (ATTRIBUTE (|Finite|)) |noBranch|))) (|Ring|) (|UnivariatePolynomialCategory| |#1|)) (T |ModMonic|)) 
((|setPoly| (*1 *2 *2) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|ModMonic| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|modulus| (*1 *2) (AND (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)) (|isDomain| *1 (|ModMonic| *3 *2)) (|ofCategory| *3 (|Ring|)))) (|reduce| (*1 *1 *2) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|ModMonic| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|lift| (*1 *2 *1) (AND (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)) (|isDomain| *1 (|ModMonic| *3 *2)) (|ofCategory| *3 (|Ring|)))) (|coerce| (*1 *1 *2) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|ModMonic| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|Vectorise| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Vector| *3)) (|isDomain| *1 (|ModMonic| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|UnVectorise| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|ModMonic| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|An| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Vector| *3)) (|isDomain| *1 (|ModMonic| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|pow| (*1 *2) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|PrimitiveArray| (|ModMonic| *3 *4))) (|isDomain| *1 (|ModMonic| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|computePowers| (*1 *2) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|PrimitiveArray| (|ModMonic| *3 *4))) (|isDomain| *1 (|ModMonic| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|frobenius| (*1 *1 *1) (AND (|ofCategory| *2 (|FiniteFieldCategory|)) (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|ModMonic| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(|Join| (|UnivariatePolynomialCategory| |#1|) (CATEGORY |domain| (SIGNATURE |setPoly| (|#2| |#2|)) (SIGNATURE |modulus| (|#2|)) (SIGNATURE |reduce| ($ |#2|)) (SIGNATURE |lift| (|#2| $)) (SIGNATURE |coerce| ($ |#2|)) (SIGNATURE |Vectorise| ((|Vector| |#1|) $)) (SIGNATURE |UnVectorise| ($ (|Vector| |#1|))) (SIGNATURE |An| ((|Vector| |#1|) $)) (SIGNATURE |pow| ((|PrimitiveArray| $))) (SIGNATURE |computePowers| ((|PrimitiveArray| $))) (IF (|has| |#1| (|FiniteFieldCategory|)) (SIGNATURE |frobenius| ($ $)) |noBranch|) (IF (|has| |#1| (|Finite|)) (ATTRIBUTE (|Finite|)) |noBranch|))) 
((~= (((|Boolean|) $ $) NIL)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|latex| (((|String|) $) NIL)) (|index| ((|#1| $) 13)) (|hash| (((|SingleInteger|) $) NIL)) (|exponent| ((|#2| $) 12)) (|construct| (($ |#1| |#2|) 16)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Record| (|:| |index| |#1|) (|:| |exponent| |#2|))) 15) (((|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)) $) 14)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 11))) 
(((|ModuleMonomial| |#1| |#2| |#3|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |exponent| (|#2| $)) (SIGNATURE |index| (|#1| $)) (SIGNATURE |coerce| ($ (|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)))) (SIGNATURE |coerce| ((|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)) $)) (SIGNATURE |construct| ($ |#1| |#2|)))) (|OrderedSet|) (|SetCategory|) (|Mapping| (|Boolean|) (|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)) (|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)))) (T |ModuleMonomial|)) 
((|exponent| (*1 *2 *1) (AND (|ofCategory| *2 (|SetCategory|)) (|isDomain| *1 (|ModuleMonomial| *3 *2 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofType| *4 (|Mapping| (|Boolean|) (|Record| (|:| |index| *3) (|:| |exponent| *2)) (|Record| (|:| |index| *3) (|:| |exponent| *2)))))) (|index| (*1 *2 *1) (AND (|ofCategory| *2 (|OrderedSet|)) (|isDomain| *1 (|ModuleMonomial| *2 *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofType| *4 (|Mapping| (|Boolean|) (|Record| (|:| |index| *2) (|:| |exponent| *3)) (|Record| (|:| |index| *2) (|:| |exponent| *3)))))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Record| (|:| |index| *3) (|:| |exponent| *4))) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *1 (|ModuleMonomial| *3 *4 *5)) (|ofType| *5 (|Mapping| (|Boolean|) *2 *2)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Record| (|:| |index| *3) (|:| |exponent| *4))) (|isDomain| *1 (|ModuleMonomial| *3 *4 *5)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|SetCategory|)) (|ofType| *5 (|Mapping| (|Boolean|) *2 *2)))) (|construct| (*1 *1 *2 *3) (AND (|isDomain| *1 (|ModuleMonomial| *2 *3 *4)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|SetCategory|)) (|ofType| *4 (|Mapping| (|Boolean|) (|Record| (|:| |index| *2) (|:| |exponent| *3)) (|Record| (|:| |index| *2) (|:| |exponent| *3))))))) 
(|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |exponent| (|#2| $)) (SIGNATURE |index| (|#1| $)) (SIGNATURE |coerce| ($ (|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)))) (SIGNATURE |coerce| ((|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)) $)) (SIGNATURE |construct| ($ |#1| |#2|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 59)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 89) (((|Union| (|BasicOperator|) "failed") $) 95)) (|retract| ((|#1| $) NIL) (((|BasicOperator|) $) 39)) (|recip| (((|Union| $ "failed") $) 90)) (|opeval| ((|#2| (|BasicOperator|) |#2|) 82)) (|one?| (((|Boolean|) $) NIL)) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) 13)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) 58)) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) 44)) (|elt| ((|#2| $ |#2|) 32)) (|conjug| ((|#1| |#1|) 100 (|has| |#1| (|CommutativeRing|)))) (|coerce| (((|OutputForm|) $) 66) (($ (|Integer|)) 17) (($ |#1|) 16) (($ (|BasicOperator|)) 23)) (|charthRoot| (((|Union| $ "failed") $) NIL (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) 36)) (|adjoint| (($ $) 99 (|has| |#1| (|CommutativeRing|))) (($ $ $) 103 (|has| |#1| (|CommutativeRing|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 20 T CONST)) (|One| (($) 9 T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) 48) (($ $ $) NIL)) (+ (($ $ $) 73)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ (|BasicOperator|) (|Integer|)) NIL) (($ $ (|Integer|)) 57)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 98) (($ $ $) 50) (($ |#1| $) 96 (|has| |#1| (|CommutativeRing|))) (($ $ |#1|) 97 (|has| |#1| (|CommutativeRing|))))) 
(((|ModuleOperator| |#1| |#2|) (|Join| (|Ring|) (|RetractableTo| |#1|) (|RetractableTo| (|BasicOperator|)) (|Eltable| |#2| |#2|) (CATEGORY |domain| (IF (|has| |#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |noBranch|) (IF (|has| |#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (PROGN (ATTRIBUTE (|Algebra| |#1|)) (SIGNATURE |adjoint| ($ $)) (SIGNATURE |adjoint| ($ $ $)) (SIGNATURE |conjug| (|#1| |#1|))) |noBranch|) (SIGNATURE |evaluate| ($ $ (|Mapping| |#2| |#2|))) (SIGNATURE |evaluateInverse| ($ $ (|Mapping| |#2| |#2|))) (SIGNATURE ** ($ (|BasicOperator|) (|Integer|))) (SIGNATURE ** ($ $ (|Integer|))) (SIGNATURE |opeval| (|#2| (|BasicOperator|) |#2|)) (SIGNATURE |makeop| ($ |#1| (|FreeGroup| (|BasicOperator|)))))) (|Ring|) (|LeftModule| |#1|)) (T |ModuleOperator|)) 
((|adjoint| (*1 *1 *1) (AND (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|ModuleOperator| *2 *3)) (|ofCategory| *3 (|LeftModule| *2)))) (|adjoint| (*1 *1 *1 *1) (AND (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|ModuleOperator| *2 *3)) (|ofCategory| *3 (|LeftModule| *2)))) (|conjug| (*1 *2 *2) (AND (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|ModuleOperator| *2 *3)) (|ofCategory| *3 (|LeftModule| *2)))) (|evaluate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|ofCategory| *4 (|LeftModule| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|ModuleOperator| *3 *4)))) (|evaluateInverse| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|ofCategory| *4 (|LeftModule| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|ModuleOperator| *3 *4)))) (** (*1 *1 *2 *3) (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|ModuleOperator| *4 *5)) (|ofCategory| *5 (|LeftModule| *4)))) (** (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|ModuleOperator| *3 *4)) (|ofCategory| *4 (|LeftModule| *3)))) (|opeval| (*1 *2 *3 *2) (AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|ModuleOperator| *4 *2)) (|ofCategory| *2 (|LeftModule| *4)))) (|makeop| (*1 *1 *2 *3) (AND (|isDomain| *3 (|FreeGroup| (|BasicOperator|))) (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|ModuleOperator| *2 *4)) (|ofCategory| *4 (|LeftModule| *2))))) 
(|Join| (|Ring|) (|RetractableTo| |#1|) (|RetractableTo| (|BasicOperator|)) (|Eltable| |#2| |#2|) (CATEGORY |domain| (IF (|has| |#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |noBranch|) (IF (|has| |#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (PROGN (ATTRIBUTE (|Algebra| |#1|)) (SIGNATURE |adjoint| ($ $)) (SIGNATURE |adjoint| ($ $ $)) (SIGNATURE |conjug| (|#1| |#1|))) |noBranch|) (SIGNATURE |evaluate| ($ $ (|Mapping| |#2| |#2|))) (SIGNATURE |evaluateInverse| ($ $ (|Mapping| |#2| |#2|))) (SIGNATURE ** ($ (|BasicOperator|) (|Integer|))) (SIGNATURE ** ($ $ (|Integer|))) (SIGNATURE |opeval| (|#2| (|BasicOperator|) |#2|)) (SIGNATURE |makeop| ($ |#1| (|FreeGroup| (|BasicOperator|)))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 33)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|reduce| (($ |#1| |#2|) 25)) (|recip| (((|Union| $ "failed") $) 47)) (|one?| (((|Boolean|) $) 35)) (|modulus| ((|#2| $) 12)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 48)) (|hash| (((|SingleInteger|) $) NIL)) (|exQuo| (((|Union| $ "failed") $ $) 46)) (|coerce| (((|OutputForm|) $) 24) (($ (|Integer|)) 19) ((|#1| $) 13)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 16 T CONST)) (|One| (($) 30 T CONST)) (= (((|Boolean|) $ $) 38)) (- (($ $) 43) (($ $ $) 37)) (+ (($ $ $) 40)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 21) (($ $ $) 20))) 
(((|ModularRing| |#1| |#2| |#3| |#4| |#5|) (|Join| (|Ring|) (CATEGORY |domain| (SIGNATURE |modulus| (|#2| $)) (SIGNATURE |coerce| (|#1| $)) (SIGNATURE |reduce| ($ |#1| |#2|)) (SIGNATURE |exQuo| ((|Union| $ "failed") $ $)) (SIGNATURE |recip| ((|Union| $ "failed") $)) (SIGNATURE |inv| ($ $)))) (|CommutativeRing|) (|AbelianMonoid|) (|Mapping| |#1| |#1| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2|) (|Mapping| (|Union| |#1| "failed") |#1| |#1| |#2|)) (T |ModularRing|)) 
((|recip| (*1 *1 *1) (|partial| AND (|isDomain| *1 (|ModularRing| *2 *3 *4 *5 *6)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 (|Mapping| *2 *2 *3)) (|ofType| *5 (|Mapping| (|Union| *3 "failed") *3 *3)) (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2 *3)))) (|modulus| (*1 *2 *1) (AND (|ofCategory| *2 (|AbelianMonoid|)) (|isDomain| *1 (|ModularRing| *3 *2 *4 *5 *6)) (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|Mapping| *3 *3 *2)) (|ofType| *5 (|Mapping| (|Union| *2 "failed") *2 *2)) (|ofType| *6 (|Mapping| (|Union| *3 "failed") *3 *3 *2)))) (|coerce| (*1 *2 *1) (AND (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|ModularRing| *2 *3 *4 *5 *6)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 (|Mapping| *2 *2 *3)) (|ofType| *5 (|Mapping| (|Union| *3 "failed") *3 *3)) (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2 *3)))) (|reduce| (*1 *1 *2 *3) (AND (|isDomain| *1 (|ModularRing| *2 *3 *4 *5 *6)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 (|Mapping| *2 *2 *3)) (|ofType| *5 (|Mapping| (|Union| *3 "failed") *3 *3)) (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2 *3)))) (|exQuo| (*1 *1 *1 *1) (|partial| AND (|isDomain| *1 (|ModularRing| *2 *3 *4 *5 *6)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 (|Mapping| *2 *2 *3)) (|ofType| *5 (|Mapping| (|Union| *3 "failed") *3 *3)) (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2 *3)))) (|inv| (*1 *1 *1) (AND (|isDomain| *1 (|ModularRing| *2 *3 *4 *5 *6)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 (|Mapping| *2 *2 *3)) (|ofType| *5 (|Mapping| (|Union| *3 "failed") *3 *3)) (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2 *3))))) 
(|Join| (|Ring|) (CATEGORY |domain| (SIGNATURE |modulus| (|#2| $)) (SIGNATURE |coerce| (|#1| $)) (SIGNATURE |reduce| ($ |#1| |#2|)) (SIGNATURE |exQuo| ((|Union| $ "failed") $ $)) (SIGNATURE |recip| ((|Union| $ "failed") $)) (SIGNATURE |inv| ($ $)))) 
((* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ |#2| $) NIL) (($ $ |#2|) 9))) 
(((|Module&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|Module| |#2|) (|CommutativeRing|)) (T |Module&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ |#1| $) 22) (($ $ |#1|) 24))) 
(((|Module| |#1|) (|Category|) (|CommutativeRing|)) (T |Module|)) 
NIL 
(|Join| (|BiModule| |t#1| |t#1|)) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|shift| (($ |#1|) 17) (($ $ |#1|) 20)) (|scale| (($ |#1|) 18) (($ $ |#1|) 21)) (|sample| (($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL) (($) 19) (($ $) 22)) (|one?| (((|Boolean|) $) NIL)) (|moebius| (($ |#1| |#1| |#1| |#1|) 8)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 16)) (|hash| (((|SingleInteger|) $) NIL)) (|eval| ((|#1| $ |#1|) 24) (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) 32)) (|conjugate| (($ $ $) NIL)) (|commutator| (($ $ $) NIL)) (|coerce| (((|OutputForm|) $) 39)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|One| (($) 9 T CONST)) (= (((|Boolean|) $ $) 44)) (/ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ $ $) 14))) 
(((|MoebiusTransform| |#1|) (|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |moebius| ($ |#1| |#1| |#1| |#1|)) (SIGNATURE |shift| ($ |#1|)) (SIGNATURE |scale| ($ |#1|)) (SIGNATURE |recip| ($)) (SIGNATURE |shift| ($ $ |#1|)) (SIGNATURE |scale| ($ $ |#1|)) (SIGNATURE |recip| ($ $)) (SIGNATURE |eval| (|#1| $ |#1|)) (SIGNATURE |eval| ((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|))))) (|Field|)) (T |MoebiusTransform|)) 
((|moebius| (*1 *1 *2 *2 *2 *2) (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|)))) (|shift| (*1 *1 *2) (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|)))) (|scale| (*1 *1 *2) (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|)))) (|recip| (*1 *1) (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|)))) (|shift| (*1 *1 *1 *2) (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|)))) (|scale| (*1 *1 *1 *2) (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|)))) (|recip| (*1 *1 *1) (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|)))) (|eval| (*1 *2 *1 *2) (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|)))) (|eval| (*1 *2 *1 *2) (AND (|isDomain| *2 (|OnePointCompletion| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|MoebiusTransform| *3))))) 
(|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |moebius| ($ |#1| |#1| |#1| |#1|)) (SIGNATURE |shift| ($ |#1|)) (SIGNATURE |scale| ($ |#1|)) (SIGNATURE |recip| ($)) (SIGNATURE |shift| ($ $ |#1|)) (SIGNATURE |scale| ($ $ |#1|)) (SIGNATURE |recip| ($ $)) (SIGNATURE |eval| (|#1| $ |#1|)) (SIGNATURE |eval| ((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|))))) 
((|rightPower| (($ $ (|PositiveInteger|)) 12)) (|leftPower| (($ $ (|PositiveInteger|)) 13)) (** (($ $ (|PositiveInteger|)) 10))) 
(((|Monad&| |#1|) (CATEGORY |domain| (SIGNATURE ** (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |leftPower| (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |rightPower| (|#1| |#1| (|PositiveInteger|)))) (|Monad|)) (T |Monad&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE ** (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |leftPower| (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |rightPower| (|#1| |#1| (|PositiveInteger|)))) 
((~= (((|Boolean|) $ $) 7)) (|rightPower| (($ $ (|PositiveInteger|)) 14)) (|leftPower| (($ $ (|PositiveInteger|)) 13)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (= (((|Boolean|) $ $) 6)) (** (($ $ (|PositiveInteger|)) 12)) (* (($ $ $) 15))) 
(((|Monad|) (|Category|)) (T |Monad|)) 
((* (*1 *1 *1 *1) (|ofCategory| *1 (|Monad|))) (|rightPower| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Monad|)) (|isDomain| *2 (|PositiveInteger|)))) (|leftPower| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Monad|)) (|isDomain| *2 (|PositiveInteger|)))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Monad|)) (|isDomain| *2 (|PositiveInteger|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE * ($ $ $)) (SIGNATURE |rightPower| ($ $ (|PositiveInteger|))) (SIGNATURE |leftPower| ($ $ (|PositiveInteger|))) (SIGNATURE ** ($ $ (|PositiveInteger|))))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((|rightPower| (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 17)) (|one?| (((|Boolean|) $) 10)) (|leftPower| (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 18)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 15))) 
(((|MonadWithUnit&| |#1|) (CATEGORY |domain| (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |leftPower| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |rightPower| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |one?| ((|Boolean|) |#1|)) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |leftPower| (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |rightPower| (|#1| |#1| (|PositiveInteger|)))) (|MonadWithUnit|)) (T |MonadWithUnit&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |leftPower| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |rightPower| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |one?| ((|Boolean|) |#1|)) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |leftPower| (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |rightPower| (|#1| |#1| (|PositiveInteger|)))) 
((~= (((|Boolean|) $ $) 7)) (|rightRecip| (((|Union| $ "failed") $) 16)) (|rightPower| (($ $ (|PositiveInteger|)) 14) (($ $ (|NonNegativeInteger|)) 21)) (|recip| (((|Union| $ "failed") $) 18)) (|one?| (((|Boolean|) $) 22)) (|leftRecip| (((|Union| $ "failed") $) 17)) (|leftPower| (($ $ (|PositiveInteger|)) 13) (($ $ (|NonNegativeInteger|)) 20)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (|One| (($) 23 T CONST)) (= (((|Boolean|) $ $) 6)) (** (($ $ (|PositiveInteger|)) 12) (($ $ (|NonNegativeInteger|)) 19)) (* (($ $ $) 15))) 
(((|MonadWithUnit|) (|Category|)) (T |MonadWithUnit|)) 
((|One| (*1 *1) (|ofCategory| *1 (|MonadWithUnit|))) (|one?| (*1 *2 *1) (AND (|ofCategory| *1 (|MonadWithUnit|)) (|isDomain| *2 (|Boolean|)))) (|rightPower| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|MonadWithUnit|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|leftPower| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|MonadWithUnit|)) (|isDomain| *2 (|NonNegativeInteger|)))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|MonadWithUnit|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|recip| (*1 *1 *1) (|partial| |ofCategory| *1 (|MonadWithUnit|))) (|leftRecip| (*1 *1 *1) (|partial| |ofCategory| *1 (|MonadWithUnit|))) (|rightRecip| (*1 *1 *1) (|partial| |ofCategory| *1 (|MonadWithUnit|)))) 
(|Join| (|Monad|) (CATEGORY |domain| (SIGNATURE (|One|) ($) |constant|) (SIGNATURE |one?| ((|Boolean|) $)) (SIGNATURE |rightPower| ($ $ (|NonNegativeInteger|))) (SIGNATURE |leftPower| ($ $ (|NonNegativeInteger|))) (SIGNATURE ** ($ $ (|NonNegativeInteger|))) (SIGNATURE |recip| ((|Union| $ "failed") $)) (SIGNATURE |leftRecip| ((|Union| $ "failed") $)) (SIGNATURE |rightRecip| ((|Union| $ "failed") $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Monad|) . T) ((|SetCategory|) . T)) 
((|size| (((|NonNegativeInteger|)) 35)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL) (((|Union| |#2| "failed") $) 25)) (|retract| (((|Integer|) $) NIL) (((|Fraction| (|Integer|)) $) NIL) ((|#2| $) 22)) (|reduce| (($ |#3|) NIL) (((|Union| $ "failed") (|Fraction| |#3|)) 45)) (|recip| (((|Union| $ "failed") $) 65)) (|random| (($) 39)) (|norm| ((|#2| $) 20)) (|generator| (($) 17)) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#2| |#2|)) 53) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|))) NIL) (($ $ (|Symbol|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) 60)) (|convert| (((|Vector| |#2|) $) NIL) (($ (|Vector| |#2|)) NIL) ((|#3| $) 10) (($ |#3|) 12)) (|characteristicPolynomial| ((|#3| $) 32)) (|basis| (((|Vector| $)) 29))) 
(((|MonogenicAlgebra&| |#1| |#2| |#3|) (CATEGORY |domain| (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |random| (|#1|)) (SIGNATURE |size| ((|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|) (|NonNegativeInteger|))) (SIGNATURE |derivationCoordinates| ((|Matrix| |#2|) (|Vector| |#1|) (|Mapping| |#2| |#2|))) (SIGNATURE |reduce| ((|Union| |#1| "failed") (|Fraction| |#3|))) (SIGNATURE |convert| (|#1| |#3|)) (SIGNATURE |reduce| (|#1| |#3|)) (SIGNATURE |generator| (|#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |convert| (|#3| |#1|)) (SIGNATURE |convert| (|#1| (|Vector| |#2|))) (SIGNATURE |convert| ((|Vector| |#2|) |#1|)) (SIGNATURE |basis| ((|Vector| |#1|))) (SIGNATURE |characteristicPolynomial| (|#3| |#1|)) (SIGNATURE |norm| (|#2| |#1|)) (SIGNATURE |recip| ((|Union| |#1| "failed") |#1|))) (|MonogenicAlgebra| |#2| |#3|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#2|)) (T |MonogenicAlgebra&|)) 
((|size| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|MonogenicAlgebra&| *3 *4 *5)) (|ofCategory| *3 (|MonogenicAlgebra| *4 *5))))) 
(CATEGORY |domain| (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |random| (|#1|)) (SIGNATURE |size| ((|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|) (|NonNegativeInteger|))) (SIGNATURE |derivationCoordinates| ((|Matrix| |#2|) (|Vector| |#1|) (|Mapping| |#2| |#2|))) (SIGNATURE |reduce| ((|Union| |#1| "failed") (|Fraction| |#3|))) (SIGNATURE |convert| (|#1| |#3|)) (SIGNATURE |reduce| (|#1| |#3|)) (SIGNATURE |generator| (|#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |convert| (|#3| |#1|)) (SIGNATURE |convert| (|#1| (|Vector| |#2|))) (SIGNATURE |convert| ((|Vector| |#2|) |#1|)) (SIGNATURE |basis| ((|Vector| |#1|))) (SIGNATURE |characteristicPolynomial| (|#3| |#1|)) (SIGNATURE |norm| (|#2| |#1|)) (SIGNATURE |recip| ((|Union| |#1| "failed") |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 89 (|has| |#1| (|Field|)))) (|unitCanonical| (($ $) 90 (|has| |#1| (|Field|)))) (|unit?| (((|Boolean|) $) 92 (|has| |#1| (|Field|)))) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) 44) (((|Matrix| |#1|)) 55)) (|trace| ((|#1| $) 50)) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) 144 (|has| |#1| (|FiniteFieldCategory|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 110 (|has| |#1| (|Field|)))) (|squareFree| (((|Factored| $) $) 111 (|has| |#1| (|Field|)))) (|sizeLess?| (((|Boolean|) $ $) 101 (|has| |#1| (|Field|)))) (|size| (((|NonNegativeInteger|)) 82 (|has| |#1| (|Finite|)))) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 166 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) 164 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) 163)) (|retract| (((|Integer|) $) 167 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) 165 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) 162)) (|represents| (($ (|Vector| |#1|) (|Vector| $)) 46) (($ (|Vector| |#1|)) 58)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 150 (|has| |#1| (|FiniteFieldCategory|)))) (|rem| (($ $ $) 105 (|has| |#1| (|Field|)))) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 51) (((|Matrix| |#1|) $) 53)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) 161 (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) 160 (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) 159) (((|Matrix| |#1|) (|Matrix| $)) 158)) (|reduce| (($ |#2|) 155) (((|Union| $ "failed") (|Fraction| |#2|)) 152 (|has| |#1| (|Field|)))) (|recip| (((|Union| $ "failed") $) 33)) (|rank| (((|PositiveInteger|)) 52)) (|random| (($) 85 (|has| |#1| (|Finite|)))) (|quo| (($ $ $) 104 (|has| |#1| (|Field|)))) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 99 (|has| |#1| (|Field|)))) (|primitiveElement| (($) 146 (|has| |#1| (|FiniteFieldCategory|)))) (|primitive?| (((|Boolean|) $) 147 (|has| |#1| (|FiniteFieldCategory|)))) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) 138 (|has| |#1| (|FiniteFieldCategory|))) (($ $) 137 (|has| |#1| (|FiniteFieldCategory|)))) (|prime?| (((|Boolean|) $) 112 (|has| |#1| (|Field|)))) (|order| (((|PositiveInteger|) $) 149 (|has| |#1| (|FiniteFieldCategory|))) (((|OnePointCompletion| (|PositiveInteger|)) $) 135 (|has| |#1| (|FiniteFieldCategory|)))) (|one?| (((|Boolean|) $) 30)) (|norm| ((|#1| $) 49)) (|nextItem| (((|Union| $ "failed") $) 139 (|has| |#1| (|FiniteFieldCategory|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 108 (|has| |#1| (|Field|)))) (|minimalPolynomial| ((|#2| $) 42 (|has| |#1| (|Field|)))) (|lookup| (((|PositiveInteger|) $) 84 (|has| |#1| (|Finite|)))) (|lift| ((|#2| $) 153)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 93 (|has| |#1| (|Field|)))) (|lcm| (($ (|List| $)) 97 (|has| |#1| (|Field|))) (($ $ $) 96 (|has| |#1| (|Field|)))) (|latex| (((|String|) $) 9)) (|inv| (($ $) 113 (|has| |#1| (|Field|)))) (|init| (($) 140 (|has| |#1| (|FiniteFieldCategory|)) CONST)) (|index| (($ (|PositiveInteger|)) 83 (|has| |#1| (|Finite|)))) (|hash| (((|SingleInteger|) $) 10)) (|generator| (($) 157)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 98 (|has| |#1| (|Field|)))) (|gcd| (($ (|List| $)) 95 (|has| |#1| (|Field|))) (($ $ $) 94 (|has| |#1| (|Field|)))) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) 143 (|has| |#1| (|FiniteFieldCategory|)))) (|factor| (((|Factored| $) $) 109 (|has| |#1| (|Field|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 107 (|has| |#1| (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 106 (|has| |#1| (|Field|)))) (|exquo| (((|Union| $ "failed") $ $) 88 (|has| |#1| (|Field|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 100 (|has| |#1| (|Field|)))) (|euclideanSize| (((|NonNegativeInteger|) $) 102 (|has| |#1| (|Field|)))) (|enumerate| (((|List| $)) 86 (|has| |#1| (|Finite|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 103 (|has| |#1| (|Field|)))) (|discriminant| ((|#1| (|Vector| $)) 45) ((|#1|) 54)) (|discreteLog| (((|NonNegativeInteger|) $) 148 (|has| |#1| (|FiniteFieldCategory|))) (((|Union| (|NonNegativeInteger|) "failed") $ $) 136 (|has| |#1| (|FiniteFieldCategory|)))) (|differentiate| (($ $) 134 (OR (|and| (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|))) (|has| |#1| (|FiniteFieldCategory|)))) (($ $ (|NonNegativeInteger|)) 132 (OR (|and| (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|))) (|has| |#1| (|FiniteFieldCategory|)))) (($ $ (|Symbol|)) 130 (|and| (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|Field|)))) (($ $ (|List| (|Symbol|))) 129 (|and| (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|Field|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 128 (|and| (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|Field|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 127 (|and| (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|Field|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) 120 (|has| |#1| (|Field|))) (($ $ (|Mapping| |#1| |#1|)) 119 (|has| |#1| (|Field|)))) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) 151 (|has| |#1| (|Field|)))) (|definingPolynomial| ((|#2|) 156)) (|createPrimitiveElement| (($) 145 (|has| |#1| (|FiniteFieldCategory|)))) (|coordinates| (((|Vector| |#1|) $ (|Vector| $)) 48) (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) 47) (((|Vector| |#1|) $) 60) (((|Matrix| |#1|) (|Vector| $)) 59)) (|convert| (((|Vector| |#1|) $) 57) (($ (|Vector| |#1|)) 56) ((|#2| $) 168) (($ |#2|) 154)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 142 (|has| |#1| (|FiniteFieldCategory|)))) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ |#1|) 36) (($ $) 87 (|has| |#1| (|Field|))) (($ (|Fraction| (|Integer|))) 81 (OR (|has| |#1| (|Field|)) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))))) (|charthRoot| (($ $) 141 (|has| |#1| (|FiniteFieldCategory|))) (((|Union| $ "failed") $) 41 (|has| |#1| (|CharacteristicNonZero|)))) (|characteristicPolynomial| ((|#2| $) 43)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|basis| (((|Vector| $)) 61)) (|associates?| (((|Boolean|) $ $) 91 (|has| |#1| (|Field|)))) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 114 (|has| |#1| (|Field|)))) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $) 133 (OR (|and| (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|))) (|has| |#1| (|FiniteFieldCategory|)))) (($ $ (|NonNegativeInteger|)) 131 (OR (|and| (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|))) (|has| |#1| (|FiniteFieldCategory|)))) (($ $ (|Symbol|)) 126 (|and| (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|Field|)))) (($ $ (|List| (|Symbol|))) 125 (|and| (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|Field|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 124 (|and| (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|Field|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 123 (|and| (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|Field|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) 122 (|has| |#1| (|Field|))) (($ $ (|Mapping| |#1| |#1|)) 121 (|has| |#1| (|Field|)))) (= (((|Boolean|) $ $) 6)) (/ (($ $ $) 118 (|has| |#1| (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 115 (|has| |#1| (|Field|)))) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 38) (($ |#1| $) 37) (($ (|Fraction| (|Integer|)) $) 117 (|has| |#1| (|Field|))) (($ $ (|Fraction| (|Integer|))) 116 (|has| |#1| (|Field|))))) 
(((|MonogenicAlgebra| |#1| |#2|) (|Category|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |t#1|)) (T |MonogenicAlgebra|)) 
((|generator| (*1 *1) (AND (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *1 (|MonogenicAlgebra| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|definingPolynomial| (*1 *2) (AND (|ofCategory| *1 (|MonogenicAlgebra| *3 *2)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|reduce| (*1 *1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|MonogenicAlgebra| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|convert| (*1 *1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|MonogenicAlgebra| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|lift| (*1 *2 *1) (AND (|ofCategory| *1 (|MonogenicAlgebra| *3 *2)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|reduce| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Fraction| *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|MonogenicAlgebra| *3 *4)))) (|derivationCoordinates| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Vector| *1)) (|isDomain| *4 (|Mapping| *5 *5)) (|ofCategory| *5 (|Field|)) (|ofCategory| *1 (|MonogenicAlgebra| *5 *6)) (|ofCategory| *5 (|CommutativeRing|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|Matrix| *5))))) 
(|Join| (|FramedAlgebra| |t#1| |t#2|) (|CommutativeRing|) (|ConvertibleTo| |t#2|) (|FullyRetractableTo| |t#1|) (|FullyLinearlyExplicitRingOver| |t#1|) (CATEGORY |domain| (SIGNATURE |generator| ($)) (SIGNATURE |definingPolynomial| (|t#2|)) (SIGNATURE |reduce| ($ |t#2|)) (SIGNATURE |convert| ($ |t#2|)) (SIGNATURE |lift| (|t#2| $)) (IF (|has| |t#1| (|Finite|)) (ATTRIBUTE (|Finite|)) |noBranch|) (IF (|has| |t#1| (|Field|)) (PROGN (ATTRIBUTE (|Field|)) (ATTRIBUTE (|DifferentialExtension| |t#1|)) (SIGNATURE |reduce| ((|Union| $ "failed") (|Fraction| |t#2|))) (SIGNATURE |derivationCoordinates| ((|Matrix| |t#1|) (|Vector| $) (|Mapping| |t#1| |t#1|)))) |noBranch|) (IF (|has| |t#1| (|FiniteFieldCategory|)) (ATTRIBUTE (|FiniteFieldCategory|)) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|Algebra| |#1|) . T) ((|Algebra| $) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|CharacteristicNonZero|))) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| |#2|) . T) ((|DifferentialExtension| |#1|) |has| |#1| (|Field|)) ((|DifferentialRing|) OR (|has| |#1| (|FiniteFieldCategory|)) (AND (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|)))) ((|DivisionRing|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|EntireRing|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|EuclideanDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|Field|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|FieldOfPrimeCharacteristic|) |has| |#1| (|FiniteFieldCategory|)) ((|Finite|) OR (|has| |#1| (|Finite|)) (|has| |#1| (|FiniteFieldCategory|))) ((|FiniteFieldCategory|) |has| |#1| (|FiniteFieldCategory|)) ((|FiniteRankAlgebra| |#1| |#2|) . T) ((|FramedAlgebra| |#1| |#2|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|GcdDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|IntegralDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LeftModule| (|Fraction| (|Integer|))) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LinearlyExplicitRingOver| (|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| (|Fraction| (|Integer|))) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|Module| |#1|) . T) ((|Module| $) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|PartialDifferentialRing| (|Symbol|)) AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PrincipalIdealDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightModule| (|Fraction| (|Integer|))) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|FiniteFieldCategory|)) ((|UniqueFactorizationDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)))) 
((|sample| (($) 14)) (|recip| (((|Union| $ "failed") $) 16)) (|one?| (((|Boolean|) $) 13)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 9)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 20))) 
(((|Monoid&| |#1|) (CATEGORY |domain| (SIGNATURE |recip| ((|Union| |#1| "failed") |#1|)) (SIGNATURE ^ (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |one?| ((|Boolean|) |#1|)) (SIGNATURE |sample| (|#1|)) (SIGNATURE ^ (|#1| |#1| (|PositiveInteger|))) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|)))) (|Monoid|)) (T |Monoid&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |recip| ((|Union| |#1| "failed") |#1|)) (SIGNATURE ^ (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |one?| ((|Boolean|) |#1|)) (SIGNATURE |sample| (|#1|)) (SIGNATURE ^ (|#1| |#1| (|PositiveInteger|))) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|)))) 
((~= (((|Boolean|) $ $) 7)) (|sample| (($) 19 T CONST)) (|recip| (((|Union| $ "failed") $) 15)) (|one?| (((|Boolean|) $) 18)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (^ (($ $ (|PositiveInteger|)) 12) (($ $ (|NonNegativeInteger|)) 16)) (|One| (($) 20 T CONST)) (= (((|Boolean|) $ $) 6)) (** (($ $ (|PositiveInteger|)) 13) (($ $ (|NonNegativeInteger|)) 17)) (* (($ $ $) 14))) 
(((|Monoid|) (|Category|)) (T |Monoid|)) 
((|One| (*1 *1) (|ofCategory| *1 (|Monoid|))) (|sample| (*1 *1) (|ofCategory| *1 (|Monoid|))) (|one?| (*1 *2 *1) (AND (|ofCategory| *1 (|Monoid|)) (|isDomain| *2 (|Boolean|)))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Monoid|)) (|isDomain| *2 (|NonNegativeInteger|)))) (^ (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Monoid|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|recip| (*1 *1 *1) (|partial| |ofCategory| *1 (|Monoid|)))) 
(|Join| (|SemiGroup|) (CATEGORY |domain| (SIGNATURE (|One|) ($) |constant|) (SIGNATURE |sample| ($) |constant|) (SIGNATURE |one?| ((|Boolean|) $)) (SIGNATURE ** ($ $ (|NonNegativeInteger|))) (SIGNATURE ^ ($ $ (|NonNegativeInteger|))) (SIGNATURE |recip| ((|Union| $ "failed") $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) 38)) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) 12)) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) 13)) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) 47))) 
(((|MonomialExtensionTools| |#1| |#2|) (CATEGORY |package| (SIGNATURE |split| ((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|))) (SIGNATURE |splitSquarefree| ((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|))) (SIGNATURE |normalDenom| (|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|))) (SIGNATURE |decompose| ((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)))) (|Field|) (|UnivariatePolynomialCategory| |#1|)) (T |MonomialExtensionTools|)) 
((|decompose| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| *6 *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Record| (|:| |poly| *6) (|:| |normal| (|Fraction| *6)) (|:| |special| (|Fraction| *6)))) (|isDomain| *1 (|MonomialExtensionTools| *5 *6)) (|isDomain| *3 (|Fraction| *6)))) (|normalDenom| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| *2)) (|isDomain| *4 (|Mapping| *2 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *5)) (|isDomain| *1 (|MonomialExtensionTools| *5 *2)) (|ofCategory| *5 (|Field|)))) (|splitSquarefree| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| *3 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Record| (|:| |normal| (|Factored| *3)) (|:| |special| (|Factored| *3)))) (|isDomain| *1 (|MonomialExtensionTools| *5 *3)))) (|split| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| *3 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Record| (|:| |normal| *3) (|:| |special| *3))) (|isDomain| *1 (|MonomialExtensionTools| *5 *3))))) 
(CATEGORY |package| (SIGNATURE |split| ((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|))) (SIGNATURE |splitSquarefree| ((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|))) (SIGNATURE |normalDenom| (|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|))) (SIGNATURE |decompose| ((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)))) 
((|reshape| ((|#7| (|List| |#5|) |#6|) NIL)) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) 26))) 
(((|MPolyCatFunctions2| |#1| |#2| |#3| |#4| |#5| |#6| |#7|) (CATEGORY |package| (SIGNATURE |map| (|#7| (|Mapping| |#5| |#4|) |#6|)) (SIGNATURE |reshape| (|#7| (|List| |#5|) |#6|))) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|OrderedAbelianMonoidSup|) (|Ring|) (|Ring|) (|PolynomialCategory| |#4| |#2| |#1|) (|PolynomialCategory| |#5| |#3| |#1|)) (T |MPolyCatFunctions2|)) 
((|reshape| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *9)) (|ofCategory| *9 (|Ring|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|Ring|)) (|ofCategory| *2 (|PolynomialCategory| *9 *7 *5)) (|isDomain| *1 (|MPolyCatFunctions2| *5 *6 *7 *8 *9 *4 *2)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|PolynomialCategory| *8 *6 *5)))) (|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *9 *8)) (|ofCategory| *8 (|Ring|)) (|ofCategory| *9 (|Ring|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|PolynomialCategory| *9 *7 *5)) (|isDomain| *1 (|MPolyCatFunctions2| *5 *6 *7 *8 *9 *4 *2)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|PolynomialCategory| *8 *6 *5))))) 
(CATEGORY |package| (SIGNATURE |map| (|#7| (|Mapping| |#5| |#4|) |#6|)) (SIGNATURE |reshape| (|#7| (|List| |#5|) |#6|))) 
((|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) 28))) 
(((|MPolyCatFunctions3| |#1| |#2| |#3| |#4| |#5| |#6| |#7|) (CATEGORY |package| (SIGNATURE |map| (|#7| (|Mapping| |#2| |#1|) |#6|))) (|OrderedSet|) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|OrderedAbelianMonoidSup|) (|Ring|) (|PolynomialCategory| |#5| |#3| |#1|) (|PolynomialCategory| |#5| |#4| |#2|)) (T |MPolyCatFunctions3|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *9 (|Ring|)) (|ofCategory| *2 (|PolynomialCategory| *9 *8 *6)) (|isDomain| *1 (|MPolyCatFunctions3| *5 *6 *7 *8 *9 *4 *2)) (|ofCategory| *8 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|PolynomialCategory| *9 *7 *5))))) 
(CATEGORY |package| (SIGNATURE |map| (|#7| (|Mapping| |#2| |#1|) |#6|))) 
((|factor| (((|Factored| |#4|) |#4|) 39))) 
(((|MPolyCatPolyFactorizer| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4|))) (|OrderedAbelianMonoidSup|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") (|Symbol|))))) (|EuclideanDomain|) (|PolynomialCategory| (|Polynomial| |#3|) |#1| |#2|)) (T |MPolyCatPolyFactorizer|)) 
((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") (|Symbol|)))))) (|ofCategory| *6 (|EuclideanDomain|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|MPolyCatPolyFactorizer| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| (|Polynomial| *6) *4 *5))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|variables| (((|List| (|OrderedVariableList| |#1|)) $) NIL)) (|univariate| (((|SparseUnivariatePolynomial| $) $ (|OrderedVariableList| |#1|)) NIL) (((|SparseUnivariatePolynomial| |#2|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#2| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#2| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#2| (|IntegralDomain|)))) (|totalDegree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|List| (|OrderedVariableList| |#1|))) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL (|has| |#2| (|GcdDomain|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#2| (|GcdDomain|)))) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Integer|) "failed") $) NIL (|has| |#2| (|RetractableTo| (|Integer|)))) (((|Union| (|OrderedVariableList| |#1|) "failed") $) NIL)) (|retract| ((|#2| $) NIL) (((|Fraction| (|Integer|)) $) NIL (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Integer|) $) NIL (|has| |#2| (|RetractableTo| (|Integer|)))) (((|OrderedVariableList| |#1|) $) NIL)) (|resultant| (($ $ $ (|OrderedVariableList| |#1|)) NIL (|has| |#2| (|CommutativeRing|)))) (|reductum| (($ $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| |#2|) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|primitivePart| (($ $) NIL (|has| |#2| (|GcdDomain|))) (($ $ (|OrderedVariableList| |#1|)) NIL (|has| |#2| (|GcdDomain|)))) (|primitiveMonomials| (((|List| $) $) NIL)) (|prime?| (((|Boolean|) $) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|pomopo!| (($ $ |#2| (|IndexedExponents| (|OrderedVariableList| |#1|)) $) NIL)) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (AND (|has| (|OrderedVariableList| |#1|) (|PatternMatchable| (|Float|))) (|has| |#2| (|PatternMatchable| (|Float|))))) (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (AND (|has| (|OrderedVariableList| |#1|) (|PatternMatchable| (|Integer|))) (|has| |#2| (|PatternMatchable| (|Integer|)))))) (|one?| (((|Boolean|) $) NIL)) (|numberOfMonomials| (((|NonNegativeInteger|) $) NIL)) (|multivariate| (($ (|SparseUnivariatePolynomial| |#2|) (|OrderedVariableList| |#1|)) NIL) (($ (|SparseUnivariatePolynomial| $) (|OrderedVariableList| |#1|)) NIL)) (|monomials| (((|List| $) $) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monomial| (($ |#2| (|IndexedExponents| (|OrderedVariableList| |#1|))) NIL) (($ $ (|OrderedVariableList| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| (|NonNegativeInteger|))) NIL)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ (|OrderedVariableList| |#1|)) NIL)) (|minimumDegree| (((|IndexedExponents| (|OrderedVariableList| |#1|)) $) NIL) (((|NonNegativeInteger|) $ (|OrderedVariableList| |#1|)) NIL) (((|List| (|NonNegativeInteger|)) $ (|List| (|OrderedVariableList| |#1|))) NIL)) (|min| (($ $ $) NIL (|has| |#2| (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#2| (|OrderedSet|)))) (|mapExponents| (($ (|Mapping| (|IndexedExponents| (|OrderedVariableList| |#1|)) (|IndexedExponents| (|OrderedVariableList| |#1|))) $) NIL)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL)) (|mainVariable| (((|Union| (|OrderedVariableList| |#1|) "failed") $) NIL)) (|leadingMonomial| (($ $) NIL)) (|leadingCoefficient| ((|#2| $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| |#2| (|GcdDomain|)))) (|lcm| (($ (|List| $)) NIL (|has| |#2| (|GcdDomain|))) (($ $ $) NIL (|has| |#2| (|GcdDomain|)))) (|latex| (((|String|) $) NIL)) (|isTimes| (((|Union| (|List| $) "failed") $) NIL)) (|isPlus| (((|Union| (|List| $) "failed") $) NIL)) (|isExpt| (((|Union| (|Record| (|:| |var| (|OrderedVariableList| |#1|)) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|ground?| (((|Boolean|) $) NIL)) (|ground| ((|#2| $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|GcdDomain|)))) (|gcd| (($ (|List| $)) NIL (|has| |#2| (|GcdDomain|))) (($ $ $) NIL (|has| |#2| (|GcdDomain|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|exquo| (((|Union| $ "failed") $ |#2|) NIL (|has| |#2| (|IntegralDomain|))) (((|Union| $ "failed") $ $) NIL (|has| |#2| (|IntegralDomain|)))) (|eval| (($ $ (|List| (|Equation| $))) NIL) (($ $ (|Equation| $)) NIL) (($ $ $ $) NIL) (($ $ (|List| $) (|List| $)) NIL) (($ $ (|OrderedVariableList| |#1|) |#2|) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| |#2|)) NIL) (($ $ (|OrderedVariableList| |#1|) $) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| $)) NIL)) (|discriminant| (($ $ (|OrderedVariableList| |#1|)) NIL (|has| |#2| (|CommutativeRing|)))) (|differentiate| (($ $ (|OrderedVariableList| |#1|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|))) NIL) (($ $ (|OrderedVariableList| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| (|NonNegativeInteger|))) NIL)) (|degree| (((|IndexedExponents| (|OrderedVariableList| |#1|)) $) NIL) (((|NonNegativeInteger|) $ (|OrderedVariableList| |#1|)) NIL) (((|List| (|NonNegativeInteger|)) $ (|List| (|OrderedVariableList| |#1|))) NIL)) (|convert| (((|Pattern| (|Float|)) $) NIL (AND (|has| (|OrderedVariableList| |#1|) (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Float|)))))) (((|Pattern| (|Integer|)) $) NIL (AND (|has| (|OrderedVariableList| |#1|) (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Integer|)))))) (((|InputForm|) $) NIL (AND (|has| (|OrderedVariableList| |#1|) (|ConvertibleTo| (|InputForm|))) (|has| |#2| (|ConvertibleTo| (|InputForm|)))))) (|content| ((|#2| $) NIL (|has| |#2| (|GcdDomain|))) (($ $ (|OrderedVariableList| |#1|)) NIL (|has| |#2| (|GcdDomain|)))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#2| (|PolynomialFactorizationExplicit|))))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ |#2|) NIL) (($ (|OrderedVariableList| |#1|)) NIL) (($ $) NIL (|has| |#2| (|IntegralDomain|))) (($ (|Fraction| (|Integer|))) NIL (OR (|has| |#2| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|))))))) (|coefficients| (((|List| |#2|) $) NIL)) (|coefficient| ((|#2| $ (|IndexedExponents| (|OrderedVariableList| |#1|))) NIL) (($ $ (|OrderedVariableList| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| (|NonNegativeInteger|))) NIL)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#2| (|PolynomialFactorizationExplicit|))) (|has| |#2| (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|CommutativeRing|)))) (|associates?| (((|Boolean|) $ $) NIL (|has| |#2| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($ $ (|OrderedVariableList| |#1|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|))) NIL) (($ $ (|OrderedVariableList| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderedVariableList| |#1|)) (|List| (|NonNegativeInteger|))) NIL)) (>= (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (/ (($ $ |#2|) NIL (|has| |#2| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#2| (|Algebra| (|Fraction| (|Integer|))))) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#2| (|Algebra| (|Fraction| (|Integer|))))) (($ |#2| $) NIL) (($ $ |#2|) NIL))) 
(((|MultivariatePolynomial| |#1| |#2|) (|PolynomialCategory| |#2| (|IndexedExponents| (|OrderedVariableList| |#1|)) (|OrderedVariableList| |#1|)) (|List| (|Symbol|)) (|Ring|)) (T |MultivariatePolynomial|)) 
NIL 
(|PolynomialCategory| |#2| (|IndexedExponents| (|OrderedVariableList| |#1|)) (|OrderedVariableList| |#1|)) 
((|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) 13)) (|pushup| ((|#4| |#4| |#2|) 30)) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) 63)) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) 76)) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) 49)) (|pushdown| ((|#4| |#4| |#2|) 52)) (|factor| (((|Factored| |#4|) |#4|) 38))) 
(((|MPolyCatRationalFunctionFactorizer| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |totalfract| ((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|)) (SIGNATURE |pushdown| (|#4| |#4| |#2|)) (SIGNATURE |pushdterm| (|#4| (|SparseUnivariatePolynomial| |#4|) |#2|)) (SIGNATURE |pushup| (|#4| |#4| |#2|)) (SIGNATURE |pushucoef| (|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|)) (SIGNATURE |pushuconst| (|#4| (|Fraction| (|Polynomial| |#3|)) |#2|)) (SIGNATURE |factor| ((|Factored| |#4|) |#4|))) (|OrderedAbelianMonoidSup|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $)))) (|IntegralDomain|) (|PolynomialCategory| (|Fraction| (|Polynomial| |#3|)) |#1| |#2|)) (T |MPolyCatRationalFunctionFactorizer|)) 
((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $))))) (|ofCategory| *6 (|IntegralDomain|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| (|Fraction| (|Polynomial| *6)) *4 *5)))) (|pushuconst| (*1 *2 *3 *4) (AND (|ofCategory| *6 (|IntegralDomain|)) (|ofCategory| *2 (|PolynomialCategory| *3 *5 *4)) (|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *5 *4 *6 *2)) (|isDomain| *3 (|Fraction| (|Polynomial| *6))) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $))))))) (|pushucoef| (*1 *2 *3 *4) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| (|Polynomial| *6))) (|ofCategory| *6 (|IntegralDomain|)) (|ofCategory| *2 (|PolynomialCategory| (|Fraction| (|Polynomial| *6)) *5 *4)) (|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *5 *4 *6 *2)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $))))))) (|pushup| (*1 *2 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $))))) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *4 *3 *5 *2)) (|ofCategory| *2 (|PolynomialCategory| (|Fraction| (|Polynomial| *5)) *4 *3)))) (|pushdterm| (*1 *2 *3 *4) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *2)) (|ofCategory| *2 (|PolynomialCategory| (|Fraction| (|Polynomial| *6)) *5 *4)) (|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *5 *4 *6 *2)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $))))) (|ofCategory| *6 (|IntegralDomain|)))) (|pushdown| (*1 *2 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $))))) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *4 *3 *5 *2)) (|ofCategory| *2 (|PolynomialCategory| (|Fraction| (|Polynomial| *5)) *4 *3)))) (|totalfract| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $))))) (|ofCategory| *6 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |sup| (|Polynomial| *6)) (|:| |inf| (|Polynomial| *6)))) (|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| (|Fraction| (|Polynomial| *6)) *4 *5))))) 
(CATEGORY |package| (SIGNATURE |totalfract| ((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|)) (SIGNATURE |pushdown| (|#4| |#4| |#2|)) (SIGNATURE |pushdterm| (|#4| (|SparseUnivariatePolynomial| |#4|) |#2|)) (SIGNATURE |pushup| (|#4| |#4| |#2|)) (SIGNATURE |pushucoef| (|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|)) (SIGNATURE |pushuconst| (|#4| (|Fraction| (|Polynomial| |#3|)) |#2|)) (SIGNATURE |factor| ((|Factored| |#4|) |#4|))) 
((|factor| (((|Factored| |#4|) |#4|) 51))) 
(((|MRationalFactorize| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4|))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|Join| (|EuclideanDomain|) (|CharacteristicZero|)) (|PolynomialCategory| (|Fraction| |#3|) |#1| |#2|)) (T |MRationalFactorize|)) 
((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|MRationalFactorize| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| (|Fraction| *6) *4 *5))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4|))) 
((|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) 18))) 
(((|MonoidRingFunctions2| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |map| ((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)))) (|Ring|) (|Ring|) (|Monoid|)) (T |MonoidRingFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|MonoidRing| *5 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *7 (|Monoid|)) (|isDomain| *2 (|MonoidRing| *6 *7)) (|isDomain| *1 (|MonoidRingFunctions2| *5 *6 *7))))) 
(CATEGORY |package| (SIGNATURE |map| ((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 26)) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) 27)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|size| (((|NonNegativeInteger|)) 20 (AND (|has| |#2| (|Finite|)) (|has| |#1| (|Finite|))))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) 55) (((|Union| |#1| "failed") $) 58)) (|retract| ((|#2| $) NIL) ((|#1| $) NIL)) (|reductum| (($ $) 75 (|has| |#2| (|OrderedSet|)))) (|recip| (((|Union| $ "failed") $) 62)) (|random| (($) 33 (AND (|has| |#2| (|Finite|)) (|has| |#1| (|Finite|))))) (|one?| (((|Boolean|) $) NIL)) (|numberOfMonomials| (((|NonNegativeInteger|) $) 53)) (|monomials| (((|List| $) $) 37)) (|monomial?| (((|Boolean|) $) NIL)) (|monomial| (($ |#1| |#2|) 16)) (|map| (($ (|Mapping| |#1| |#1|) $) 52)) (|lookup| (((|PositiveInteger|) $) 30 (AND (|has| |#2| (|Finite|)) (|has| |#1| (|Finite|))))) (|leadingMonomial| ((|#2| $) 74 (|has| |#2| (|OrderedSet|)))) (|leadingCoefficient| ((|#1| $) 73 (|has| |#2| (|OrderedSet|)))) (|latex| (((|String|) $) NIL)) (|index| (($ (|PositiveInteger|)) 25 (AND (|has| |#2| (|Finite|)) (|has| |#1| (|Finite|))))) (|hash| (((|SingleInteger|) $) NIL)) (|enumerate| (((|List| $)) NIL (AND (|has| |#2| (|Finite|)) (|has| |#1| (|Finite|))))) (|coerce| (((|OutputForm|) $) 72) (($ (|Integer|)) 44) (($ |#2|) 40) (($ |#1|) 41) (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) 11)) (|coefficients| (((|List| |#1|) $) 39)) (|coefficient| ((|#1| $ |#2|) 83)) (|charthRoot| (((|Union| $ "failed") $) NIL (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 12 T CONST)) (|One| (($) 31 T CONST)) (= (((|Boolean|) $ $) 76)) (- (($ $) 46) (($ $ $) NIL)) (+ (($ $ $) 24)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 50) (($ $ $) 85) (($ |#1| $) 48 (|has| |#1| (|CommutativeRing|))) (($ $ |#1|) NIL (|has| |#1| (|CommutativeRing|))))) 
(((|MonoidRing| |#1| |#2|) (|Join| (|Ring|) (|RetractableTo| |#2|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |monomial| ($ |#1| |#2|)) (SIGNATURE |coefficient| (|#1| $ |#2|)) (SIGNATURE |coerce| ($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))))) (SIGNATURE |terms| ((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (SIGNATURE |monomial?| ((|Boolean|) $)) (SIGNATURE |coefficients| ((|List| |#1|) $)) (SIGNATURE |monomials| ((|List| $) $)) (SIGNATURE |numberOfMonomials| ((|NonNegativeInteger|) $)) (IF (|has| |#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |noBranch|) (IF (|has| |#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |#1|)) |noBranch|) (IF (|has| |#1| (|Finite|)) (IF (|has| |#2| (|Finite|)) (ATTRIBUTE (|Finite|)) |noBranch|) |noBranch|) (IF (|has| |#2| (|OrderedSet|)) (PROGN (SIGNATURE |leadingMonomial| (|#2| $)) (SIGNATURE |leadingCoefficient| (|#1| $)) (SIGNATURE |reductum| ($ $))) |noBranch|))) (|Ring|) (|Monoid|)) (T |MonoidRing|)) 
((|monomial| (*1 *1 *2 *3) (AND (|isDomain| *1 (|MonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|Monoid|)))) (|coefficient| (*1 *2 *1 *3) (AND (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|MonoidRing| *2 *3)) (|ofCategory| *3 (|Monoid|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |coef| *3) (|:| |monom| *4)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|Monoid|)) (|isDomain| *1 (|MonoidRing| *3 *4)))) (|terms| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |coef| *3) (|:| |monom| *4)))) (|isDomain| *1 (|MonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|Monoid|)))) (|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|MonoidRing| *3 *4)) (|ofCategory| *4 (|Monoid|)))) (|monomial?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|MonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|Monoid|)))) (|coefficients| (*1 *2 *1) (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|MonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|Monoid|)))) (|monomials| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|MonoidRing| *3 *4))) (|isDomain| *1 (|MonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|Monoid|)))) (|numberOfMonomials| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|MonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|Monoid|)))) (|leadingMonomial| (*1 *2 *1) (AND (|ofCategory| *2 (|Monoid|)) (|ofCategory| *2 (|OrderedSet|)) (|isDomain| *1 (|MonoidRing| *3 *2)) (|ofCategory| *3 (|Ring|)))) (|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|MonoidRing| *2 *3)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *3 (|Monoid|)))) (|reductum| (*1 *1 *1) (AND (|isDomain| *1 (|MonoidRing| *2 *3)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|Monoid|))))) 
(|Join| (|Ring|) (|RetractableTo| |#2|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |monomial| ($ |#1| |#2|)) (SIGNATURE |coefficient| (|#1| $ |#2|)) (SIGNATURE |coerce| ($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))))) (SIGNATURE |terms| ((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (SIGNATURE |monomial?| ((|Boolean|) $)) (SIGNATURE |coefficients| ((|List| |#1|) $)) (SIGNATURE |monomials| ((|List| $) $)) (SIGNATURE |numberOfMonomials| ((|NonNegativeInteger|) $)) (IF (|has| |#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |noBranch|) (IF (|has| |#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |#1|)) |noBranch|) (IF (|has| |#1| (|Finite|)) (IF (|has| |#2| (|Finite|)) (ATTRIBUTE (|Finite|)) |noBranch|) |noBranch|) (IF (|has| |#2| (|OrderedSet|)) (PROGN (SIGNATURE |leadingMonomial| (|#2| $)) (SIGNATURE |leadingCoefficient| (|#1| $)) (SIGNATURE |reductum| ($ $))) |noBranch|))) 
((~= (((|Boolean|) $ $) 18)) (|union| (($ |#1| $) 72) (($ $ |#1|) 71) (($ $ $) 70)) (|symmetricDifference| (($ $ $) 68)) (|subset?| (((|Boolean|) $ $) 69)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|set| (($ (|List| |#1|)) 64) (($) 63)) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) 42 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 52 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) 7 T CONST)) (|removeDuplicates!| (($ $) 58)) (|removeDuplicates| (($ $) 55 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove!| (($ |#1| $) 44 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) |#1|) $) 43 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remove| (($ |#1| $) 54 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#1|) $) 51 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 53 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 50 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 49 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22)) (|intersect| (($ $ $) 65)) (|inspect| ((|#1| $) 36)) (|insert!| (($ |#1| $) 37) (($ |#1| $ (|NonNegativeInteger|)) 59)) (|hash| (((|SingleInteger|) $) 21)) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) 48)) (|extract!| ((|#1| $) 38)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) 57)) (|difference| (($ $ |#1|) 67) (($ $ $) 66)) (|dictionary| (($) 46) (($ (|List| |#1|)) 45)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|convert| (((|InputForm|) $) 56 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 47)) (|coerce| (((|OutputForm|) $) 20)) (|brace| (($ (|List| |#1|)) 62) (($) 61)) (|bag| (($ (|List| |#1|)) 39)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19)) (< (((|Boolean|) $ $) 60)) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|MultisetAggregate| |#1|) (|Category|) (|SetCategory|)) (T |MultisetAggregate|)) 
NIL 
(|Join| (|MultiDictionary| |t#1|) (|SetAggregate| |t#1|)) 
(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|MultiDictionary| |#1|) . T) ((|SetAggregate| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|union| (($ |#1| $) NIL) (($ $ |#1|) NIL) (($ $ $) 77)) (|symmetricDifference| (($ $ $) 80)) (|subset?| (((|Boolean|) $ $) 83)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|set| (($ (|List| |#1|)) 24) (($) 15)) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) 71 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) NIL T CONST)) (|removeDuplicates!| (($ $) 72)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|remove!| (($ |#1| $) 61 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) |#1|) $) 64 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ |#1| $ (|Integer|)) 62) (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) 65)) (|remove| (($ |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ |#1| $ (|Integer|)) 67) (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) 68)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|parts| (((|List| |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|multiset| (($) 13) (($ |#1|) 26) (($ (|List| |#1|)) 21)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#1|) $) 38)) (|member?| (((|Boolean|) |#1| $) 57 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 75 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 76)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL)) (|intersect| (($ $ $) 78)) (|inspect| ((|#1| $) 54)) (|insert!| (($ |#1| $) 55) (($ |#1| $ (|NonNegativeInteger|)) 73)) (|hash| (((|SingleInteger|) $) NIL)) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) NIL)) (|extract!| ((|#1| $) 53)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) 49)) (|empty| (($) 12)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) 47)) (|difference| (($ $ |#1|) NIL) (($ $ $) 79)) (|dictionary| (($) 14) (($ (|List| |#1|)) 23)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 60 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) 66)) (|convert| (((|InputForm|) $) 36 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 20)) (|coerce| (((|OutputForm|) $) 44)) (|brace| (($ (|List| |#1|)) 25) (($) 16)) (|bag| (($ (|List| |#1|)) 22)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 81)) (< (((|Boolean|) $ $) 82)) (|#| (((|NonNegativeInteger|) $) 59 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|Multiset| |#1|) (|Join| (|MultisetAggregate| |#1|) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (ATTRIBUTE |shallowlyMutable|) (SIGNATURE |multiset| ($)) (SIGNATURE |multiset| ($ |#1|)) (SIGNATURE |multiset| ($ (|List| |#1|))) (SIGNATURE |members| ((|List| |#1|) $)) (SIGNATURE |remove| ($ |#1| $ (|Integer|))) (SIGNATURE |remove| ($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|))) (SIGNATURE |remove!| ($ |#1| $ (|Integer|))) (SIGNATURE |remove!| ($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|))))) (|SetCategory|)) (T |Multiset|)) 
((|multiset| (*1 *1) (AND (|isDomain| *1 (|Multiset| *2)) (|ofCategory| *2 (|SetCategory|)))) (|multiset| (*1 *1 *2) (AND (|isDomain| *1 (|Multiset| *2)) (|ofCategory| *2 (|SetCategory|)))) (|multiset| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Multiset| *3)))) (|members| (*1 *2 *1) (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|Multiset| *3)) (|ofCategory| *3 (|SetCategory|)))) (|remove| (*1 *1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|Multiset| *2)) (|ofCategory| *2 (|SetCategory|)))) (|remove| (*1 *1 *2 *1 *3) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *4)) (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *1 (|Multiset| *4)))) (|remove!| (*1 *1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|Multiset| *2)) (|ofCategory| *2 (|SetCategory|)))) (|remove!| (*1 *1 *2 *1 *3) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *4)) (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *1 (|Multiset| *4))))) 
(|Join| (|MultisetAggregate| |#1|) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (ATTRIBUTE |shallowlyMutable|) (SIGNATURE |multiset| ($)) (SIGNATURE |multiset| ($ |#1|)) (SIGNATURE |multiset| ($ (|List| |#1|))) (SIGNATURE |members| ((|List| |#1|) $)) (SIGNATURE |remove| ($ |#1| $ (|Integer|))) (SIGNATURE |remove| ($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|))) (SIGNATURE |remove!| ($ |#1| $ (|Integer|))) (SIGNATURE |remove!| ($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|))))) 
((|systemCommand| (((|Void|) (|String|)) 8))) 
(((|MoreSystemCommands|) (CATEGORY |package| (SIGNATURE |systemCommand| ((|Void|) (|String|))))) (T |MoreSystemCommands|)) 
((|systemCommand| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|MoreSystemCommands|))))) 
(CATEGORY |package| (SIGNATURE |systemCommand| ((|Void|) (|String|)))) 
((|mergeDifference| (((|List| |#1|) (|List| |#1|) (|List| |#1|)) 10))) 
(((|MergeThing| |#1|) (CATEGORY |package| (SIGNATURE |mergeDifference| ((|List| |#1|) (|List| |#1|) (|List| |#1|)))) (|OrderedSet|)) (T |MergeThing|)) 
((|mergeDifference| (*1 *2 *2 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|MergeThing| *3))))) 
(CATEGORY |package| (SIGNATURE |mergeDifference| ((|List| |#1|) (|List| |#1|) (|List| |#1|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|variables| (((|List| |#2|) $) 134)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 127 (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) 126 (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) 124 (|has| |#1| (|IntegralDomain|)))) (|tanh| (($ $) 83 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|tan| (($ $) 66 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sqrt| (($ $) 65 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sinh| (($ $) 82 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sin| (($ $) 67 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sech| (($ $) 81 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sec| (($ $) 68 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sample| (($) 16 T CONST)) (|reductum| (($ $) 118)) (|recip| (((|Union| $ "failed") $) 33)) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) 96) (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) 95)) (|pole?| (((|Boolean|) $) 135)) (|pi| (($) 93 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|order| (((|NonNegativeInteger|) $ |#2|) 98) (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) 97)) (|one?| (((|Boolean|) $) 30)) (|nthRoot| (($ $ (|Integer|)) 64 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|monomial?| (((|Boolean|) $) 116)) (|monomial| (($ $ (|List| |#2|) (|List| (|IndexedExponents| |#2|))) 133) (($ $ |#2| (|IndexedExponents| |#2|)) 132) (($ |#1| (|IndexedExponents| |#2|)) 117) (($ $ |#2| (|NonNegativeInteger|)) 100) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) 99)) (|map| (($ (|Mapping| |#1| |#1|) $) 115)) (|log| (($ $) 90 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|leadingMonomial| (($ $) 113)) (|leadingCoefficient| ((|#1| $) 112)) (|latex| (((|String|) $) 9)) (|integrate| (($ $ |#2|) 94 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|hash| (((|SingleInteger|) $) 10)) (|extend| (($ $ (|NonNegativeInteger|)) 101)) (|exquo| (((|Union| $ "failed") $ $) 128 (|has| |#1| (|IntegralDomain|)))) (|exp| (($ $) 91 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|eval| (($ $ |#2| $) 109) (($ $ (|List| |#2|) (|List| $)) 108) (($ $ (|List| (|Equation| $))) 107) (($ $ (|Equation| $)) 106) (($ $ $ $) 105) (($ $ (|List| $) (|List| $)) 104)) (|differentiate| (($ $ |#2|) 41) (($ $ (|List| |#2|)) 40) (($ $ |#2| (|NonNegativeInteger|)) 39) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) 38)) (|degree| (((|IndexedExponents| |#2|) $) 114)) (|csch| (($ $) 80 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|csc| (($ $) 69 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|coth| (($ $) 79 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cot| (($ $) 70 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cosh| (($ $) 78 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cos| (($ $) 71 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|complete| (($ $) 136)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ |#1|) 131 (|has| |#1| (|CommutativeRing|))) (($ $) 129 (|has| |#1| (|IntegralDomain|))) (($ (|Fraction| (|Integer|))) 121 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|coefficient| ((|#1| $ (|IndexedExponents| |#2|)) 119) (($ $ |#2| (|NonNegativeInteger|)) 103) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) 102)) (|charthRoot| (((|Union| $ "failed") $) 130 (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|atanh| (($ $) 89 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|atan| (($ $) 77 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|associates?| (((|Boolean|) $ $) 125 (|has| |#1| (|IntegralDomain|)))) (|asinh| (($ $) 88 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asin| (($ $) 76 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asech| (($ $) 87 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asec| (($ $) 75 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acsch| (($ $) 86 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acsc| (($ $) 74 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acoth| (($ $) 85 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acot| (($ $) 73 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acosh| (($ $) 84 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acos| (($ $) 72 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $ |#2|) 37) (($ $ (|List| |#2|)) 36) (($ $ |#2| (|NonNegativeInteger|)) 35) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) 34)) (= (((|Boolean|) $ $) 6)) (/ (($ $ |#1|) 120 (|has| |#1| (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ $) 92 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) 63 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ (|Fraction| (|Integer|))) 123 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ (|Fraction| (|Integer|)) $) 122 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ |#1| $) 111) (($ $ |#1|) 110))) 
(((|MultivariateTaylorSeriesCategory| |#1| |#2|) (|Category|) (|Ring|) (|OrderedSet|)) (T |MultivariateTaylorSeriesCategory|)) 
((|coefficient| (*1 *1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *2)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|OrderedSet|)))) (|coefficient| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *5)) (|isDomain| *3 (|List| (|NonNegativeInteger|))) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *5)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedSet|)))) (|extend| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)))) (|monomial| (*1 *1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *2)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|OrderedSet|)))) (|monomial| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *5)) (|isDomain| *3 (|List| (|NonNegativeInteger|))) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *5)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedSet|)))) (|order| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *3)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|order| (*1 *2 *1 *3 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *3)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|)))) (|polynomial| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *5)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Polynomial| *4)))) (|polynomial| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *5)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Polynomial| *4)))) (|integrate| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))))) 
(|Join| (|PartialDifferentialRing| |t#2|) (|PowerSeriesCategory| |t#1| (|IndexedExponents| |t#2|) |t#2|) (|InnerEvalable| |t#2| $) (|Evalable| $) (CATEGORY |domain| (SIGNATURE |coefficient| ($ $ |t#2| (|NonNegativeInteger|))) (SIGNATURE |coefficient| ($ $ (|List| |t#2|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |extend| ($ $ (|NonNegativeInteger|))) (SIGNATURE |monomial| ($ $ |t#2| (|NonNegativeInteger|))) (SIGNATURE |monomial| ($ $ (|List| |t#2|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |order| ((|NonNegativeInteger|) $ |t#2|)) (SIGNATURE |order| ((|NonNegativeInteger|) $ |t#2| (|NonNegativeInteger|))) (SIGNATURE |polynomial| ((|Polynomial| |t#1|) $ (|NonNegativeInteger|))) (SIGNATURE |polynomial| ((|Polynomial| |t#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|))) (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |integrate| ($ $ |t#2|)) (ATTRIBUTE (|RadicalCategory|)) (ATTRIBUTE (|TranscendentalFunctionCategory|))) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| (|IndexedExponents| |#2|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Evalable| $) . T) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|InnerEvalable| |#2| $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|Module| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialRing| |#2|) . T) ((|PowerSeriesCategory| |#1| (|IndexedExponents| |#2|) |#2|) . T) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|))))) 
((|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) 28) (((|Factored| |#4|) |#4|) 24))) 
(((|MultivariateFactorize| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4|)) (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)))) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|Join| (|EuclideanDomain|) (|CharacteristicZero|)) (|PolynomialCategory| |#3| |#2| |#1|)) (T |MultivariateFactorize|)) 
((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *7 (|PolynomialCategory| *6 *5 *4)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *7))) (|isDomain| *1 (|MultivariateFactorize| *4 *5 *6 *7)) (|isDomain| *3 (|SparseUnivariatePolynomial| *7)))) (|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|MultivariateFactorize| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *6 *5 *4))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4|)) (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)))) 
((|univcase| (((|Factored| |#4|) |#4| |#2|) 116)) (|squareFreePrim| (((|Factored| |#4|) |#4|) NIL)) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) 107) (((|Factored| |#4|) |#4|) 38)) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) 65)) (|normDeriv2| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) 133)) (|myDegree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|)) 58)) (|lift| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|)) 62)) (|intChoose| (((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) 22)) (|consnewpol| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) 54)) (|compdegd| (((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) 130)) (|coefChoose| ((|#4| (|Integer|) (|Factored| |#4|)) 55)) (|check| (((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) NIL))) 
(((|MultivariateSquareFree| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |squareFree| ((|Factored| |#4|) |#4|)) (SIGNATURE |squareFree| ((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |squareFreePrim| ((|Factored| |#4|) |#4|)) (SIGNATURE |compdegd| ((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))))) (SIGNATURE |univcase| ((|Factored| |#4|) |#4| |#2|)) (SIGNATURE |consnewpol| ((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|))) (SIGNATURE |nsqfree| ((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|)))) (SIGNATURE |intChoose| ((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|)))) (SIGNATURE |coefChoose| (|#4| (|Integer|) (|Factored| |#4|))) (SIGNATURE |check| ((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))))) (SIGNATURE |lift| ((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|))) (SIGNATURE |myDegree| ((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|))) (SIGNATURE |normDeriv2| ((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|EuclideanDomain|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |MultivariateSquareFree|)) 
((|normDeriv2| (*1 *2 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *6)) (|isDomain| *3 (|Integer|)) (|ofCategory| *6 (|EuclideanDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|MultivariateSquareFree| *4 *5 *6 *7)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)))) (|myDegree| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *9)) (|isDomain| *4 (|List| *7)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *9 (|PolynomialCategory| *8 *6 *7)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|EuclideanDomain|)) (|isDomain| *2 (|List| (|NonNegativeInteger|))) (|isDomain| *1 (|MultivariateSquareFree| *6 *7 *8 *9)) (|isDomain| *5 (|NonNegativeInteger|)))) (|lift| (*1 *2 *3 *4 *4 *5 *6 *7 *8) (|partial| AND (|isDomain| *4 (|SparseUnivariatePolynomial| *11)) (|isDomain| *6 (|List| *10)) (|isDomain| *7 (|List| (|NonNegativeInteger|))) (|isDomain| *8 (|List| *11)) (|ofCategory| *10 (|OrderedSet|)) (|ofCategory| *11 (|EuclideanDomain|)) (|ofCategory| *9 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|PolynomialCategory| *11 *9 *10)) (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *5))) (|isDomain| *1 (|MultivariateSquareFree| *9 *10 *11 *5)) (|isDomain| *3 (|SparseUnivariatePolynomial| *5)))) (|check| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| *6)) (|:| |exponent| (|Integer|))))) (|ofCategory| *6 (|EuclideanDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|MultivariateSquareFree| *4 *5 *6 *7)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)))) (|coefChoose| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *4 (|Factored| *2)) (|ofCategory| *2 (|PolynomialCategory| *7 *5 *6)) (|isDomain| *1 (|MultivariateSquareFree| *5 *6 *7 *2)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|EuclideanDomain|)))) (|intChoose| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *9)) (|isDomain| *4 (|List| *7)) (|isDomain| *5 (|List| (|List| *8))) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|EuclideanDomain|)) (|ofCategory| *9 (|PolynomialCategory| *8 *6 *7)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Record| (|:| |upol| (|SparseUnivariatePolynomial| *8)) (|:| |Lval| (|List| *8)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| *8)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| *8))) (|isDomain| *1 (|MultivariateSquareFree| *6 *7 *8 *9)))) (|nsqfree| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|List| *7)) (|isDomain| *5 (|List| (|List| *8))) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|EuclideanDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *9 (|PolynomialCategory| *8 *6 *7)) (|isDomain| *2 (|Record| (|:| |unitPart| *9) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| *9)) (|:| |exponent| (|Integer|))))))) (|isDomain| *1 (|MultivariateSquareFree| *6 *7 *8 *9)) (|isDomain| *3 (|SparseUnivariatePolynomial| *9)))) (|consnewpol| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|Integer|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|EuclideanDomain|)) (|ofCategory| *9 (|PolynomialCategory| *8 *6 *7)) (|isDomain| *2 (|Record| (|:| |pol| (|SparseUnivariatePolynomial| *9)) (|:| |polval| (|SparseUnivariatePolynomial| *8)))) (|isDomain| *1 (|MultivariateSquareFree| *6 *7 *8 *9)) (|isDomain| *3 (|SparseUnivariatePolynomial| *9)) (|isDomain| *4 (|SparseUnivariatePolynomial| *8)))) (|univcase| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *6 (|EuclideanDomain|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|MultivariateSquareFree| *5 *4 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *6 *5 *4)))) (|compdegd| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| *6)) (|:| |exponent| (|Integer|))))) (|ofCategory| *6 (|EuclideanDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|MultivariateSquareFree| *4 *5 *6 *7)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)))) (|squareFreePrim| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|EuclideanDomain|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|MultivariateSquareFree| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *6 *4 *5)))) (|squareFree| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|EuclideanDomain|)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *7))) (|isDomain| *1 (|MultivariateSquareFree| *4 *5 *6 *7)) (|isDomain| *3 (|SparseUnivariatePolynomial| *7)))) (|squareFree| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|EuclideanDomain|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|MultivariateSquareFree| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *6 *4 *5))))) 
(CATEGORY |package| (SIGNATURE |squareFree| ((|Factored| |#4|) |#4|)) (SIGNATURE |squareFree| ((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |squareFreePrim| ((|Factored| |#4|) |#4|)) (SIGNATURE |compdegd| ((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))))) (SIGNATURE |univcase| ((|Factored| |#4|) |#4| |#2|)) (SIGNATURE |consnewpol| ((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|))) (SIGNATURE |nsqfree| ((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|)))) (SIGNATURE |intChoose| ((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|)))) (SIGNATURE |coefChoose| (|#4| (|Integer|) (|Factored| |#4|))) (SIGNATURE |check| ((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))))) (SIGNATURE |lift| ((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|))) (SIGNATURE |myDegree| ((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|))) (SIGNATURE |normDeriv2| ((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|variables| (((|List| (|Symbol|)) $) NIL)) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) NIL (|has| |#2| (|IntegralDomain|)))) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|tower| (((|List| (|Kernel| $)) $) NIL)) (|summation| (($ $ (|SegmentBinding| $)) NIL) (($ $ (|Symbol|)) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|subst| (($ $ (|Equation| $)) NIL) (($ $ (|List| (|Equation| $))) NIL) (($ $ (|List| (|Kernel| $)) (|List| $)) NIL)) (|squareFreePart| (($ $) NIL (|has| |#2| (|IntegralDomain|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#2| (|IntegralDomain|)))) (|sizeLess?| (((|Boolean|) $ $) NIL (|has| |#2| (|IntegralDomain|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Kernel| $) "failed") $) NIL) (((|Union| (|Symbol|) "failed") $) NIL) (((|Union| 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(((|MyUnivariatePolynomial| |#1| |#2|) (|Join| (|UnivariatePolynomialCategory| |#2|) (CATEGORY |domain| (ATTRIBUTE (|RetractableTo| (|Symbol|))) (SIGNATURE |coerce| ($ (|Variable| |#1|))) (SIGNATURE |fmecg| ($ $ (|NonNegativeInteger|) |#2| $)) (IF (|has| |#2| (SIGNATURE |univariate| ((|SparseUnivariatePolynomial| |#2|) |#2| (|Symbol|)))) (SIGNATURE |coerce| ($ |#2|)) |noBranch|) (SIGNATURE |coerce| ($ (|Polynomial| |#2|))))) (|Symbol|) (|Ring|)) (T |MyUnivariatePolynomial|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *1 (|MyUnivariatePolynomial| *3 *2)) (|ofType| *3 (|Symbol|)) (|ofCategory| *2 (|Ring|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Variable| *3)) (|ofType| *3 (|Symbol|)) (|isDomain| *1 (|MyUnivariatePolynomial| *3 *4)) (|ofCategory| *4 (|Ring|)))) (|fmecg| (*1 *1 *1 *2 *3 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|MyUnivariatePolynomial| *4 *3)) (|ofType| *4 (|Symbol|)) (|ofCategory| *3 (|Ring|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|MyUnivariatePolynomial| *3 *4)) (|ofType| *3 (|Symbol|))))) 
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((|plenaryPower| (($ $ (|PositiveInteger|)) 12))) 
(((|NonAssociativeAlgebra&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |plenaryPower| (|#1| |#1| (|PositiveInteger|)))) (|NonAssociativeAlgebra| |#2|) (|CommutativeRing|)) (T |NonAssociativeAlgebra&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |plenaryPower| (|#1| |#1| (|PositiveInteger|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|rightPower| (($ $ (|PositiveInteger|)) 27)) (|plenaryPower| (($ $ (|PositiveInteger|)) 32)) (|leftPower| (($ $ (|PositiveInteger|)) 28)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|commutator| (($ $ $) 24)) (|coerce| (((|OutputForm|) $) 11)) (|associator| (($ $ $ $) 25)) (|antiCommutator| (($ $ $) 23)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 29)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 26) (($ $ |#1|) 34) (($ |#1| $) 33))) 
(((|NonAssociativeAlgebra| |#1|) (|Category|) (|CommutativeRing|)) (T |NonAssociativeAlgebra|)) 
((|plenaryPower| (*1 *1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|NonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|))))) 
(|Join| (|NonAssociativeRng|) (|Module| |t#1|) (CATEGORY |domain| (SIGNATURE |plenaryPower| ($ $ (|PositiveInteger|))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| |#1|) . T) ((|Module| |#1|) . T) ((|Monad|) . T) ((|NonAssociativeRng|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T)) 
((|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) 24)) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) 23))) 
(((|NagPolynomialRootsPackage|) (CATEGORY |package| (SIGNATURE |c02aff| ((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|))) (SIGNATURE |c02agf| ((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|))))) (T |NagPolynomialRootsPackage|)) 
((|c02agf| (*1 *2 *3 *4 *5 *4) (AND (|isDomain| *3 (|Matrix| (|DoubleFloat|))) (|isDomain| *4 (|Integer|)) (|isDomain| *5 (|Boolean|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagPolynomialRootsPackage|)))) (|c02aff| (*1 *2 *3 *4 *5 *4) (AND (|isDomain| *3 (|Matrix| (|DoubleFloat|))) (|isDomain| *4 (|Integer|)) (|isDomain| *5 (|Boolean|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagPolynomialRootsPackage|))))) 
(CATEGORY |package| (SIGNATURE |c02aff| ((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|))) (SIGNATURE |c02agf| ((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)))) 
((|c05pbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp35| FCN)))) 43)) (|c05nbf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp6| FCN)))) 39)) (|c05adf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) 32))) 
(((|NagRootFindingPackage|) (CATEGORY |package| (SIGNATURE |c05adf| ((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F))))) (SIGNATURE |c05nbf| ((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp6| FCN))))) (SIGNATURE |c05pbf| ((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp35| FCN))))))) (T |NagRootFindingPackage|)) 
((|c05pbf| (*1 *2 *3 *3 *3 *4 *5 *3 *6) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *4 (|Matrix| (|DoubleFloat|))) (|isDomain| *5 (|DoubleFloat|)) (|isDomain| *6 (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp35| FCN)))) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagRootFindingPackage|)))) (|c05nbf| (*1 *2 *3 *3 *4 *5 *3 *6) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *4 (|Matrix| (|DoubleFloat|))) (|isDomain| *5 (|DoubleFloat|)) (|isDomain| *6 (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp6| FCN)))) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagRootFindingPackage|)))) (|c05adf| (*1 *2 *3 *3 *3 *3 *4 *5) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *5 (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagRootFindingPackage|))))) 
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(((|NagSpecialFunctionsPackage|) (CATEGORY |package| (SIGNATURE |s01eaf| ((|Result|) (|Complex| (|DoubleFloat|)) (|Integer|))) (SIGNATURE |s13aaf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s13acf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s13adf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s14aaf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s14abf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s14baf| ((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s15adf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s15aef| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17acf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17adf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17aef| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17aff| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17agf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17ahf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17ajf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17akf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17dcf| ((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|))) (SIGNATURE |s17def| ((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|))) (SIGNATURE |s17dgf| ((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|))) (SIGNATURE |s17dhf| ((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|))) (SIGNATURE |s17dlf| ((|Result|) (|Integer|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|))) (SIGNATURE |s18acf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s18adf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s18aef| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s18aff| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s18dcf| ((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|))) (SIGNATURE |s18def| ((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|))) (SIGNATURE |s19aaf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s19abf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s19acf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s19adf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s20acf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s20adf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s21baf| ((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s21bbf| ((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s21bcf| ((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s21bdf| ((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|))))) (T |NagSpecialFunctionsPackage|)) 
((|s21bdf| (*1 *2 *3 *3 *3 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s21bcf| (*1 *2 *3 *3 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s21bbf| (*1 *2 *3 *3 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s21baf| (*1 *2 *3 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s20adf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s20acf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s19adf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s19acf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s19abf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s19aaf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s18def| (*1 *2 *3 *4 *5 *6 *5) (AND (|isDomain| *4 (|Complex| (|DoubleFloat|))) (|isDomain| *5 (|Integer|)) (|isDomain| *6 (|String|)) (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s18dcf| (*1 *2 *3 *4 *5 *6 *5) (AND (|isDomain| *4 (|Complex| (|DoubleFloat|))) (|isDomain| *5 (|Integer|)) (|isDomain| *6 (|String|)) (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s18aff| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s18aef| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s18adf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s18acf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s17dlf| (*1 *2 *3 *4 *5 *3 *6 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *5 (|Complex| (|DoubleFloat|))) (|isDomain| *6 (|String|)) (|isDomain| *4 (|DoubleFloat|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s17dhf| (*1 *2 *3 *4 *3 *5) (AND (|isDomain| *3 (|String|)) (|isDomain| *4 (|Complex| (|DoubleFloat|))) (|isDomain| *5 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s17dgf| (*1 *2 *3 *4 *3 *5) (AND (|isDomain| *3 (|String|)) (|isDomain| *4 (|Complex| (|DoubleFloat|))) (|isDomain| *5 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s17def| (*1 *2 *3 *4 *5 *6 *5) (AND (|isDomain| *4 (|Complex| (|DoubleFloat|))) (|isDomain| *5 (|Integer|)) (|isDomain| *6 (|String|)) (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s17dcf| (*1 *2 *3 *4 *5 *6 *5) (AND (|isDomain| *4 (|Complex| (|DoubleFloat|))) (|isDomain| *5 (|Integer|)) (|isDomain| *6 (|String|)) (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s17akf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s17ajf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s17ahf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s17agf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s17aff| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s17aef| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s17adf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s17acf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s15aef| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s15adf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s14baf| (*1 *2 *3 *3 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s14abf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s14aaf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s13adf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s13acf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s13aaf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|)))) (|s01eaf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Complex| (|DoubleFloat|))) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|NagSpecialFunctionsPackage|))))) 
(CATEGORY |package| (SIGNATURE |s01eaf| ((|Result|) (|Complex| (|DoubleFloat|)) (|Integer|))) (SIGNATURE |s13aaf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s13acf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s13adf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s14aaf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s14abf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s14baf| ((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s15adf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s15aef| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17acf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17adf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17aef| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17aff| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17agf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17ahf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17ajf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17akf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s17dcf| ((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|))) (SIGNATURE |s17def| ((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|))) (SIGNATURE |s17dgf| ((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|))) (SIGNATURE |s17dhf| ((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|))) (SIGNATURE |s17dlf| ((|Result|) (|Integer|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|))) (SIGNATURE |s18acf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s18adf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s18aef| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s18aff| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s18dcf| ((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|))) (SIGNATURE |s18def| ((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|))) (SIGNATURE |s19aaf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s19abf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s19acf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s19adf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s20acf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s20adf| ((|Result|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s21baf| ((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s21bbf| ((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s21bcf| ((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|))) (SIGNATURE |s21bdf| ((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)))) 
((|restorePrecision| (((|Void|)) 18)) (|fortranLinkerArgs| (((|String|)) 22)) (|fortranCompilerName| (((|String|)) 21)) (|dimensionsOf| (((|SExpression|) (|Symbol|) (|Matrix| (|Integer|))) 35) (((|SExpression|) (|Symbol|) (|Matrix| (|DoubleFloat|))) 31)) (|checkPrecision| (((|Boolean|)) 16)) (|aspFilename| (((|String|) (|String|)) 25))) 
(((|NAGLinkSupportPackage|) (CATEGORY |package| (SIGNATURE |fortranCompilerName| ((|String|))) (SIGNATURE |fortranLinkerArgs| ((|String|))) (SIGNATURE |aspFilename| ((|String|) (|String|))) (SIGNATURE |dimensionsOf| ((|SExpression|) (|Symbol|) (|Matrix| (|DoubleFloat|)))) (SIGNATURE |dimensionsOf| ((|SExpression|) (|Symbol|) (|Matrix| (|Integer|)))) (SIGNATURE |checkPrecision| ((|Boolean|))) (SIGNATURE |restorePrecision| ((|Void|))))) (T |NAGLinkSupportPackage|)) 
((|restorePrecision| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|NAGLinkSupportPackage|)))) (|checkPrecision| (*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|NAGLinkSupportPackage|)))) (|dimensionsOf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|Matrix| (|Integer|))) (|isDomain| *2 (|SExpression|)) (|isDomain| *1 (|NAGLinkSupportPackage|)))) (|dimensionsOf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|Matrix| (|DoubleFloat|))) (|isDomain| *2 (|SExpression|)) (|isDomain| *1 (|NAGLinkSupportPackage|)))) (|aspFilename| (*1 *2 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|NAGLinkSupportPackage|)))) (|fortranLinkerArgs| (*1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|NAGLinkSupportPackage|)))) (|fortranCompilerName| (*1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|NAGLinkSupportPackage|))))) 
(CATEGORY |package| (SIGNATURE |fortranCompilerName| ((|String|))) (SIGNATURE |fortranLinkerArgs| ((|String|))) (SIGNATURE |aspFilename| ((|String|) (|String|))) (SIGNATURE |dimensionsOf| ((|SExpression|) (|Symbol|) (|Matrix| (|DoubleFloat|)))) (SIGNATURE |dimensionsOf| ((|SExpression|) (|Symbol|) (|Matrix| (|Integer|)))) (SIGNATURE |checkPrecision| ((|Boolean|))) (SIGNATURE |restorePrecision| ((|Void|)))) 
((|commutator| (($ $ $) 10)) (|associator| (($ $ $ $) 9)) (|antiCommutator| (($ $ $) 12))) 
(((|NonAssociativeRng&| |#1|) (CATEGORY |domain| (SIGNATURE |antiCommutator| (|#1| |#1| |#1|)) (SIGNATURE |commutator| (|#1| |#1| |#1|)) (SIGNATURE |associator| (|#1| |#1| |#1| |#1|))) (|NonAssociativeRng|)) (T |NonAssociativeRng&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |antiCommutator| (|#1| |#1| |#1|)) (SIGNATURE |commutator| (|#1| |#1| |#1|)) (SIGNATURE |associator| (|#1| |#1| |#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|rightPower| (($ $ (|PositiveInteger|)) 27)) (|leftPower| (($ $ (|PositiveInteger|)) 28)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|commutator| (($ $ $) 24)) (|coerce| (((|OutputForm|) $) 11)) (|associator| (($ $ $ $) 25)) (|antiCommutator| (($ $ $) 23)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 29)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 26))) 
(((|NonAssociativeRng|) (|Category|)) (T |NonAssociativeRng|)) 
((|associator| (*1 *1 *1 *1 *1) (|ofCategory| *1 (|NonAssociativeRng|))) (|commutator| (*1 *1 *1 *1) (|ofCategory| *1 (|NonAssociativeRng|))) (|antiCommutator| (*1 *1 *1 *1) (|ofCategory| *1 (|NonAssociativeRng|)))) 
(|Join| (|AbelianGroup|) (|Monad|) (CATEGORY |domain| (SIGNATURE |associator| ($ $ $ $)) (SIGNATURE |commutator| ($ $ $)) (SIGNATURE |antiCommutator| ($ $ $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Monad|) . T) ((|SetCategory|) . T)) 
((|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) 10))) 
(((|NonAssociativeRing&| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|NonAssociativeRing|)) (T |NonAssociativeRing&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|rightRecip| (((|Union| $ "failed") $) 39)) (|rightPower| (($ $ (|PositiveInteger|)) 27) (($ $ (|NonNegativeInteger|)) 34)) (|recip| (((|Union| $ "failed") $) 37)) (|one?| (((|Boolean|) $) 33)) (|leftRecip| (((|Union| $ "failed") $) 38)) (|leftPower| (($ $ (|PositiveInteger|)) 28) (($ $ (|NonNegativeInteger|)) 35)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|commutator| (($ $ $) 24)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 30)) (|characteristic| (((|NonNegativeInteger|)) 31)) (|associator| (($ $ $ $) 25)) (|antiCommutator| (($ $ $) 23)) (|Zero| (($) 17 T CONST)) (|One| (($) 32 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 29) (($ $ (|NonNegativeInteger|)) 36)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 26))) 
(((|NonAssociativeRing|) (|Category|)) (T |NonAssociativeRing|)) 
((|characteristic| (*1 *2) (AND (|ofCategory| *1 (|NonAssociativeRing|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|NonAssociativeRing|))))) 
(|Join| (|NonAssociativeRng|) (|MonadWithUnit|) (CATEGORY |domain| (SIGNATURE |characteristic| ((|NonNegativeInteger|))) (SIGNATURE |coerce| ($ (|Integer|))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Monad|) . T) ((|MonadWithUnit|) . T) ((|NonAssociativeRng|) . T) ((|SetCategory|) . T)) 
((|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) 27)) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) 19)) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) 16) (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) 15))) 
(((|NumericComplexEigenPackage| |#1|) (CATEGORY |package| (SIGNATURE |characteristicPolynomial| ((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))))) (SIGNATURE |characteristicPolynomial| ((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|))) (SIGNATURE |complexEigenvalues| ((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|)) (SIGNATURE |complexEigenvectors| ((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|))) (|Join| (|Field|) (|OrderedRing|))) (T |NumericComplexEigenPackage|)) 
((|complexEigenvectors| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Matrix| (|Complex| (|Fraction| (|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |outval| (|Complex| *4)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| *4))))))) (|isDomain| *1 (|NumericComplexEigenPackage| *4)) (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|))))) (|complexEigenvalues| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Matrix| (|Complex| (|Fraction| (|Integer|))))) (|isDomain| *2 (|List| (|Complex| *4))) (|isDomain| *1 (|NumericComplexEigenPackage| *4)) (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|))))) (|characteristicPolynomial| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Matrix| (|Complex| (|Fraction| (|Integer|))))) (|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Polynomial| (|Complex| (|Fraction| (|Integer|))))) (|isDomain| *1 (|NumericComplexEigenPackage| *5)) (|ofCategory| *5 (|Join| (|Field|) (|OrderedRing|))))) (|characteristicPolynomial| (*1 *2 *3) (AND (|isDomain| *3 (|Matrix| (|Complex| (|Fraction| (|Integer|))))) (|isDomain| *2 (|Polynomial| (|Complex| (|Fraction| (|Integer|))))) (|isDomain| *1 (|NumericComplexEigenPackage| *4)) (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))) 
(CATEGORY |package| (SIGNATURE |characteristicPolynomial| ((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))))) (SIGNATURE |characteristicPolynomial| ((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|))) (SIGNATURE |complexEigenvalues| ((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|)) (SIGNATURE |complexEigenvectors| ((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|))) 
((|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) 25))) 
(((|NumericContinuedFraction| |#1|) (CATEGORY |package| (SIGNATURE |continuedFraction| ((|ContinuedFraction| (|Integer|)) |#1|))) (|FloatingPointSystem|)) (T |NumericContinuedFraction|)) 
((|continuedFraction| (*1 *2 *3) (AND (|isDomain| *2 (|ContinuedFraction| (|Integer|))) (|isDomain| *1 (|NumericContinuedFraction| *3)) (|ofCategory| *3 (|FloatingPointSystem|))))) 
(CATEGORY |package| (SIGNATURE |continuedFraction| ((|ContinuedFraction| (|Integer|)) |#1|))) 
((|leftRemainder| ((|#1| |#1| |#1|) 24)) (|leftQuotient| ((|#1| |#1| |#1|) 23)) (|leftLcm| ((|#1| |#1| |#1|) 31)) (|leftGcd| ((|#1| |#1| |#1|) 27)) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) 26)) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) 22))) 
(((|NonCommutativeOperatorDivision| |#1| |#2|) (CATEGORY |package| (SIGNATURE |leftDivide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |leftQuotient| (|#1| |#1| |#1|)) (SIGNATURE |leftRemainder| (|#1| |#1| |#1|)) (SIGNATURE |leftExactQuotient| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE |leftGcd| (|#1| |#1| |#1|)) (SIGNATURE |leftLcm| (|#1| |#1| |#1|))) (|MonogenicLinearOperator| |#2|) (|Field|)) (T |NonCommutativeOperatorDivision|)) 
((|leftLcm| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|NonCommutativeOperatorDivision| *2 *3)) (|ofCategory| *2 (|MonogenicLinearOperator| *3)))) (|leftGcd| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|NonCommutativeOperatorDivision| *2 *3)) (|ofCategory| *2 (|MonogenicLinearOperator| *3)))) (|leftExactQuotient| (*1 *2 *2 *2) (|partial| AND (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|NonCommutativeOperatorDivision| *2 *3)) (|ofCategory| *2 (|MonogenicLinearOperator| *3)))) (|leftRemainder| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|NonCommutativeOperatorDivision| *2 *3)) (|ofCategory| *2 (|MonogenicLinearOperator| *3)))) (|leftQuotient| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|NonCommutativeOperatorDivision| *2 *3)) (|ofCategory| *2 (|MonogenicLinearOperator| *3)))) (|leftDivide| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) (|isDomain| *1 (|NonCommutativeOperatorDivision| *3 *4)) (|ofCategory| *3 (|MonogenicLinearOperator| *4))))) 
(CATEGORY |package| (SIGNATURE |leftDivide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |leftQuotient| (|#1| |#1| |#1|)) (SIGNATURE |leftRemainder| (|#1| |#1| |#1|)) (SIGNATURE |leftExactQuotient| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE |leftGcd| (|#1| |#1| |#1|)) (SIGNATURE |leftLcm| (|#1| |#1| |#1|))) 
((|newton| (((|SparseUnivariatePolynomial| |#1|) (|List| |#1|)) 25))) 
(((|NewtonInterpolation| |#1|) (CATEGORY |package| (SIGNATURE |newton| ((|SparseUnivariatePolynomial| |#1|) (|List| |#1|)))) (|IntegralDomain|)) (T |NewtonInterpolation|)) 
((|newton| (*1 *2 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|isDomain| *1 (|NewtonInterpolation| *4))))) 
(CATEGORY |package| (SIGNATURE |newton| ((|SparseUnivariatePolynomial| |#1|) (|List| |#1|)))) 
((|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) 58)) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) 56)) (|discriminant| (((|Integer|)) 68))) 
(((|NumberFieldIntegralBasis| |#1| |#2|) (CATEGORY |package| (SIGNATURE |discriminant| ((|Integer|))) (SIGNATURE |integralBasis| ((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))))) (SIGNATURE |localIntegralBasis| ((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)))) (|UnivariatePolynomialCategory| (|Integer|)) (|FramedAlgebra| (|Integer|) |#1|)) (T |NumberFieldIntegralBasis|)) 
((|localIntegralBasis| (*1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Record| (|:| |basis| (|Matrix| *3)) (|:| |basisDen| *3) (|:| |basisInv| (|Matrix| *3)))) (|isDomain| *1 (|NumberFieldIntegralBasis| *4 *5)) (|ofCategory| *5 (|FramedAlgebra| *3 *4)))) (|integralBasis| (*1 *2) (AND (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))) (|isDomain| *2 (|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) (|isDomain| *1 (|NumberFieldIntegralBasis| *3 *4)) (|ofCategory| *4 (|FramedAlgebra| (|Integer|) *3)))) (|discriminant| (*1 *2) (AND (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|NumberFieldIntegralBasis| *3 *4)) (|ofCategory| *4 (|FramedAlgebra| *2 *3))))) 
(CATEGORY |package| (SIGNATURE |discriminant| ((|Integer|))) (SIGNATURE |integralBasis| ((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))))) (SIGNATURE |localIntegralBasis| ((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)))) 
((~= (((|Boolean|) $ $) NIL)) (|retract| (((|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) $) 15)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 14) (($ (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 8) (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 10) (($ (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) 12)) (= (((|Boolean|) $ $) NIL))) 
(((|NumericalIntegrationProblem|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |coerce| ($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |coerce| ($ (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))))) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE |retract| ((|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) $))))) (T |NumericalIntegrationProblem|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|NumericalIntegrationProblem|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|isDomain| *1 (|NumericalIntegrationProblem|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|isDomain| *1 (|NumericalIntegrationProblem|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) (|isDomain| *1 (|NumericalIntegrationProblem|)))) (|retract| (*1 *2 *1) (AND (|isDomain| *2 (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) (|isDomain| *1 (|NumericalIntegrationProblem|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |coerce| ($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |coerce| ($ (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))))) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE |retract| ((|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) $)))) 
((|solveInField| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) 14) (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) 13)) (|solve| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) 16) (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) 15))) 
(((|NonLinearSolvePackage| |#1|) (CATEGORY |package| (SIGNATURE |solveInField| ((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)))) (SIGNATURE |solveInField| ((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)))) (SIGNATURE |solve| ((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)))) (SIGNATURE |solve| ((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))))) (|IntegralDomain|)) (T |NonLinearSolvePackage|)) 
((|solve| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Polynomial| *4))) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| (|List| (|Equation| (|Fraction| (|Polynomial| *4)))))) (|isDomain| *1 (|NonLinearSolvePackage| *4)))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|List| (|List| (|Equation| (|Fraction| (|Polynomial| *5)))))) (|isDomain| *1 (|NonLinearSolvePackage| *5)))) (|solveInField| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Polynomial| *4))) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| (|List| (|Equation| (|Fraction| (|Polynomial| *4)))))) (|isDomain| *1 (|NonLinearSolvePackage| *4)))) (|solveInField| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|List| (|List| (|Equation| (|Fraction| (|Polynomial| *5)))))) (|isDomain| *1 (|NonLinearSolvePackage| *5))))) 
(CATEGORY |package| (SIGNATURE |solveInField| ((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)))) (SIGNATURE |solveInField| ((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)))) (SIGNATURE |solve| ((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)))) (SIGNATURE |solve| ((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|sup| (($ $ $) 6)) (|subtractIfCan| (((|Union| $ "failed") $ $) 10)) (|shift| (($ $ (|Integer|)) 7)) (|sample| (($) NIL T CONST)) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($ $) NIL)) (|quo| (($ $ $) NIL)) (|qcoerce| (($ (|Integer|)) 8)) (|one?| (((|Boolean|) $) NIL)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|gcd| (($ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (^ (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|PositiveInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|PositiveInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ $ $) NIL))) 
(((|NonNegativeInteger|) (|Join| (|OrderedAbelianMonoidSup|) (|Monoid|) (CATEGORY |domain| (SIGNATURE |quo| ($ $ $)) (SIGNATURE |rem| ($ $ $)) (SIGNATURE |gcd| ($ $ $)) (SIGNATURE |divide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |exquo| ((|Union| $ "failed") $ $)) (SIGNATURE |shift| ($ $ (|Integer|))) (SIGNATURE |random| ($ $)) (SIGNATURE |qcoerce| ($ (|Integer|)))))) (T |NonNegativeInteger|)) 
((|quo| (*1 *1 *1 *1) (|isDomain| *1 (|NonNegativeInteger|))) (|rem| (*1 *1 *1 *1) (|isDomain| *1 (|NonNegativeInteger|))) (|gcd| (*1 *1 *1 *1) (|isDomain| *1 (|NonNegativeInteger|))) (|divide| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |quotient| (|NonNegativeInteger|)) (|:| |remainder| (|NonNegativeInteger|)))) (|isDomain| *1 (|NonNegativeInteger|)))) (|exquo| (*1 *1 *1 *1) (|partial| |isDomain| *1 (|NonNegativeInteger|))) (|shift| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|NonNegativeInteger|)))) (|random| (*1 *1 *1) (|isDomain| *1 (|NonNegativeInteger|))) (|qcoerce| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|NonNegativeInteger|))))) 
(|Join| (|OrderedAbelianMonoidSup|) (|Monoid|) (CATEGORY |domain| (SIGNATURE |quo| ($ $ $)) (SIGNATURE |rem| ($ $ $)) (SIGNATURE |gcd| ($ $ $)) (SIGNATURE |divide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |exquo| ((|Union| $ "failed") $ $)) (SIGNATURE |shift| ($ $ (|Integer|))) (SIGNATURE |random| ($ $)) (SIGNATURE |qcoerce| ($ (|Integer|))))) 
((|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) 35))) 
(((|NonLinearFirstOrderODESolver| |#1| |#2|) (CATEGORY |package| (SIGNATURE |solve| ((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)))) (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|)) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (T |NonLinearFirstOrderODESolver|)) 
((|solve| (*1 *2 *2 *2 *3 *4) (|partial| AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *1 (|NonLinearFirstOrderODESolver| *5 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedFunctionSpace| *5) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|)))))) 
(CATEGORY |package| (SIGNATURE |solve| ((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)))) 
((|coerce| (((|None|) |#1|) 8))) 
(((|NoneFunctions1| |#1|) (CATEGORY |package| (SIGNATURE |coerce| ((|None|) |#1|))) (|Type|)) (T |NoneFunctions1|)) 
((|coerce| (*1 *2 *3) (AND (|isDomain| *2 (|None|)) (|isDomain| *1 (|NoneFunctions1| *3)) (|ofCategory| *3 (|Type|))))) 
(CATEGORY |package| (SIGNATURE |coerce| ((|None|) |#1|))) 
((~= (((|Boolean|) $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 7)) (= (((|Boolean|) $ $) 9))) 
(((|None|) (|SetCategory|)) (T |None|)) 
NIL 
(|SetCategory|) 
((|norm| ((|#2| |#4|) 35))) 
(((|NormInMonogenicAlgebra| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |norm| (|#2| |#4|))) (|GcdDomain|) (|UnivariatePolynomialCategory| |#1|) (|MonogenicAlgebra| |#1| |#2|) (|UnivariatePolynomialCategory| |#3|)) (T |NormInMonogenicAlgebra|)) 
((|norm| (*1 *2 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|MonogenicAlgebra| *4 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|NormInMonogenicAlgebra| *4 *2 *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |norm| (|#2| |#4|))) 
((|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) 56)) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) 33)) (|normalizedAssociate| ((|#4| |#4| |#5|) 72)) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) 76)) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) 15))) 
(((|NormalizationPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |recip| ((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|)) (SIGNATURE |normalizedAssociate| (|#4| |#4| |#5|)) (SIGNATURE |normalize| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|)) (SIGNATURE |outputArgs| ((|Void|) (|String|) (|String|) |#4| |#5|)) (SIGNATURE |normInvertible?| ((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |NormalizationPackage|)) 
((|normInvertible?| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| *4)))) (|isDomain| *1 (|NormalizationPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|outputArgs| (*1 *2 *3 *3 *4 *5) (AND (|isDomain| *3 (|String|)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|ofCategory| *4 (|RecursivePolynomialCategory| *6 *7 *8)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|NormalizationPackage| *6 *7 *8 *4 *5)) (|ofCategory| *5 (|RegularTriangularSetCategory| *6 *7 *8 *4)))) (|normalize| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4)))) (|isDomain| *1 (|NormalizationPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|normalizedAssociate| (*1 *2 *2 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *1 (|NormalizationPackage| *4 *5 *6 *2 *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *2)))) (|recip| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| *3))) (|isDomain| *1 (|NormalizationPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(CATEGORY |package| (SIGNATURE |recip| ((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|)) (SIGNATURE |normalizedAssociate| (|#4| |#4| |#5|)) (SIGNATURE |normalize| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|)) (SIGNATURE |outputArgs| ((|Void|) (|String|) (|String|) |#4| |#5|)) (SIGNATURE |normInvertible?| ((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|))) 
((|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) 43)) (|normFactors| (((|List| |#4|) |#4|) 15)) (|Frobenius| ((|#4| |#4|) 11))) 
(((|NormRetractPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |normFactors| ((|List| |#4|) |#4|)) (SIGNATURE |retractIfCan| ((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|)) (SIGNATURE |Frobenius| (|#4| |#4|))) (|FiniteFieldCategory|) (|FiniteAlgebraicExtensionField| |#1|) (|UnivariatePolynomialCategory| |#2|) (|UnivariatePolynomialCategory| |#3|) (|PositiveInteger|)) (T |NormRetractPackage|)) 
((|Frobenius| (*1 *2 *2) (AND (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofCategory| *4 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|NormRetractPackage| *3 *4 *5 *2 *6)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *5)) (|ofType| *6 (|PositiveInteger|)))) (|retractIfCan| (*1 *2 *3) (|partial| AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|ofCategory| *5 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4))) (|isDomain| *1 (|NormRetractPackage| *4 *5 *6 *3 *7)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *6)) (|ofType| *7 (|PositiveInteger|)))) (|normFactors| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|ofCategory| *5 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|NormRetractPackage| *4 *5 *6 *3 *7)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *6)) (|ofType| *7 (|PositiveInteger|))))) 
(CATEGORY |package| (SIGNATURE |normFactors| ((|List| |#4|) |#4|)) (SIGNATURE |retractIfCan| ((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|)) (SIGNATURE |Frobenius| (|#4| |#4|))) 
((~= (((|Boolean|) $ $) NIL)) (|sample| (($) NIL T CONST)) (|retract| (($ (|UnivariateFormalPowerSeries| |#1|)) 21)) (|recip| (((|Union| $ "failed") $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 26)) (|hash| (((|SingleInteger|) $) NIL)) (|conjugate| (($ $ $) NIL)) (|commutator| (($ $ $) NIL)) (|coerce| (((|OutputForm|) $) 11)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|One| (($) 18 T CONST)) (= (((|Boolean|) $ $) NIL)) (/ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ $ $) 24))) 
(((|NottinghamGroup| |#1|) (|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |retract| ($ (|UnivariateFormalPowerSeries| |#1|))))) (|FiniteFieldCategory|)) (T |NottinghamGroup|)) 
((|retract| (*1 *1 *2) (AND (|isDomain| *2 (|UnivariateFormalPowerSeries| *3)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|isDomain| *1 (|NottinghamGroup| *3))))) 
(|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |retract| ($ (|UnivariateFormalPowerSeries| |#1|))))) 
((|npcoef| (((|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| (|List| |#1|)) (|:| |nlead| (|List| |#5|))) (|SparseUnivariatePolynomial| |#5|) (|List| |#1|) (|List| |#5|)) 51)) (|listexp| (((|List| (|NonNegativeInteger|)) |#1|) 12))) 
(((|NPCoef| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |npcoef| ((|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| (|List| |#1|)) (|:| |nlead| (|List| |#5|))) (|SparseUnivariatePolynomial| |#5|) (|List| |#1|) (|List| |#5|))) (SIGNATURE |listexp| ((|List| (|NonNegativeInteger|)) |#1|))) (|UnivariatePolynomialCategory| |#4|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|EuclideanDomain|) (|PolynomialCategory| |#4| |#2| |#3|)) (T |NPCoef|)) 
((|listexp| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|EuclideanDomain|)) (|isDomain| *2 (|List| (|NonNegativeInteger|))) (|isDomain| *1 (|NPCoef| *3 *4 *5 *6 *7)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *6)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)))) (|npcoef| (*1 *2 *3 *4 *5) (AND (|ofCategory| *6 (|UnivariatePolynomialCategory| *9)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|ofCategory| *9 (|EuclideanDomain|)) (|ofCategory| *10 (|PolynomialCategory| *9 *7 *8)) (|isDomain| *2 (|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| *10))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| *10))))) (|:| |nfacts| (|List| *6)) (|:| |nlead| (|List| *10)))) (|isDomain| *1 (|NPCoef| *6 *7 *8 *9 *10)) (|isDomain| *3 (|SparseUnivariatePolynomial| *10)) (|isDomain| *4 (|List| *6)) (|isDomain| *5 (|List| *10))))) 
(CATEGORY |package| (SIGNATURE |npcoef| ((|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| (|List| |#1|)) (|:| |nlead| (|List| |#5|))) (|SparseUnivariatePolynomial| |#5|) (|List| |#1|) (|List| |#5|))) (SIGNATURE |listexp| ((|List| (|NonNegativeInteger|)) |#1|))) 
((|slope| (((|Record| (|:| |height| (|Integer|)) (|:| |base| (|Integer|)) (|:| |quotient| (|Integer|)) (|:| |reste| (|Integer|)) (|:| |type| (|Union| "left" "center" "right" "vertical" "horizontal"))) (|List| |#2|)) 18) (((|Record| (|:| |height| (|Integer|)) (|:| |base| (|Integer|)) (|:| |quotient| (|Integer|)) (|:| |reste| (|Integer|)) (|:| |type| (|Union| "left" "center" "right" "vertical" "horizontal"))) |#2| |#2|) 16)) (|newtonPolygon| (((|List| (|List| |#2|)) |#2| (|Integer|) (|Integer|) (|Union| "left" "center" "right" "vertical" "horizontal")) 32)) (|negAndPosEdge| (((|List| (|List| |#2|)) |#2| (|List| (|List| |#2|))) 24)) (|multiplicity| (((|NonNegativeInteger|) (|List| (|List| |#2|))) 27))) 
(((|NewtonPolygon| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |newtonPolygon| ((|List| (|List| |#2|)) |#2| (|Integer|) (|Integer|) (|Union| "left" "center" "right" "vertical" "horizontal"))) (SIGNATURE |multiplicity| ((|NonNegativeInteger|) (|List| (|List| |#2|)))) (SIGNATURE |negAndPosEdge| ((|List| (|List| |#2|)) |#2| (|List| (|List| |#2|)))) (SIGNATURE |slope| ((|Record| (|:| |height| (|Integer|)) (|:| |base| (|Integer|)) (|:| |quotient| (|Integer|)) (|:| |reste| (|Integer|)) (|:| |type| (|Union| "left" "center" "right" "vertical" "horizontal"))) |#2| |#2|)) (SIGNATURE |slope| ((|Record| (|:| |height| (|Integer|)) (|:| |base| (|Integer|)) (|:| |quotient| (|Integer|)) (|:| |reste| (|Integer|)) (|:| |type| (|Union| "left" "center" "right" "vertical" "horizontal"))) (|List| |#2|)))) (|Ring|) (|FiniteAbelianMonoidRing| |#1| |#3|) (|DirectProductCategory| |#4| (|NonNegativeInteger|)) (|NonNegativeInteger|)) (T |NewtonPolygon|)) 
((|slope| (*1 *2 *3) (AND (|isDomain| *3 (|List| *5)) (|ofCategory| *5 (|FiniteAbelianMonoidRing| *4 *6)) (|ofCategory| *6 (|DirectProductCategory| *7 (|NonNegativeInteger|))) (|ofType| *7 (|NonNegativeInteger|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Record| (|:| |height| (|Integer|)) (|:| |base| (|Integer|)) (|:| |quotient| (|Integer|)) (|:| |reste| (|Integer|)) (|:| |type| (|Union| "left" "center" "right" "vertical" "horizontal")))) (|isDomain| *1 (|NewtonPolygon| *4 *5 *6 *7)))) (|slope| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *6 (|NonNegativeInteger|))) (|ofType| *6 (|NonNegativeInteger|)) (|isDomain| *2 (|Record| (|:| |height| (|Integer|)) (|:| |base| (|Integer|)) (|:| |quotient| (|Integer|)) (|:| |reste| (|Integer|)) (|:| |type| (|Union| "left" "center" "right" "vertical" "horizontal")))) (|isDomain| *1 (|NewtonPolygon| *4 *3 *5 *6)) (|ofCategory| *3 (|FiniteAbelianMonoidRing| *4 *5)))) (|negAndPosEdge| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|FiniteAbelianMonoidRing| *4 *5)) (|ofCategory| *5 (|DirectProductCategory| *6 (|NonNegativeInteger|))) (|ofType| *6 (|NonNegativeInteger|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|NewtonPolygon| *4 *3 *5 *6)))) (|multiplicity| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|List| *5))) (|ofCategory| *5 (|FiniteAbelianMonoidRing| *4 *6)) (|ofCategory| *6 (|DirectProductCategory| *7 *2)) (|ofType| *7 *2) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|NewtonPolygon| *4 *5 *6 *7)))) (|newtonPolygon| (*1 *2 *3 *4 *4 *5) (AND (|isDomain| *4 (|Integer|)) (|isDomain| *5 (|Union| "left" "center" "right" "vertical" "horizontal")) (|ofCategory| *6 (|Ring|)) (|ofCategory| *7 (|DirectProductCategory| *8 (|NonNegativeInteger|))) (|ofType| *8 (|NonNegativeInteger|)) (|isDomain| *2 (|List| (|List| *3))) (|isDomain| *1 (|NewtonPolygon| *6 *3 *7 *8)) (|ofCategory| *3 (|FiniteAbelianMonoidRing| *6 *7))))) 
(CATEGORY |package| (SIGNATURE |newtonPolygon| ((|List| (|List| |#2|)) |#2| (|Integer|) (|Integer|) (|Union| "left" "center" "right" "vertical" "horizontal"))) (SIGNATURE |multiplicity| ((|NonNegativeInteger|) (|List| (|List| |#2|)))) (SIGNATURE |negAndPosEdge| ((|List| (|List| |#2|)) |#2| (|List| (|List| |#2|)))) (SIGNATURE |slope| ((|Record| (|:| |height| (|Integer|)) (|:| |base| (|Integer|)) (|:| |quotient| (|Integer|)) (|:| |reste| (|Integer|)) (|:| |type| (|Union| "left" "center" "right" "vertical" "horizontal"))) |#2| |#2|)) (SIGNATURE |slope| ((|Record| (|:| |height| (|Integer|)) (|:| |base| (|Integer|)) (|:| |quotient| (|Integer|)) (|:| |reste| (|Integer|)) (|:| |type| (|Union| "left" "center" "right" "vertical" "horizontal"))) (|List| |#2|)))) 
((|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|) 27)) (|realEigenvalues| (((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|) 19)) (|characteristicPolynomial| (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|)) 16) (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) 15))) 
(((|NumericRealEigenPackage| |#1|) (CATEGORY |package| (SIGNATURE |characteristicPolynomial| ((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))))) (SIGNATURE |characteristicPolynomial| ((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|))) (SIGNATURE |realEigenvalues| ((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|)) (SIGNATURE |realEigenvectors| ((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|))) (|Join| (|Field|) (|OrderedRing|))) (T |NumericRealEigenPackage|)) 
((|realEigenvectors| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Integer|)))) (|isDomain| *2 (|List| (|Record| (|:| |outval| *4) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| *4)))))) (|isDomain| *1 (|NumericRealEigenPackage| *4)) (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|))))) (|realEigenvalues| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Integer|)))) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|NumericRealEigenPackage| *4)) (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|))))) (|characteristicPolynomial| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Integer|)))) (|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Polynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|NumericRealEigenPackage| *5)) (|ofCategory| *5 (|Join| (|Field|) (|OrderedRing|))))) (|characteristicPolynomial| (*1 *2 *3) (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Integer|)))) (|isDomain| *2 (|Polynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|NumericRealEigenPackage| *4)) (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))) 
(CATEGORY |package| (SIGNATURE |characteristicPolynomial| ((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))))) (SIGNATURE |characteristicPolynomial| ((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|))) (SIGNATURE |realEigenvalues| ((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|)) (SIGNATURE |realEigenvectors| ((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 10)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) NIL)) (|variable| (((|Symbol|) $) NIL)) (|value| (((|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|truncate| (($ $ (|Integer|) (|Integer|)) NIL) (($ $ (|Integer|)) NIL)) (|third| (((|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) $) NIL)) (|terms| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) NIL)) (|tail| (($ $) NIL)) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|split!| (($ $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|shift| (($ $ (|Integer|)) 36)) (|setvalue!| (((|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) $ (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setrest!| (($ $ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setlast!| (((|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) $ (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setfirst!| (((|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) $ (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| (((|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) $ (|Integer|) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) $ (|UniversalSegment| (|Integer|)) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) $ "last" (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "rest" $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) $ "first" (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) $ "value" (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|series| (($ (|Integer|) |#1| $) 41)) (|select| (($ (|Mapping| (|Boolean|) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) NIL)) (|second| (((|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) $) NIL)) (|sbt| (($ $ $) 51)) (|sample| (($) NIL T CONST)) (|rst| (($ $) 21)) (|rest| (($ $ (|NonNegativeInteger|)) NIL) (($ $) 14)) (|removeZeroes| (($ (|Integer|) $) 78) (($ $) 31)) (|removeFirstZeroes| (($ $) 35)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|SetCategory|))))) (|remove| (($ (|Mapping| (|Boolean|) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) NIL) (($ (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|SetCategory|))))) (|rem| (($ $ $) NIL)) (|reductum| (($ $) NIL)) (|reduce| (((|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|Mapping| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $ (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|SetCategory|)))) (((|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|Mapping| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $ (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|Mapping| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|recip| (((|Union| $ "failed") $) 38)) (|quo| (($ $ $) NIL)) (|qsetelt!| (((|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) $ (|Integer|) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| (((|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) $ (|Integer|)) NIL)) (|printInfo| (((|Boolean|) (|Boolean|)) 30) (((|Boolean|)) 29)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|possiblyInfinite?| (((|Boolean|) $) NIL)) (|posExpnPart| (($ $) 22)) (|pole?| (((|Boolean|) $) NIL)) (|parts| (((|List| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|orderIfNegative| (((|Union| (|Integer|) "failed") $) 16)) (|order| (((|Integer|) $ (|Integer|)) NIL) (((|Integer|) $) 19) (((|Integer|) $) 19)) (|one?| (((|Boolean|) $) NIL)) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) NIL)) (|nodes| (((|List| $) $) NIL)) (|node?| (((|Boolean|) $ $) NIL (|has| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|SetCategory|)))) (|new| (($ (|NonNegativeInteger|) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) NIL)) (|multiplyExponents| (($ $ (|PositiveInteger|)) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monomial2series| (($ (|List| $) (|List| (|NonNegativeInteger|)) (|Integer|)) 85)) (|monomial| (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|Integer|))) NIL) (($ $ (|SingletonAsOrderedSet|) (|Integer|)) NIL) (($ |#1| (|Integer|)) NIL)) (|minIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|members| (((|List| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|SetCategory|))))) (|maxIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|map!| (($ (|Mapping| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL) (($ (|Mapping| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $ $) NIL) (($ (|Mapping| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|leaves| (((|List| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) NIL)) (|leaf?| (((|Boolean|) $) NIL)) (|leadingMonomial| (($ $) NIL)) (|leadingCoefficient| ((|#1| $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|lazyEvaluate| (($ $) NIL)) (|lazy?| (((|Boolean|) $) NIL)) (|latex| (((|String|) $) NIL)) (|last| (($ $ (|NonNegativeInteger|)) NIL) (((|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) $) NIL)) (|inv| (($ $) 39)) (|insert| (($ (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)) $ (|Integer|)) NIL) (($ $ $ (|Integer|)) NIL)) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ 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(|NonNegativeInteger|))) NIL)) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) 54)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (/ (($ $ |#1|) NIL (|has| |#1| (|Field|)))) (- (($ $) NIL) (($ $ $) 63)) (+ (($ $ $) 73)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 61)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 59) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ |#1| $) 58) (($ $ |#1|) NIL))) 
(((|NewSparseMultivariatePolynomial| |#1| |#2|) (|Join| (|RecursivePolynomialCategory| |#1| (|IndexedExponents| |#2|) |#2|) (|CoercibleTo| (|SparseMultivariatePolynomial| |#1| |#2|)) (|RetractableTo| (|SparseMultivariatePolynomial| |#1| |#2|))) (|Ring|) (|OrderedSet|)) (T |NewSparseMultivariatePolynomial|)) 
NIL 
(|Join| (|RecursivePolynomialCategory| |#1| (|IndexedExponents| |#2|) |#2|) (|CoercibleTo| (|SparseMultivariatePolynomial| |#1| |#2|)) (|RetractableTo| (|SparseMultivariatePolynomial| |#1| |#2|))) 
((|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) 13))) 
(((|NewSparseUnivariatePolynomialFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)))) (|Ring|) (|Ring|)) (T |NewSparseUnivariatePolynomialFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|NewSparseUnivariatePolynomial| *5)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|Ring|)) (|isDomain| *2 (|NewSparseUnivariatePolynomial| *6)) (|isDomain| *1 (|NewSparseUnivariatePolynomialFunctions2| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |map| ((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)))) 
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(|RetractableTo| (|Integer|)))) (((|Union| (|SingletonAsOrderedSet|) "failed") $) NIL) (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $) 10)) (|retract| ((|#1| $) NIL) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|SingletonAsOrderedSet|) $) NIL) (((|SparseUnivariatePolynomial| |#1|) $) NIL)) (|resultant| (($ $ $ (|SingletonAsOrderedSet|)) NIL (|has| |#1| (|CommutativeRing|))) ((|#1| $ $) 43 (|has| |#1| (|CommutativeRing|)))) (|rem| (($ $ $) NIL (|has| |#1| (|Field|)))) (|reductum| (($ $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| |#1|) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|quo| (($ $ $) NIL (|has| |#1| (|Field|)))) (|pseudoRemainder| (($ $ $) NIL)) (|pseudoQuotient| (($ $ $) 71 (|has| |#1| (|IntegralDomain|)))) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) 70 (|has| |#1| (|IntegralDomain|)))) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL (|has| |#1| (|Field|)))) (|primitivePart| (($ $) NIL (|has| |#1| (|GcdDomain|))) (($ $ (|SingletonAsOrderedSet|)) NIL (|has| |#1| (|GcdDomain|)))) (|primitiveMonomials| (((|List| $) $) NIL)) (|prime?| (((|Boolean|) $) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|pomopo!| (($ $ |#1| (|NonNegativeInteger|) $) NIL)) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (AND (|has| (|SingletonAsOrderedSet|) (|PatternMatchable| (|Float|))) (|has| |#1| (|PatternMatchable| (|Float|))))) (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (AND (|has| (|SingletonAsOrderedSet|) (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Integer|)))))) (|order| (((|NonNegativeInteger|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|one?| (((|Boolean|) $) NIL)) (|numberOfMonomials| (((|NonNegativeInteger|) $) NIL)) (|nextItem| (((|Union| $ "failed") $) NIL (|has| |#1| (|StepThrough|)))) (|multivariate| (($ (|SparseUnivariatePolynomial| |#1|) (|SingletonAsOrderedSet|)) NIL) (($ (|SparseUnivariatePolynomial| $) (|SingletonAsOrderedSet|)) NIL)) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) (|monomials| (((|List| $) $) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monomial| (($ |#1| (|NonNegativeInteger|)) NIL) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL)) (|monicModulo| (($ $ $) 20)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ (|SingletonAsOrderedSet|)) NIL) (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|minimumDegree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|SingletonAsOrderedSet|)) NIL) (((|List| (|NonNegativeInteger|)) $ (|List| (|SingletonAsOrderedSet|))) NIL)) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|mapExponents| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) NIL)) (|mainVariable| (((|Union| (|SingletonAsOrderedSet|) "failed") $) NIL)) (|leadingMonomial| (($ $) NIL)) (|leadingCoefficient| ((|#1| $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| |#1| (|GcdDomain|)))) (|lcm| (($ (|List| $)) NIL (|has| |#1| (|GcdDomain|))) (($ $ $) NIL (|has| |#1| (|GcdDomain|)))) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) 26)) (|lazyPseudoRemainder| (($ $ $) 29)) (|lazyPseudoQuotient| (($ $ $) 32)) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) 31)) (|latex| (((|String|) $) NIL)) (|lastSubResultant| (($ $ $) 41 (|has| |#1| (|IntegralDomain|)))) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) NIL)) (|isTimes| (((|Union| (|List| $) "failed") $) NIL)) (|isPlus| (((|Union| (|List| $) "failed") $) NIL)) (|isExpt| (((|Union| (|Record| (|:| |var| (|SingletonAsOrderedSet|)) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) NIL)) (|integrate| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|init| (($) NIL (|has| |#1| (|StepThrough|)) CONST)) (|hash| (((|SingleInteger|) $) NIL)) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) 67 (|has| |#1| (|IntegralDomain|)))) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) 63 (|has| |#1| (|IntegralDomain|)))) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) 55 (|has| |#1| (|IntegralDomain|)))) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) 51 (|has| |#1| (|IntegralDomain|)))) (|ground?| (((|Boolean|) $) 13)) (|ground| ((|#1| $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|GcdDomain|)))) (|gcd| (($ (|List| $)) NIL (|has| |#1| (|GcdDomain|))) (($ $ $) NIL (|has| |#1| (|GcdDomain|)))) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) 19)) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) 59 (|has| |#1| (|IntegralDomain|)))) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) 47 (|has| |#1| (|IntegralDomain|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL (|has| |#1| (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|exquo| (((|Union| $ "failed") $ |#1|) NIL (|has| |#1| (|IntegralDomain|))) (((|Union| $ "failed") $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) 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(((|SparseUnivariatePolynomial| |#1|) $) 7) (($ (|SparseUnivariatePolynomial| |#1|)) 8) (($ (|Fraction| (|Integer|))) NIL (OR (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))))) (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|coefficients| (((|List| |#1|) $) NIL)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) NIL) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|CommutativeRing|)))) (|associates?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 21 T CONST)) (|One| (($) 24 T CONST)) (D (($ $ (|SingletonAsOrderedSet|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|))) NIL) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL) (($ $ (|Symbol|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#1| |#1|)) NIL)) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (/ (($ $ |#1|) NIL (|has| |#1| (|Field|)))) (- (($ $) 28) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ |#1| $) 23) (($ $ |#1|) NIL))) 
(((|NewSparseUnivariatePolynomial| |#1|) (|Join| (|UnivariatePolynomialCategory| |#1|) (|CoercibleTo| (|SparseUnivariatePolynomial| |#1|)) (|RetractableTo| (|SparseUnivariatePolynomial| |#1|)) (CATEGORY |domain| (SIGNATURE |fmecg| ($ $ (|NonNegativeInteger|) |#1| $)) (SIGNATURE |monicModulo| ($ $ $)) (SIGNATURE |lazyResidueClass| ((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $)) (SIGNATURE |lazyPseudoRemainder| ($ $ $)) (SIGNATURE |lazyPseudoDivide| ((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |lazyPseudoQuotient| ($ $ $)) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |subResultantsChain| ((|List| $) $ $)) (SIGNATURE |lastSubResultant| ($ $ $)) (SIGNATURE |extendedSubResultantGcd| ((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $)) (SIGNATURE |halfExtendedSubResultantGcd1| ((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $)) (SIGNATURE |halfExtendedSubResultantGcd2| ((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $)) (SIGNATURE |extendedResultant| ((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $)) (SIGNATURE |halfExtendedResultant1| ((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $)) (SIGNATURE |halfExtendedResultant2| ((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $))) |noBranch|))) (|Ring|)) (T |NewSparseUnivariatePolynomial|)) 
((|fmecg| (*1 *1 *1 *2 *3 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|Ring|)))) (|monicModulo| (*1 *1 *1 *1) (AND (|isDomain| *1 (|NewSparseUnivariatePolynomial| *2)) (|ofCategory| *2 (|Ring|)))) (|lazyResidueClass| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |polnum| (|NewSparseUnivariatePolynomial| *3)) (|:| |polden| *3) (|:| |power| (|NonNegativeInteger|)))) (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|Ring|)))) (|lazyPseudoRemainder| (*1 *1 *1 *1) (AND (|isDomain| *1 (|NewSparseUnivariatePolynomial| *2)) (|ofCategory| *2 (|Ring|)))) (|lazyPseudoDivide| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |coef| *3) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| (|NewSparseUnivariatePolynomial| *3)) (|:| |remainder| (|NewSparseUnivariatePolynomial| *3)))) (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|Ring|)))) (|lazyPseudoQuotient| (*1 *1 *1 *1) (AND (|isDomain| *1 (|NewSparseUnivariatePolynomial| *2)) (|ofCategory| *2 (|Ring|)))) (|subResultantsChain| (*1 *2 *1 *1) (AND (|isDomain| *2 (|List| (|NewSparseUnivariatePolynomial| *3))) (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)))) (|lastSubResultant| (*1 *1 *1 *1) (AND (|isDomain| *1 (|NewSparseUnivariatePolynomial| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|Ring|)))) (|extendedSubResultantGcd| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |gcd| (|NewSparseUnivariatePolynomial| *3)) (|:| |coef1| (|NewSparseUnivariatePolynomial| *3)) (|:| |coef2| (|NewSparseUnivariatePolynomial| *3)))) (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)))) (|halfExtendedSubResultantGcd1| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |gcd| (|NewSparseUnivariatePolynomial| *3)) (|:| |coef1| (|NewSparseUnivariatePolynomial| *3)))) (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)))) (|halfExtendedSubResultantGcd2| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |gcd| (|NewSparseUnivariatePolynomial| *3)) (|:| |coef2| (|NewSparseUnivariatePolynomial| *3)))) (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)))) (|extendedResultant| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |resultant| *3) (|:| |coef1| (|NewSparseUnivariatePolynomial| *3)) (|:| |coef2| (|NewSparseUnivariatePolynomial| *3)))) (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)))) (|halfExtendedResultant1| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |resultant| *3) (|:| |coef1| (|NewSparseUnivariatePolynomial| *3)))) (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)))) (|halfExtendedResultant2| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |resultant| *3) (|:| |coef2| (|NewSparseUnivariatePolynomial| *3)))) (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))))) 
(|Join| (|UnivariatePolynomialCategory| |#1|) (|CoercibleTo| (|SparseUnivariatePolynomial| |#1|)) (|RetractableTo| (|SparseUnivariatePolynomial| |#1|)) (CATEGORY |domain| (SIGNATURE |fmecg| ($ $ (|NonNegativeInteger|) |#1| $)) (SIGNATURE |monicModulo| ($ $ $)) (SIGNATURE |lazyResidueClass| ((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $)) (SIGNATURE |lazyPseudoRemainder| ($ $ $)) (SIGNATURE |lazyPseudoDivide| ((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |lazyPseudoQuotient| ($ $ $)) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |subResultantsChain| ((|List| $) $ $)) (SIGNATURE |lastSubResultant| ($ $ $)) (SIGNATURE |extendedSubResultantGcd| ((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $)) (SIGNATURE |halfExtendedSubResultantGcd1| ((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $)) (SIGNATURE |halfExtendedSubResultantGcd2| ((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $)) (SIGNATURE |extendedResultant| ((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $)) (SIGNATURE |halfExtendedResultant1| ((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $)) (SIGNATURE |halfExtendedResultant2| ((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $))) |noBranch|))) 
((|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) 32 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) 22)) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) 34 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) 
(((|NumberTheoreticPolynomialFunctions| |#1|) (CATEGORY |package| (SIGNATURE |cyclotomic| (|#1| (|NonNegativeInteger|) |#1|)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |bernoulliB| (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE |eulerE| (|#1| (|NonNegativeInteger|) |#1|))) |noBranch|)) (|CommutativeRing|)) (T |NumberTheoreticPolynomialFunctions|)) 
((|eulerE| (*1 *2 *3 *2) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|NumberTheoreticPolynomialFunctions| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|CommutativeRing|)))) (|bernoulliB| (*1 *2 *3 *2) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|NumberTheoreticPolynomialFunctions| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|CommutativeRing|)))) (|cyclotomic| (*1 *2 *3 *2) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|NumberTheoreticPolynomialFunctions| *2)) (|ofCategory| *2 (|CommutativeRing|))))) 
(CATEGORY |package| (SIGNATURE |cyclotomic| (|#1| (|NonNegativeInteger|) |#1|)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |bernoulliB| (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE |eulerE| (|#1| (|NonNegativeInteger|) |#1|))) |noBranch|)) 
((~= (((|Boolean|) $ $) 7)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 78)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 79) (((|List| $) (|List| |#4|) (|Boolean|)) 104)) (|variables| (((|List| |#3|) $) 32)) (|trivialIdeal?| (((|Boolean|) $) 25)) (|triangular?| (((|Boolean|) $) 16 (|has| |#1| (|IntegralDomain|)))) (|stronglyReduced?| (((|Boolean|) |#4| $) 94) (((|Boolean|) $) 90)) (|stronglyReduce| ((|#4| |#4| $) 85)) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) 119)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 26)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 43)) (|select| (($ (|Mapping| (|Boolean|) |#4|) $) 64 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| |#4| "failed") $ |#3|) 72)) (|sample| (($) 44 T CONST)) (|roughUnitIdeal?| (((|Boolean|) $) 21 (|has| |#1| (|IntegralDomain|)))) (|roughSubIdeal?| (((|Boolean|) $ $) 23 (|has| |#1| (|IntegralDomain|)))) (|roughEqualIdeals?| (((|Boolean|) $ $) 22 (|has| |#1| (|IntegralDomain|)))) (|roughBase?| (((|Boolean|) $) 24 (|has| |#1| (|IntegralDomain|)))) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 86)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) 17 (|has| |#1| (|IntegralDomain|)))) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) 18 (|has| |#1| (|IntegralDomain|)))) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 35)) (|retract| (($ (|List| |#4|)) 34)) (|rest| (((|Union| $ "failed") $) 75)) (|removeZero| ((|#4| |#4| $) 82)) (|removeDuplicates| (($ $) 67 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove| (($ |#4| $) 66 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#4|) $) 63 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 19 (|has| |#1| (|IntegralDomain|)))) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) 95)) (|reduceByQuasiMonic| ((|#4| |#4| $) 80)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 65 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 62 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 61 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 87)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 98)) (|purelyTranscendental?| (((|Boolean|) |#4| $) 129)) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) 126)) (|purelyAlgebraic?| (((|Boolean|) |#4| $) 130) (((|Boolean|) $) 127)) (|parts| (((|List| |#4|) $) 51 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|normalized?| (((|Boolean|) |#4| $) 97) (((|Boolean|) $) 96)) (|mvar| ((|#3| $) 33)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 42)) (|members| (((|List| |#4|) $) 52 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#4| $) 54 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#4| |#4|) $) 47 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#4| |#4|) $) 46)) (|mainVariables| (((|List| |#3|) $) 31)) (|mainVariable?| (((|Boolean|) |#3| $) 30)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 41)) (|latex| (((|String|) $) 9)) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) 121)) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) 120)) (|last| (((|Union| |#4| "failed") $) 76)) (|invertibleSet| (((|List| $) |#4| $) 122)) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) 125)) (|invertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) 124) (((|Boolean|) |#4| $) 123)) (|intersect| (((|List| $) |#4| $) 118) (((|List| $) (|List| |#4|) $) 117) (((|List| $) (|List| |#4|) (|List| $)) 116) (((|List| $) |#4| (|List| $)) 115)) (|internalAugment| (($ |#4| $) 110) (($ (|List| |#4|) $) 109)) (|initials| (((|List| |#4|) $) 100)) (|initiallyReduced?| (((|Boolean|) |#4| $) 92) (((|Boolean|) $) 88)) (|initiallyReduce| ((|#4| |#4| $) 83)) (|infRittWu?| (((|Boolean|) $ $) 103)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 20 (|has| |#1| (|IntegralDomain|)))) (|headReduced?| (((|Boolean|) |#4| $) 93) (((|Boolean|) $) 89)) (|headReduce| ((|#4| |#4| $) 84)) (|hash| (((|SingleInteger|) $) 10)) (|first| (((|Union| |#4| "failed") $) 77)) (|find| (((|Union| |#4| "failed") (|Mapping| (|Boolean|) |#4|) $) 60)) (|extendIfCan| (((|Union| $ "failed") $ |#4|) 71)) (|extend| (($ $ |#4|) 70) (((|List| $) |#4| $) 108) (((|List| $) |#4| (|List| $)) 107) (((|List| $) (|List| |#4|) $) 106) (((|List| $) (|List| |#4|) (|List| $)) 105)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) 49 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 58 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ |#4| |#4|) 57 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|Equation| |#4|)) 56 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|List| (|Equation| |#4|))) 55 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 37)) (|empty?| (((|Boolean|) $) 40)) (|empty| (($) 39)) (|degree| (((|NonNegativeInteger|) $) 99)) (|count| (((|NonNegativeInteger|) |#4| $) 53 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#4|) $) 50 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) 38)) (|convert| (((|InputForm|) $) 68 (|has| |#4| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#4|)) 59)) (|collectUpper| (($ $ |#3|) 27)) (|collectUnder| (($ $ |#3|) 29)) (|collectQuasiMonic| (($ $) 81)) (|collect| (($ $ |#3|) 28)) (|coerce| (((|OutputForm|) $) 11) (((|List| |#4|) $) 36)) (|coHeight| (((|NonNegativeInteger|) $) 69 (|has| |#3| (|Finite|)))) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 102) (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 101)) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) 91)) (|augment| (((|List| $) |#4| $) 114) (((|List| $) |#4| (|List| $)) 113) (((|List| $) (|List| |#4|) $) 112) (((|List| $) (|List| |#4|) (|List| $)) 111)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) 48 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|algebraicVariables| (((|List| |#3|) $) 74)) (|algebraicCoefficients?| (((|Boolean|) |#4| $) 128)) (|algebraic?| (((|Boolean|) |#3| $) 73)) (= (((|Boolean|) $ $) 6)) (|#| (((|NonNegativeInteger|) $) 45 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|NormalizedTriangularSetCategory| |#1| |#2| |#3| |#4|) (|Category|) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |t#1| |t#2| |t#3|)) (T |NormalizedTriangularSetCategory|)) 
NIL 
(|Join| (|RegularTriangularSetCategory| |t#1| |t#2| |t#3| |t#4|)) 
(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|TriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|Type|) . T)) 
((|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) 60 (AND (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|OrderedSet|)))) (((|Union| (|Float|) "failed") (|Expression| |#1|)) 52 (AND (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|OrderedSet|)))) (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) 39 (|has| |#1| (|IntegralDomain|))) (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) 35 (|has| |#1| (|IntegralDomain|))) (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) 30 (|has| |#1| (|Ring|))) (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) 24 (|has| |#1| (|Ring|)))) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) 92 (AND (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|OrderedSet|)))) (((|Float|) (|Expression| |#1|)) 87 (AND (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|OrderedSet|)))) (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) 84 (|has| |#1| (|IntegralDomain|))) (((|Float|) (|Fraction| (|Polynomial| |#1|))) 81 (|has| |#1| (|IntegralDomain|))) (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) 80 (|has| |#1| (|Ring|))) (((|Float|) (|Polynomial| |#1|)) 77 (|has| |#1| (|Ring|))) (((|Float|) |#1| (|PositiveInteger|)) 73) (((|Float|) |#1|) 22)) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) 68 (AND (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|OrderedSet|)))) (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) 58 (AND (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|OrderedSet|)))) (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) 61 (AND (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|OrderedSet|)))) (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) 59 (AND (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|OrderedSet|)))) (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) 44 (|has| |#1| (|IntegralDomain|))) (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) 43 (|has| |#1| (|IntegralDomain|))) (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) 38 (|has| |#1| (|IntegralDomain|))) (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) 37 (|has| |#1| (|IntegralDomain|))) (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) 28 (|has| |#1| (|Ring|))) (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) 26 (|has| |#1| (|Ring|))) (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) 17 (|has| |#1| (|CommutativeRing|))) (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) 14 (|has| |#1| (|CommutativeRing|)))) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) 95 (AND (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|OrderedSet|)))) (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) 94 (AND (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|OrderedSet|)))) (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) 93 (AND (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|OrderedSet|)))) (((|Complex| (|Float|)) (|Expression| |#1|)) 91 (AND (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|OrderedSet|)))) (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) 86 (|has| |#1| (|IntegralDomain|))) (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) 85 (|has| |#1| (|IntegralDomain|))) (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) 83 (|has| |#1| (|IntegralDomain|))) (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) 82 (|has| |#1| (|IntegralDomain|))) (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) 79 (|has| |#1| (|Ring|))) (((|Complex| (|Float|)) (|Polynomial| |#1|)) 78 (|has| |#1| (|Ring|))) (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) 75 (|has| |#1| (|CommutativeRing|))) (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) 74 (|has| |#1| (|CommutativeRing|))) (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) 16 (|has| |#1| (|CommutativeRing|))) (((|Complex| (|Float|)) (|Complex| |#1|)) 12 (|has| |#1| (|CommutativeRing|))) (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) 27) (((|Complex| (|Float|)) |#1|) 25))) 
(((|Numeric| |#1|) (CATEGORY |package| (SIGNATURE |numeric| ((|Float|) |#1|)) (SIGNATURE |numeric| ((|Float|) |#1| (|PositiveInteger|))) (SIGNATURE |complexNumeric| ((|Complex| (|Float|)) |#1|)) (SIGNATURE |complexNumeric| ((|Complex| (|Float|)) |#1| (|PositiveInteger|))) (IF (|has| |#1| (|CommutativeRing|)) (PROGN (SIGNATURE |complexNumeric| ((|Complex| (|Float|)) (|Complex| |#1|))) (SIGNATURE |complexNumeric| ((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|))) (SIGNATURE |complexNumeric| ((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)))) (SIGNATURE |complexNumeric| ((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)))) |noBranch|) (IF (|has| |#1| (|Ring|)) (PROGN (SIGNATURE |numeric| ((|Float|) (|Polynomial| |#1|))) (SIGNATURE |numeric| ((|Float|) (|Polynomial| |#1|) (|PositiveInteger|))) (SIGNATURE |complexNumeric| ((|Complex| (|Float|)) (|Polynomial| |#1|))) (SIGNATURE |complexNumeric| ((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)))) |noBranch|) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |numeric| ((|Float|) (|Fraction| (|Polynomial| |#1|)))) (SIGNATURE |numeric| ((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|))) (SIGNATURE |complexNumeric| ((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)))) (SIGNATURE |complexNumeric| ((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|))) (SIGNATURE |complexNumeric| ((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))))) (SIGNATURE |complexNumeric| ((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|))) (IF (|has| |#1| (|OrderedSet|)) (PROGN (SIGNATURE |numeric| ((|Float|) (|Expression| |#1|))) (SIGNATURE |numeric| ((|Float|) (|Expression| |#1|) (|PositiveInteger|))) (SIGNATURE |complexNumeric| ((|Complex| (|Float|)) (|Expression| |#1|))) (SIGNATURE |complexNumeric| ((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|))) (SIGNATURE |complexNumeric| ((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)))) (SIGNATURE |complexNumeric| ((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)))) |noBranch|)) |noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (PROGN (SIGNATURE |complexNumericIfCan| ((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)))) (SIGNATURE |complexNumericIfCan| ((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)))) |noBranch|) (IF (|has| |#1| (|Ring|)) (PROGN (SIGNATURE |numericIfCan| ((|Union| (|Float|) "failed") (|Polynomial| |#1|))) (SIGNATURE |numericIfCan| ((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|))) (SIGNATURE |complexNumericIfCan| ((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|))) (SIGNATURE |complexNumericIfCan| ((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)))) |noBranch|) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |numericIfCan| ((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)))) (SIGNATURE |numericIfCan| ((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|))) (SIGNATURE |complexNumericIfCan| ((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)))) (SIGNATURE |complexNumericIfCan| ((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|))) (SIGNATURE |complexNumericIfCan| ((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))))) (SIGNATURE |complexNumericIfCan| ((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|))) (IF (|has| |#1| (|OrderedSet|)) (PROGN (SIGNATURE |numericIfCan| ((|Union| (|Float|) "failed") (|Expression| |#1|))) (SIGNATURE |numericIfCan| ((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|))) (SIGNATURE |complexNumericIfCan| ((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|))) (SIGNATURE |complexNumericIfCan| ((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|))) (SIGNATURE |complexNumericIfCan| ((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)))) (SIGNATURE |complexNumericIfCan| ((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)))) |noBranch|)) |noBranch|)) (|ConvertibleTo| (|Float|))) (T |Numeric|)) 
((|complexNumericIfCan| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Expression| (|Complex| *5))) (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *5 (|ConvertibleTo| (|Float|))) (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *5)))) (|complexNumericIfCan| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|Expression| (|Complex| *4))) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *4 (|ConvertibleTo| (|Float|))) (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *4)))) (|complexNumericIfCan| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Expression| *5)) (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *5 (|ConvertibleTo| (|Float|))) (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *5)))) (|complexNumericIfCan| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|Expression| *4)) 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(((|NumberFormats|) (CATEGORY |package| (SIGNATURE |FormatArabic| ((|String|) (|PositiveInteger|))) (SIGNATURE |ScanArabic| ((|PositiveInteger|) (|String|))) (SIGNATURE |FormatRoman| ((|String|) (|PositiveInteger|))) (SIGNATURE |ScanRoman| ((|PositiveInteger|) (|String|))) (SIGNATURE |ScanFloatIgnoreSpaces| ((|Float|) (|String|))) (SIGNATURE |ScanFloatIgnoreSpacesIfCan| ((|Union| (|Float|) "failed") (|String|))))) (T |NumberFormats|)) 
((|ScanFloatIgnoreSpacesIfCan| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Float|)) (|isDomain| *1 (|NumberFormats|)))) (|ScanFloatIgnoreSpaces| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Float|)) (|isDomain| *1 (|NumberFormats|)))) (|ScanRoman| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|NumberFormats|)))) (|FormatRoman| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|String|)) (|isDomain| *1 (|NumberFormats|)))) (|ScanArabic| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|NumberFormats|)))) (|FormatArabic| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|String|)) (|isDomain| *1 (|NumberFormats|))))) 
(CATEGORY |package| (SIGNATURE |FormatArabic| ((|String|) (|PositiveInteger|))) (SIGNATURE |ScanArabic| ((|PositiveInteger|) (|String|))) (SIGNATURE |FormatRoman| ((|String|) (|PositiveInteger|))) (SIGNATURE |ScanRoman| ((|PositiveInteger|) (|String|))) (SIGNATURE |ScanFloatIgnoreSpaces| ((|Float|) (|String|))) (SIGNATURE |ScanFloatIgnoreSpacesIfCan| ((|Union| (|Float|) "failed") (|String|)))) 
((~= (((|Boolean|) $ $) 7)) (|numericalIntegration| (((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) 14) (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) 12)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 15) (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 13)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (= (((|Boolean|) $ $) 6))) 
(((|NumericalIntegrationCategory|) (|Category|)) (T |NumericalIntegrationCategory|)) 
((|measure| (*1 *2 *3 *4) (AND (|ofCategory| *1 (|NumericalIntegrationCategory|)) (|isDomain| *3 (|RoutinesTable|)) (|isDomain| *4 (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|isDomain| *2 (|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|)))))) (|numericalIntegration| (*1 *2 *3 *2) (AND (|ofCategory| *1 (|NumericalIntegrationCategory|)) (|isDomain| *2 (|Result|)) (|isDomain| *3 (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) (|measure| (*1 *2 *3 *4) (AND (|ofCategory| *1 (|NumericalIntegrationCategory|)) (|isDomain| *3 (|RoutinesTable|)) (|isDomain| *4 (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|isDomain| *2 (|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|)))))) (|numericalIntegration| (*1 *2 *3 *2) (AND (|ofCategory| *1 (|NumericalIntegrationCategory|)) (|isDomain| *2 (|Result|)) (|isDomain| *3 (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))))) 
(|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE |measure| ((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |numericalIntegration| ((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|))) (SIGNATURE |measure| ((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |numericalIntegration| ((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|))))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((|rk4qc| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) 44) (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) 43)) (|rk4f| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) 50)) (|rk4a| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) 41)) (|rk4| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) 52) (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) 51))) 
(((|NumericalOrdinaryDifferentialEquations|) (CATEGORY |package| (SIGNATURE |rk4| ((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)))) (SIGNATURE |rk4| ((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)))) (SIGNATURE |rk4a| ((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)))) (SIGNATURE |rk4qc| ((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)))) (SIGNATURE |rk4qc| ((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)))) (SIGNATURE |rk4f| ((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)))))) (T |NumericalOrdinaryDifferentialEquations|)) 
((|rk4f| (*1 *2 *3 *4 *5 *5 *4 *6) (AND (|isDomain| *4 (|Integer|)) (|isDomain| *6 (|Mapping| (|Void|) (|Vector| *5) (|Vector| *5) (|Float|))) (|isDomain| *3 (|Vector| (|Float|))) (|isDomain| *5 (|Float|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|NumericalOrdinaryDifferentialEquations|)))) (|rk4qc| (*1 *2 *3 *4 *5 *6 *5 *3 *7 *3 *3 *3 *3 *3 *3 *3) (AND (|isDomain| *4 (|Integer|)) (|isDomain| *6 (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|)))) (|isDomain| *7 (|Mapping| (|Void|) (|Vector| *5) (|Vector| *5) (|Float|))) (|isDomain| *3 (|Vector| (|Float|))) (|isDomain| *5 (|Float|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|NumericalOrdinaryDifferentialEquations|)))) (|rk4qc| (*1 *2 *3 *4 *5 *6 *5 *3 *7) (AND (|isDomain| *4 (|Integer|)) (|isDomain| *6 (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|)))) (|isDomain| *7 (|Mapping| (|Void|) (|Vector| *5) (|Vector| *5) (|Float|))) (|isDomain| *3 (|Vector| (|Float|))) (|isDomain| *5 (|Float|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|NumericalOrdinaryDifferentialEquations|)))) (|rk4a| (*1 *2 *3 *4 *5 *5 *5 *5 *4 *6) (AND (|isDomain| *4 (|Integer|)) (|isDomain| *6 (|Mapping| (|Void|) (|Vector| *5) (|Vector| *5) (|Float|))) (|isDomain| *3 (|Vector| (|Float|))) (|isDomain| *5 (|Float|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|NumericalOrdinaryDifferentialEquations|)))) (|rk4| (*1 *2 *3 *4 *5 *5 *6 *3 *3 *3 *3) (AND (|isDomain| *4 (|Integer|)) (|isDomain| *6 (|Mapping| (|Void|) (|Vector| *5) (|Vector| *5) (|Float|))) (|isDomain| *3 (|Vector| (|Float|))) (|isDomain| *5 (|Float|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|NumericalOrdinaryDifferentialEquations|)))) (|rk4| (*1 *2 *3 *4 *5 *5 *6) (AND (|isDomain| *4 (|Integer|)) (|isDomain| *6 (|Mapping| (|Void|) (|Vector| *5) (|Vector| *5) (|Float|))) (|isDomain| *3 (|Vector| (|Float|))) (|isDomain| *5 (|Float|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|NumericalOrdinaryDifferentialEquations|))))) 
(CATEGORY |package| (SIGNATURE |rk4| ((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)))) (SIGNATURE |rk4| ((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)))) (SIGNATURE |rk4a| ((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)))) (SIGNATURE |rk4qc| ((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)))) (SIGNATURE |rk4qc| ((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)))) (SIGNATURE |rk4f| ((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))))) 
((|trapezoidalo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) 53)) (|trapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) 30)) (|simpsono| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) 52)) (|simpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) 28)) (|rombergo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) 51)) (|romberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) 18)) (|atrapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) 31)) (|asimpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) 29)) (|aromberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) 27))) 
(((|NumericalQuadrature|) (CATEGORY |package| (SIGNATURE |aromberg| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |asimpson| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |atrapezoidal| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |romberg| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|))) (SIGNATURE |simpson| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|))) (SIGNATURE |trapezoidal| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|))) (SIGNATURE |rombergo| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|))) (SIGNATURE |simpsono| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|))) (SIGNATURE |trapezoidalo| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|))))) (T |NumericalQuadrature|)) 
((|trapezoidalo| (*1 *2 *3 *4 *4 *4 *4 *5 *5) (AND (|isDomain| *3 (|Mapping| (|Float|) (|Float|))) (|isDomain| *4 (|Float|)) (|isDomain| *2 (|Record| (|:| |value| *4) (|:| |error| *4) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|)))) (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|)))) (|simpsono| (*1 *2 *3 *4 *4 *4 *4 *5 *5) (AND (|isDomain| *3 (|Mapping| (|Float|) (|Float|))) (|isDomain| *4 (|Float|)) (|isDomain| *2 (|Record| (|:| |value| *4) (|:| |error| *4) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|)))) (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|)))) (|rombergo| (*1 *2 *3 *4 *4 *4 *4 *5 *5) (AND (|isDomain| *3 (|Mapping| (|Float|) (|Float|))) (|isDomain| *4 (|Float|)) (|isDomain| *2 (|Record| (|:| |value| *4) (|:| |error| *4) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|)))) (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|)))) (|trapezoidal| (*1 *2 *3 *4 *4 *4 *4 *5 *5) (AND (|isDomain| *3 (|Mapping| (|Float|) (|Float|))) (|isDomain| *4 (|Float|)) (|isDomain| *2 (|Record| (|:| |value| *4) (|:| |error| *4) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|)))) (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|)))) (|simpson| (*1 *2 *3 *4 *4 *4 *4 *5 *5) (AND (|isDomain| *3 (|Mapping| (|Float|) (|Float|))) (|isDomain| *4 (|Float|)) (|isDomain| *2 (|Record| (|:| |value| *4) (|:| |error| *4) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|)))) (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|)))) (|romberg| (*1 *2 *3 *4 *4 *4 *4 *5 *5) (AND (|isDomain| *3 (|Mapping| (|Float|) (|Float|))) (|isDomain| *4 (|Float|)) (|isDomain| *2 (|Record| (|:| |value| *4) (|:| |error| *4) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|)))) (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|)))) (|atrapezoidal| (*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) (AND (|isDomain| *3 (|Mapping| (|Float|) (|Float|))) (|isDomain| *4 (|Float|)) (|isDomain| *2 (|Record| (|:| |value| *4) (|:| |error| *4) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|)))) (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|)))) (|asimpson| (*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) (AND (|isDomain| *3 (|Mapping| (|Float|) (|Float|))) (|isDomain| *4 (|Float|)) (|isDomain| *2 (|Record| (|:| |value| *4) (|:| |error| *4) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|)))) (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|)))) (|aromberg| (*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) (AND (|isDomain| *3 (|Mapping| (|Float|) (|Float|))) (|isDomain| *4 (|Float|)) (|isDomain| *2 (|Record| (|:| |value| *4) (|:| |error| *4) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|)))) (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|))))) 
(CATEGORY |package| (SIGNATURE |aromberg| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |asimpson| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |atrapezoidal| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |romberg| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|))) (SIGNATURE |simpson| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|))) (SIGNATURE |trapezoidal| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|))) (SIGNATURE |rombergo| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|))) (SIGNATURE |simpsono| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|))) (SIGNATURE |trapezoidalo| ((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)))) 
((|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) 45))) 
(((|NumericTubePlot| |#1|) (CATEGORY |package| (SIGNATURE |tube| ((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)))) (|PlottableSpaceCurveCategory|)) (T |NumericTubePlot|)) 
((|tube| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|DoubleFloat|)) (|isDomain| *5 (|Integer|)) (|isDomain| *2 (|TubePlot| *3)) (|isDomain| *1 (|NumericTubePlot| *3)) (|ofCategory| *3 (|PlottableSpaceCurveCategory|))))) 
(CATEGORY |package| (SIGNATURE |tube| ((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 23)) (|subtractIfCan| (((|Union| $ "failed") $ $) 25)) (|sample| (($) 22 T CONST)) (|min| (($ $ $) 12)) (|max| (($ $ $) 13)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (|Zero| (($) 21 T CONST)) (>= (((|Boolean|) $ $) 15)) (> (((|Boolean|) $ $) 16)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 14)) (< (((|Boolean|) $ $) 17)) (- (($ $ $) 27) (($ $) 26)) (+ (($ $ $) 19)) (* (($ (|PositiveInteger|) $) 20) (($ (|NonNegativeInteger|) $) 24) (($ (|Integer|) $) 28))) 
(((|OrderedAbelianGroup|) (|Category|)) (T |OrderedAbelianGroup|)) 
NIL 
(|Join| (|OrderedCancellationAbelianMonoid|) (|AbelianGroup|)) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedSet|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 23)) (|sample| (($) 22 T CONST)) (|min| (($ $ $) 12)) (|max| (($ $ $) 13)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (|Zero| (($) 21 T CONST)) (>= (((|Boolean|) $ $) 15)) (> (((|Boolean|) $ $) 16)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 14)) (< (((|Boolean|) $ $) 17)) (+ (($ $ $) 19)) (* (($ (|PositiveInteger|) $) 20) (($ (|NonNegativeInteger|) $) 24))) 
(((|OrderedAbelianMonoid|) (|Category|)) (T |OrderedAbelianMonoid|)) 
NIL 
(|Join| (|OrderedAbelianSemiGroup|) (|AbelianMonoid|)) 
(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedSet|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 23)) (|sup| (($ $ $) 26)) (|subtractIfCan| (((|Union| $ "failed") $ $) 25)) (|sample| (($) 22 T CONST)) (|min| (($ $ $) 12)) (|max| (($ $ $) 13)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (|Zero| (($) 21 T CONST)) (>= (((|Boolean|) $ $) 15)) (> (((|Boolean|) $ $) 16)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 14)) (< (((|Boolean|) $ $) 17)) (+ (($ $ $) 19)) (* (($ (|PositiveInteger|) $) 20) (($ (|NonNegativeInteger|) $) 24))) 
(((|OrderedAbelianMonoidSup|) (|Category|)) (T |OrderedAbelianMonoidSup|)) 
((|sup| (*1 *1 *1 *1) (|ofCategory| *1 (|OrderedAbelianMonoidSup|)))) 
(|Join| (|OrderedCancellationAbelianMonoid|) (CATEGORY |domain| (SIGNATURE |sup| ($ $ $)))) 
(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedSet|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) 7)) (|min| (($ $ $) 12)) (|max| (($ $ $) 13)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (>= (((|Boolean|) $ $) 15)) (> (((|Boolean|) $ $) 16)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 14)) (< (((|Boolean|) $ $) 17)) (+ (($ $ $) 19)) (* (($ (|PositiveInteger|) $) 20))) 
(((|OrderedAbelianSemiGroup|) (|Category|)) (T |OrderedAbelianSemiGroup|)) 
NIL 
(|Join| (|OrderedSet|) (|AbelianSemiGroup|)) 
(((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|OrderedSet|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 23)) (|subtractIfCan| (((|Union| $ "failed") $ $) 25)) (|sample| (($) 22 T CONST)) (|min| (($ $ $) 12)) (|max| (($ $ $) 13)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (|Zero| (($) 21 T CONST)) (>= (((|Boolean|) $ $) 15)) (> (((|Boolean|) $ $) 16)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 14)) (< (((|Boolean|) $ $) 17)) (+ (($ $ $) 19)) (* (($ (|PositiveInteger|) $) 20) (($ (|NonNegativeInteger|) $) 24))) 
(((|OrderedCancellationAbelianMonoid|) (|Category|)) (T |OrderedCancellationAbelianMonoid|)) 
NIL 
(|Join| (|OrderedAbelianMonoid|) (|CancellationAbelianMonoid|)) 
(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedSet|) . T) ((|SetCategory|) . T)) 
((|zero?| (((|Boolean|) $) 41)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL) (((|Union| |#2| "failed") $) 44)) (|retract| (((|Integer|) $) NIL) (((|Fraction| (|Integer|)) $) NIL) ((|#2| $) 42)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 78)) (|rational?| (((|Boolean|) $) 72)) (|rational| (((|Fraction| (|Integer|)) $) 76)) (|norm| ((|#2| $) 26)) (|map| (($ (|Mapping| |#2| |#2|) $) 23)) (|inv| (($ $) 61)) (|convert| (((|InputForm|) $) 67)) (|conjugate| (($ $) 21)) (|coerce| (((|OutputForm|) $) 56) (($ (|Integer|)) 39) (($ |#2|) 37) (($ (|Fraction| (|Integer|))) NIL)) (|characteristic| (((|NonNegativeInteger|)) 10)) (|abs| ((|#2| $) 71)) (= (((|Boolean|) $ $) 29)) (< (((|Boolean|) $ $) 69)) (- (($ $) 31) (($ $ $) NIL)) (+ (($ $ $) 30)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 35) (($ $ $) NIL) (($ $ |#2|) NIL) (($ |#2| $) 32))) 
(((|OctonionCategory&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |inv| (|#1| |#1|)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |rational?| ((|Boolean|) |#1|)) (SIGNATURE |abs| (|#2| |#1|)) (SIGNATURE |norm| (|#2| |#1|)) (SIGNATURE |conjugate| (|#1| |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |characteristic| ((|NonNegativeInteger|))) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE |zero?| ((|Boolean|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|)) (SIGNATURE + (|#1| |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|))) (|OctonionCategory| |#2|) (|CommutativeRing|)) (T |OctonionCategory&|)) 
((|characteristic| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|OctonionCategory&| *3 *4)) (|ofCategory| *3 (|OctonionCategory| *4))))) 
(CATEGORY |domain| (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |inv| (|#1| |#1|)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |rational?| ((|Boolean|) |#1|)) (SIGNATURE |abs| (|#2| |#1|)) (SIGNATURE |norm| (|#2| |#1|)) (SIGNATURE |conjugate| (|#1| |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |characteristic| ((|NonNegativeInteger|))) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE |zero?| ((|Boolean|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|)) (SIGNATURE + (|#1| |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|size| (((|NonNegativeInteger|)) 51 (|has| |#1| (|Finite|)))) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 93 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) 91 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) 89)) (|retract| (((|Integer|) $) 94 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) 92 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) 88)) (|recip| (((|Union| $ "failed") $) 33)) (|real| ((|#1| $) 78)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 65 (|has| |#1| (|IntegerNumberSystem|)))) (|rational?| (((|Boolean|) $) 67 (|has| |#1| (|IntegerNumberSystem|)))) (|rational| (((|Fraction| (|Integer|)) $) 66 (|has| |#1| (|IntegerNumberSystem|)))) (|random| (($) 54 (|has| |#1| (|Finite|)))) (|one?| (((|Boolean|) $) 30)) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) 69)) (|norm| ((|#1| $) 70)) (|min| (($ $ $) 61 (|has| |#1| (|OrderedSet|)))) (|max| (($ $ $) 60 (|has| |#1| (|OrderedSet|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 80)) (|lookup| (((|PositiveInteger|) $) 53 (|has| |#1| (|Finite|)))) (|latex| (((|String|) $) 9)) (|inv| (($ $) 64 (|has| |#1| (|Field|)))) (|index| (($ (|PositiveInteger|)) 52 (|has| |#1| (|Finite|)))) (|imagk| ((|#1| $) 75)) (|imagj| ((|#1| $) 76)) (|imagi| ((|#1| $) 77)) (|imagK| ((|#1| $) 71)) (|imagJ| ((|#1| $) 72)) (|imagI| ((|#1| $) 73)) (|imagE| ((|#1| $) 74)) (|hash| (((|SingleInteger|) $) 10)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) 86 (|has| |#1| (|Evalable| |#1|))) (($ $ |#1| |#1|) 85 (|has| |#1| (|Evalable| |#1|))) (($ $ (|Equation| |#1|)) 84 (|has| |#1| (|Evalable| |#1|))) (($ $ (|List| (|Equation| |#1|))) 83 (|has| |#1| (|Evalable| |#1|))) (($ $ (|List| (|Symbol|)) (|List| |#1|)) 82 (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|))) (($ $ (|Symbol|) |#1|) 81 (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|)))) (|enumerate| (((|List| $)) 55 (|has| |#1| (|Finite|)))) (|elt| (($ $ |#1|) 87 (|has| |#1| (|Eltable| |#1| |#1|)))) (|convert| (((|InputForm|) $) 62 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|conjugate| (($ $) 79)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ |#1|) 36) (($ (|Fraction| (|Integer|))) 90 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))))) (|charthRoot| (((|Union| $ "failed") $) 63 (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|abs| ((|#1| $) 68 (|has| |#1| (|RealNumberSystem|)))) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (>= (((|Boolean|) $ $) 58 (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) 57 (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 59 (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) 56 (|has| |#1| (|OrderedSet|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 38) (($ |#1| $) 37))) 
(((|OctonionCategory| |#1|) (|Category|) (|CommutativeRing|)) (T |OctonionCategory|)) 
((|conjugate| (*1 *1 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|real| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagi| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagj| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagk| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagE| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagI| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagJ| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagK| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|norm| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|octon| (*1 *1 *2 *2 *2 *2 *2 *2 *2 *2) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|abs| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|RealNumberSystem|)))) (|rational?| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|)))) (|rational| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|rationalIfCan| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|OctonionCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|inv| (*1 *1 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|Field|))))) 
(|Join| (|Algebra| |t#1|) (|FullyRetractableTo| |t#1|) (|FullyEvalableOver| |t#1|) (CATEGORY |domain| (SIGNATURE |conjugate| ($ $)) (SIGNATURE |real| (|t#1| $)) (SIGNATURE |imagi| (|t#1| $)) (SIGNATURE |imagj| (|t#1| $)) (SIGNATURE |imagk| (|t#1| $)) (SIGNATURE |imagE| (|t#1| $)) (SIGNATURE |imagI| (|t#1| $)) (SIGNATURE |imagJ| (|t#1| $)) (SIGNATURE |imagK| (|t#1| $)) (SIGNATURE |norm| (|t#1| $)) (SIGNATURE |octon| ($ |t#1| |t#1| |t#1| |t#1| |t#1| |t#1| |t#1| |t#1|)) (IF (|has| |t#1| (|Finite|)) (ATTRIBUTE (|Finite|)) |noBranch|) (IF (|has| |t#1| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |noBranch|) (IF (|has| |t#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |noBranch|) (IF (|has| |t#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |noBranch|) (IF (|has| |t#1| (|RealNumberSystem|)) (SIGNATURE |abs| (|t#1| $)) |noBranch|) (IF (|has| |t#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") $))) |noBranch|) (IF (|has| |t#1| (|Field|)) (SIGNATURE |inv| ($ $)) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| |#1| $) |has| |#1| (|Eltable| |#1| |#1|)) ((|Evalable| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Finite|) |has| |#1| (|Finite|)) ((|FullyEvalableOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|InnerEvalable| (|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) 20))) 
(((|OctonionCategoryFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#3| (|Mapping| |#4| |#2|) |#1|))) (|OctonionCategory| |#2|) (|CommutativeRing|) (|OctonionCategory| |#4|) (|CommutativeRing|)) (T |OctonionCategoryFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|CommutativeRing|)) (|ofCategory| *6 (|CommutativeRing|)) (|ofCategory| *2 (|OctonionCategory| *6)) (|isDomain| *1 (|OctonionCategoryFunctions2| *4 *5 *2 *6)) (|ofCategory| *4 (|OctonionCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |map| (|#3| (|Mapping| |#4| |#2|) |#1|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|size| (((|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL) (((|Union| (|Quaternion| |#1|) "failed") $) 35) (((|Union| (|Integer|) "failed") $) NIL (OR (|has| (|Quaternion| |#1|) (|RetractableTo| (|Integer|))) (|has| |#1| (|RetractableTo| (|Integer|))))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (OR (|has| (|Quaternion| |#1|) (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))))) (|retract| ((|#1| $) NIL) (((|Quaternion| |#1|) $) 33) (((|Integer|) $) NIL (OR (|has| (|Quaternion| |#1|) (|RetractableTo| (|Integer|))) (|has| |#1| (|RetractableTo| (|Integer|))))) (((|Fraction| (|Integer|)) $) NIL (OR (|has| (|Quaternion| |#1|) (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))))) (|recip| (((|Union| $ "failed") $) NIL)) (|real| ((|#1| $) 16)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|IntegerNumberSystem|)))) (|rational?| (((|Boolean|) $) NIL (|has| |#1| (|IntegerNumberSystem|)))) (|rational| (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|IntegerNumberSystem|)))) (|random| (($) NIL (|has| |#1| (|Finite|)))) (|one?| (((|Boolean|) $) NIL)) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) 28) (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) 29)) (|norm| ((|#1| $) NIL)) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|lookup| (((|PositiveInteger|) $) NIL (|has| |#1| (|Finite|)))) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL (|has| |#1| (|Field|)))) (|index| (($ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|imagk| ((|#1| $) 22)) (|imagj| ((|#1| $) 20)) (|imagi| ((|#1| $) 18)) (|imagK| ((|#1| $) 26)) (|imagJ| ((|#1| $) 25)) (|imagI| ((|#1| $) 24)) (|imagE| ((|#1| $) 23)) (|hash| (((|SingleInteger|) $) NIL)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ |#1| |#1|) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ (|Equation| |#1|)) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ (|List| (|Equation| |#1|))) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ (|List| (|Symbol|)) (|List| |#1|)) NIL (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|))) (($ $ (|Symbol|) |#1|) NIL (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|)))) (|enumerate| (((|List| $)) NIL (|has| |#1| (|Finite|)))) (|elt| (($ $ |#1|) NIL (|has| |#1| (|Eltable| |#1| |#1|)))) (|convert| (((|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|conjugate| (($ $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ |#1|) NIL) (($ (|Quaternion| |#1|)) 30) (($ (|Fraction| (|Integer|))) NIL (OR (|has| (|Quaternion| |#1|) (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))))) (|charthRoot| (((|Union| $ "failed") $) NIL (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|abs| ((|#1| $) NIL (|has| |#1| (|RealNumberSystem|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 8 T CONST)) (|One| (($) 12 T CONST)) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 40) (($ $ |#1|) NIL) (($ |#1| $) NIL))) 
(((|Octonion| |#1|) (|Join| (|OctonionCategory| |#1|) (|FullyRetractableTo| (|Quaternion| |#1|)) (CATEGORY |domain| (SIGNATURE |octon| ($ (|Quaternion| |#1|) (|Quaternion| |#1|))))) (|CommutativeRing|)) (T |Octonion|)) 
((|octon| (*1 *1 *2 *2) (AND (|isDomain| *2 (|Quaternion| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *1 (|Octonion| *3))))) 
(|Join| (|OctonionCategory| |#1|) (|FullyRetractableTo| (|Quaternion| |#1|)) (CATEGORY |domain| (SIGNATURE |octon| ($ (|Quaternion| |#1|) (|Quaternion| |#1|))))) 
((~= (((|Boolean|) $ $) 7)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 13)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 12)) (= (((|Boolean|) $ $) 6))) 
(((|OrdinaryDifferentialEquationsSolverCategory|) (|Category|)) (T |OrdinaryDifferentialEquationsSolverCategory|)) 
((|measure| (*1 *2 *3 *4) (AND (|ofCategory| *1 (|OrdinaryDifferentialEquationsSolverCategory|)) (|isDomain| *3 (|RoutinesTable|)) (|isDomain| *4 (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|isDomain| *2 (|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)))))) (|ODESolve| (*1 *2 *3) (AND (|ofCategory| *1 (|OrdinaryDifferentialEquationsSolverCategory|)) (|isDomain| *3 (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|isDomain| *2 (|Result|))))) 
(|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE |measure| ((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |ODESolve| ((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) 19))) 
(((|ConstantLODE| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |constDsolve| ((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)))) (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|)) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|)) (|LinearOrdinaryDifferentialOperatorCategory| |#2|)) (T |ConstantLODE|)) 
((|constDsolve| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|Symbol|)) (|ofCategory| *6 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|ofCategory| *4 (|Join| (|AlgebraicallyClosedFunctionSpace| *6) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (|isDomain| *2 (|Record| (|:| |particular| *4) (|:| |basis| (|List| *4)))) (|isDomain| *1 (|ConstantLODE| *6 *4 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |constDsolve| ((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)))) 
((|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) 26) (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) 27) (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) 16) (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) 17) (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) 22) (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) 24) (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) 36) (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) 34))) 
(((|ElementaryFunctionODESolver| |#1| |#2|) (CATEGORY |package| (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|))) (SIGNATURE |solve| ((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|))) (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|))) (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|))) (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|))) (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|))) (SIGNATURE |solve| ((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|))) (SIGNATURE |solve| ((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)))) (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|)) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (T |ElementaryFunctionODESolver|)) 
((|solve| (*1 *2 *2 *3 *4 *5) (|partial| AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *4 (|Equation| *2)) (|isDomain| *5 (|List| *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedFunctionSpace| *6) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (|ofCategory| *6 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *1 (|ElementaryFunctionODESolver| *6 *2)))) (|solve| (*1 *2 *3 *4 *3 *5) (|partial| AND (|isDomain| *3 (|Equation| *2)) (|isDomain| *4 (|BasicOperator|)) (|isDomain| *5 (|List| *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedFunctionSpace| *6) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (|isDomain| *1 (|ElementaryFunctionODESolver| *6 *2)) (|ofCategory| *6 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))))) (|solve| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|BasicOperator|)) (|isDomain| *5 (|Symbol|)) (|ofCategory| *6 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *2 (|Union| (|Record| (|:| |particular| *3) (|:| |basis| (|List| *3))) *3 "failed")) (|isDomain| *1 (|ElementaryFunctionODESolver| *6 *3)) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedFunctionSpace| *6) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))))) (|solve| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Equation| *7)) (|isDomain| *4 (|BasicOperator|)) (|isDomain| *5 (|Symbol|)) (|ofCategory| *7 (|Join| (|AlgebraicallyClosedFunctionSpace| *6) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (|ofCategory| *6 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *2 (|Union| (|Record| (|:| |particular| *7) (|:| |basis| (|List| *7))) *7 "failed")) (|isDomain| *1 (|ElementaryFunctionODESolver| *6 *7)))) (|solve| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *3 (|List| *7)) (|isDomain| *4 (|List| (|BasicOperator|))) (|isDomain| *5 (|Symbol|)) (|ofCategory| *7 (|Join| (|AlgebraicallyClosedFunctionSpace| *6) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (|ofCategory| *6 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *2 (|Record| (|:| |particular| (|Vector| *7)) (|:| |basis| (|List| (|Vector| *7))))) (|isDomain| *1 (|ElementaryFunctionODESolver| *6 *7)))) (|solve| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *3 (|List| (|Equation| *7))) (|isDomain| *4 (|List| (|BasicOperator|))) (|isDomain| *5 (|Symbol|)) (|ofCategory| *7 (|Join| (|AlgebraicallyClosedFunctionSpace| *6) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (|ofCategory| *6 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *2 (|Record| (|:| |particular| (|Vector| *7)) (|:| |basis| (|List| (|Vector| *7))))) (|isDomain| *1 (|ElementaryFunctionODESolver| *6 *7)))) (|solve| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Matrix| *6)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *6 (|Join| (|AlgebraicallyClosedFunctionSpace| *5) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (|ofCategory| *5 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|Vector| *6))) (|isDomain| *1 (|ElementaryFunctionODESolver| *5 *6)))) (|solve| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *3 (|Matrix| *7)) (|isDomain| *5 (|Symbol|)) (|ofCategory| *7 (|Join| (|AlgebraicallyClosedFunctionSpace| *6) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (|ofCategory| *6 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *2 (|Record| (|:| |particular| (|Vector| *7)) (|:| |basis| (|List| (|Vector| *7))))) (|isDomain| *1 (|ElementaryFunctionODESolver| *6 *7)) (|isDomain| *4 (|Vector| *7))))) 
(CATEGORY |package| (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|))) (SIGNATURE |solve| ((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|))) (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|))) (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|))) (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|))) (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|))) (SIGNATURE |solve| ((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|))) (SIGNATURE |solve| ((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)))) 
((|showTheIFTable| (($) 9)) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 26)) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) 23)) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) 20)) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) 18)) (|clearTheIFTable| (((|Void|)) 12))) 
(((|ODEIntensityFunctionsTable|) (CATEGORY |domain| (SIGNATURE |showTheIFTable| ($)) (SIGNATURE |clearTheIFTable| ((|Void|))) (SIGNATURE |keys| ((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $)) (SIGNATURE |iFTable| ($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))))) (SIGNATURE |insert!| ($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) (SIGNATURE |showIntensityFunctions| ((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))))) (T |ODEIntensityFunctionsTable|)) 
((|showIntensityFunctions| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|isDomain| *2 (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))) (|isDomain| *1 (|ODEIntensityFunctionsTable|)))) (|insert!| (*1 *1 *2) (AND (|isDomain| *2 (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) (|isDomain| *1 (|ODEIntensityFunctionsTable|)))) (|iFTable| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) (|isDomain| *1 (|ODEIntensityFunctionsTable|)))) (|keys| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (|isDomain| *1 (|ODEIntensityFunctionsTable|)))) (|clearTheIFTable| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ODEIntensityFunctionsTable|)))) (|showTheIFTable| (*1 *1) (|isDomain| *1 (|ODEIntensityFunctionsTable|)))) 
(CATEGORY |domain| (SIGNATURE |showTheIFTable| ($)) (SIGNATURE |clearTheIFTable| ((|Void|))) (SIGNATURE |keys| ((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $)) (SIGNATURE |iFTable| ($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))))) (SIGNATURE |insert!| ($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) (SIGNATURE |showIntensityFunctions| ((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) 
((|int| ((|#2| |#2| (|Symbol|)) 15)) (|expint| ((|#2| |#2| (|Symbol|)) 47)) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) 11))) 
(((|ODEIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |int| (|#2| |#2| (|Symbol|))) (SIGNATURE |expint| (|#2| |#2| (|Symbol|))) (SIGNATURE |diff| ((|Mapping| |#2| |#2|) (|Symbol|)))) (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|)) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (T |ODEIntegration|)) 
((|diff| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *2 (|Mapping| *5 *5)) (|isDomain| *1 (|ODEIntegration| *4 *5)) (|ofCategory| *5 (|Join| (|AlgebraicallyClosedFunctionSpace| *4) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))))) (|expint| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *1 (|ODEIntegration| *4 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedFunctionSpace| *4) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))))) (|int| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *1 (|ODEIntegration| *4 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedFunctionSpace| *4) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|)))))) 
(CATEGORY |package| (SIGNATURE |int| (|#2| |#2| (|Symbol|))) (SIGNATURE |expint| (|#2| |#2| (|Symbol|))) (SIGNATURE |diff| ((|Mapping| |#2| |#2|) (|Symbol|)))) 
((|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) 114) (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) 115) (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) 117) (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) 118) (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) 119) (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) 120) (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) 105) (((|Result|) (|NumericalODEProblem|)) 106)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) 71) (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) 73))) 
(((|AnnaOrdinaryDifferentialEquationPackage|) (CATEGORY |package| (SIGNATURE |solve| ((|Result|) (|NumericalODEProblem|))) (SIGNATURE |solve| ((|Result|) (|NumericalODEProblem|) (|RoutinesTable|))) (SIGNATURE |solve| ((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)))) (SIGNATURE |solve| ((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|))) (SIGNATURE |solve| ((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|))) (SIGNATURE |solve| ((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|))) (SIGNATURE |solve| ((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|))) (SIGNATURE |solve| ((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|))) (SIGNATURE |measure| ((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|))) (SIGNATURE |measure| ((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|))))) (T |AnnaOrdinaryDifferentialEquationPackage|)) 
((|measure| (*1 *2 *3 *4) (AND (|isDomain| *3 (|NumericalODEProblem|)) (|isDomain| *4 (|RoutinesTable|)) (|isDomain| *2 (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) (|isDomain| *1 (|AnnaOrdinaryDifferentialEquationPackage|)))) (|measure| (*1 *2 *3) (AND (|isDomain| *3 (|NumericalODEProblem|)) (|isDomain| *2 (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) (|isDomain| *1 (|AnnaOrdinaryDifferentialEquationPackage|)))) (|solve| (*1 *2 *3 *4 *4 *5 *6 *5 *4 *4) (AND (|isDomain| *3 (|Vector| (|Expression| *4))) (|isDomain| *5 (|List| (|Float|))) (|isDomain| *6 (|Expression| (|Float|))) (|isDomain| *4 (|Float|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaOrdinaryDifferentialEquationPackage|)))) (|solve| (*1 *2 *3 *4 *4 *5 *6 *5 *4) (AND (|isDomain| *3 (|Vector| (|Expression| *4))) (|isDomain| *5 (|List| (|Float|))) (|isDomain| *6 (|Expression| (|Float|))) (|isDomain| *4 (|Float|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaOrdinaryDifferentialEquationPackage|)))) (|solve| (*1 *2 *3 *4 *4 *5 *5 *4) (AND (|isDomain| *3 (|Vector| (|Expression| (|Float|)))) (|isDomain| *4 (|Float|)) (|isDomain| *5 (|List| *4)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaOrdinaryDifferentialEquationPackage|)))) (|solve| (*1 *2 *3 *4 *4 *5 *6 *4) (AND (|isDomain| *3 (|Vector| (|Expression| *4))) (|isDomain| *5 (|List| (|Float|))) (|isDomain| *6 (|Expression| (|Float|))) (|isDomain| *4 (|Float|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaOrdinaryDifferentialEquationPackage|)))) (|solve| (*1 *2 *3 *4 *4 *5 *4) (AND (|isDomain| *3 (|Vector| (|Expression| (|Float|)))) (|isDomain| *4 (|Float|)) (|isDomain| *5 (|List| *4)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaOrdinaryDifferentialEquationPackage|)))) (|solve| (*1 *2 *3 *4 *4 *5) (AND (|isDomain| *3 (|Vector| (|Expression| (|Float|)))) (|isDomain| *4 (|Float|)) (|isDomain| *5 (|List| *4)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaOrdinaryDifferentialEquationPackage|)))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|NumericalODEProblem|)) (|isDomain| *4 (|RoutinesTable|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaOrdinaryDifferentialEquationPackage|)))) (|solve| (*1 *2 *3) (AND (|isDomain| *3 (|NumericalODEProblem|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaOrdinaryDifferentialEquationPackage|))))) 
(CATEGORY |package| (SIGNATURE |solve| ((|Result|) (|NumericalODEProblem|))) (SIGNATURE |solve| ((|Result|) (|NumericalODEProblem|) (|RoutinesTable|))) (SIGNATURE |solve| ((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)))) (SIGNATURE |solve| ((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|))) (SIGNATURE |solve| ((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|))) (SIGNATURE |solve| ((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|))) (SIGNATURE |solve| ((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|))) (SIGNATURE |solve| ((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|))) (SIGNATURE |measure| ((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|))) (SIGNATURE |measure| ((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)))) 
((|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) 32))) 
(((|PureAlgebraicLODE| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |algDsolve| ((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|)))) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|)) (T |PureAlgebraicLODE|)) 
((|algDsolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| *4)) (|ofCategory| *4 (|FunctionFieldCategory| *5 *6 *7)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|isDomain| *2 (|Record| (|:| |particular| (|Union| *4 "failed")) (|:| |basis| (|List| *4)))) (|isDomain| *1 (|PureAlgebraicLODE| *5 *6 *7 *4))))) 
(CATEGORY |package| (SIGNATURE |algDsolve| ((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|))) 
((|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) 51)) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) 59) (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) 58) (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) 20) (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) 21)) (|indicialEquation| ((|#2| |#4| |#1|) 60) ((|#2| |#3| |#1|) 27)) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) 93) (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) 90))) 
(((|PrimitiveRatDE| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |denomLODE| ((|Union| |#2| "failed") |#3| (|Fraction| |#2|))) (SIGNATURE |denomLODE| (|#2| |#3| (|List| (|Fraction| |#2|)))) (SIGNATURE |indicialEquations| ((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|)) (SIGNATURE |indicialEquations| ((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|)) (SIGNATURE |indicialEquation| (|#2| |#3| |#1|)) (SIGNATURE |indicialEquations| ((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|)) (SIGNATURE |indicialEquations| ((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|)) (SIGNATURE |indicialEquation| (|#2| |#4| |#1|)) (SIGNATURE |splitDenominator| ((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|)))) (|UnivariatePolynomialCategory| |#1|) (|LinearOrdinaryDifferentialOperatorCategory| |#2|) (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| |#2|))) (T |PrimitiveRatDE|)) 
((|splitDenominator| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|Record| (|:| |eq| *7) (|:| |rh| (|List| (|Fraction| *6))))) (|isDomain| *1 (|PrimitiveRatDE| *5 *6 *7 *3)) (|isDomain| *4 (|List| (|Fraction| *6))) (|ofCategory| *7 (|LinearOrdinaryDifferentialOperatorCategory| *6)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *6))))) (|indicialEquation| (*1 *2 *3 *4) (AND (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|PrimitiveRatDE| *4 *2 *5 *3)) (|ofCategory| *4 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *5 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *2))))) (|indicialEquations| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *4 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|List| (|Record| (|:| |center| *4) (|:| |equation| *4)))) (|isDomain| *1 (|PrimitiveRatDE| *5 *4 *6 *3)) (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *4)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *4))))) (|indicialEquations| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|List| (|Record| (|:| |center| *5) (|:| |equation| *5)))) (|isDomain| *1 (|PrimitiveRatDE| *4 *5 *6 *3)) (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *5)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *5))))) (|indicialEquation| (*1 *2 *3 *4) (AND (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|PrimitiveRatDE| *4 *2 *3 *5)) (|ofCategory| *4 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *5 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *2))))) (|indicialEquations| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *4 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|List| (|Record| (|:| |center| *4) (|:| |equation| *4)))) (|isDomain| *1 (|PrimitiveRatDE| *5 *4 *3 *6)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4)) (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *4))))) (|indicialEquations| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|List| (|Record| (|:| |center| *5) (|:| |equation| *5)))) (|isDomain| *1 (|PrimitiveRatDE| *4 *5 *3 *6)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *5)) (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *5))))) (|denomLODE| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| (|Fraction| *2))) (|ofCategory| *2 (|UnivariatePolynomialCategory| *5)) (|isDomain| *1 (|PrimitiveRatDE| *5 *2 *3 *6)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *2))))) (|denomLODE| (*1 *2 *3 *4) (|partial| AND (|isDomain| *4 (|Fraction| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *5)) (|isDomain| *1 (|PrimitiveRatDE| *5 *2 *3 *6)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |denomLODE| ((|Union| |#2| "failed") |#3| (|Fraction| |#2|))) (SIGNATURE |denomLODE| (|#2| |#3| (|List| (|Fraction| |#2|)))) (SIGNATURE |indicialEquations| ((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|)) (SIGNATURE |indicialEquations| ((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|)) (SIGNATURE |indicialEquation| (|#2| |#3| |#1|)) (SIGNATURE |indicialEquations| ((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|)) (SIGNATURE |indicialEquations| ((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|)) (SIGNATURE |indicialEquation| (|#2| |#4| |#1|)) (SIGNATURE |splitDenominator| ((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))))) 
((~= (((|Boolean|) $ $) NIL)) (|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) 9)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 11) (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) 8)) (= (((|Boolean|) $ $) NIL))) 
(((|NumericalODEProblem|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE |retract| ((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $))))) (T |NumericalODEProblem|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|NumericalODEProblem|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|isDomain| *1 (|NumericalODEProblem|)))) (|retract| (*1 *2 *1) (AND (|isDomain| *2 (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|isDomain| *1 (|NumericalODEProblem|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE |retract| ((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $)))) 
((|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) 118)) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) 45)) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) 95)) (|denomRicDE| ((|#2| |#3|) 37)) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) 82)) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) 63) ((|#3| |#3| |#2|) 79))) 
(((|PrimitiveRatRicDE| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |denomRicDE| (|#2| |#3|)) (SIGNATURE |leadingCoefficientRicDE| ((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|)) (SIGNATURE |constantCoefficientRicDE| ((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|))) (SIGNATURE |polyRicDE| ((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|))) (SIGNATURE |singRicDE| ((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|))) (SIGNATURE |changeVar| (|#3| |#3| |#2|)) (SIGNATURE |changeVar| (|#3| |#3| (|Fraction| |#2|)))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|)))) (|UnivariatePolynomialCategory| |#1|) (|LinearOrdinaryDifferentialOperatorCategory| |#2|) (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| |#2|))) (T |PrimitiveRatRicDE|)) 
((|changeVar| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Fraction| *5)) (|ofCategory| *4 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|PrimitiveRatRicDE| *4 *5 *2 *6)) (|ofCategory| *2 (|LinearOrdinaryDifferentialOperatorCategory| *5)) (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *3)))) (|changeVar| (*1 *2 *2 *3) (AND (|ofCategory| *4 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|PrimitiveRatRicDE| *4 *3 *2 *5)) (|ofCategory| *2 (|LinearOrdinaryDifferentialOperatorCategory| *3)) (|ofCategory| *5 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *3))))) (|singRicDE| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|Mapping| (|List| *7) *7 (|SparseUnivariatePolynomial| *7))) (|isDomain| *5 (|Mapping| (|Factored| *7) *7)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|ofCategory| *6 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |frac| (|Fraction| *7)) (|:| |eq| *3)))) (|isDomain| *1 (|PrimitiveRatRicDE| *6 *7 *3 *8)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *7)) (|ofCategory| *8 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *7))))) (|polyRicDE| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| (|List| *5) *6)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|List| (|Record| (|:| |poly| *6) (|:| |eq| *3)))) (|isDomain| *1 (|PrimitiveRatRicDE| *5 *6 *3 *7)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *6)) (|ofCategory| *7 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *6))))) (|constantCoefficientRicDE| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| (|List| *5) *6)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|List| (|Record| (|:| |constant| *5) (|:| |eq| *3)))) (|isDomain| *1 (|PrimitiveRatRicDE| *5 *6 *3 *7)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *6)) (|ofCategory| *7 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *6))))) (|leadingCoefficientRicDE| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| *5)))) (|isDomain| *1 (|PrimitiveRatRicDE| *4 *5 *3 *6)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *5)) (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *5))))) (|denomRicDE| (*1 *2 *3) (AND (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|PrimitiveRatRicDE| *4 *2 *3 *5)) (|ofCategory| *4 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *5 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *2)))))) 
(CATEGORY |package| (SIGNATURE |denomRicDE| (|#2| |#3|)) (SIGNATURE |leadingCoefficientRicDE| ((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|)) (SIGNATURE |constantCoefficientRicDE| ((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|))) (SIGNATURE |polyRicDE| ((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|))) (SIGNATURE |singRicDE| ((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|))) (SIGNATURE |changeVar| (|#3| |#3| |#2|)) (SIGNATURE |changeVar| (|#3| |#3| (|Fraction| |#2|)))) 
((|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) 117) (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) 116) (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) 111) (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) 109)) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) 77) ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) 81))) 
(((|RationalLODE| |#1| |#2|) (CATEGORY |package| (SIGNATURE |ratDsolve| ((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|))) (SIGNATURE |ratDsolve| ((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|)))) (SIGNATURE |ratDsolve| ((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|))) (SIGNATURE |ratDsolve| ((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|)))) (SIGNATURE |indicialEquationAtInfinity| (|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)))) (SIGNATURE |indicialEquationAtInfinity| (|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|)))) (|UnivariatePolynomialCategory| |#1|)) (T |RationalLODE|)) 
((|indicialEquationAtInfinity| (*1 *2 *3) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *2 (|Fraction| *2))) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|RationalLODE| *4 *2)) (|ofCategory| *4 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))))) (|indicialEquationAtInfinity| (*1 *2 *3) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| (|Fraction| *2))) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|RationalLODE| *4 *2)) (|ofCategory| *4 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))))) (|ratDsolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *6 (|Fraction| *6))) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|isDomain| *2 (|Record| (|:| |basis| (|List| (|Fraction| *6))) (|:| |mat| (|Matrix| *5)))) (|isDomain| *1 (|RationalLODE| *5 *6)) (|isDomain| *4 (|List| (|Fraction| *6))))) (|ratDsolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *6 (|Fraction| *6))) (|isDomain| *4 (|Fraction| *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|isDomain| *2 (|Record| (|:| |particular| (|Union| *4 "failed")) (|:| |basis| (|List| *4)))) (|isDomain| *1 (|RationalLODE| *5 *6)))) (|ratDsolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| (|Fraction| *6))) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|isDomain| *2 (|Record| (|:| |basis| (|List| (|Fraction| *6))) (|:| |mat| (|Matrix| *5)))) (|isDomain| *1 (|RationalLODE| *5 *6)) (|isDomain| *4 (|List| (|Fraction| *6))))) (|ratDsolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| (|Fraction| *6))) (|isDomain| *4 (|Fraction| *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|isDomain| *2 (|Record| (|:| |particular| (|Union| *4 "failed")) (|:| |basis| (|List| *4)))) (|isDomain| *1 (|RationalLODE| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |ratDsolve| ((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|))) (SIGNATURE |ratDsolve| ((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|)))) (SIGNATURE |ratDsolve| ((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|))) (SIGNATURE |ratDsolve| ((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|)))) (SIGNATURE |indicialEquationAtInfinity| (|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)))) (SIGNATURE |indicialEquationAtInfinity| (|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) 
((|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) 47))) 
(((|ReduceLODE| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |reduceLODE| ((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|))) (|Field|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|UnivariatePolynomialCategory| |#1|) (|MonogenicAlgebra| |#1| |#3|) (|LinearOrdinaryDifferentialOperatorCategory| |#4|)) (T |ReduceLODE|)) 
((|reduceLODE| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Field|)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *4 (|MonogenicAlgebra| *5 *7)) (|isDomain| *2 (|Record| (|:| |mat| (|Matrix| *6)) (|:| |vec| (|Vector| *5)))) (|isDomain| *1 (|ReduceLODE| *5 *6 *7 *4 *3)) (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *5)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |reduceLODE| ((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|))) 
((|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) 43)) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) 133 (|has| |#1| (|AlgebraicallyClosedField|))) (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) 134 (|has| |#1| (|AlgebraicallyClosedField|))) (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) 135 (|has| |#1| (|AlgebraicallyClosedField|))) (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) 136 (|has| |#1| (|AlgebraicallyClosedField|))) (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) 36) (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) 37) (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) 34) (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) 35)) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) 80))) 
(((|RationalRicDE| |#1| |#2|) (CATEGORY |package| (SIGNATURE |ricDsolve| ((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|))) (SIGNATURE |ricDsolve| ((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|))) (SIGNATURE |ricDsolve| ((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|))) (SIGNATURE |ricDsolve| ((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|))) (SIGNATURE |singRicDE| ((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|))) (SIGNATURE |polyRicDE| ((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|))) (IF (|has| |#1| (|AlgebraicallyClosedField|)) (PROGN (SIGNATURE |ricDsolve| ((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)))) (SIGNATURE |ricDsolve| ((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|))) (SIGNATURE |ricDsolve| ((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)))) (SIGNATURE |ricDsolve| ((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)))) |noBranch|)) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|)))) (|UnivariatePolynomialCategory| |#1|)) (T |RationalRicDE|)) 
((|ricDsolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *6 (|Fraction| *6))) (|isDomain| *4 (|Mapping| (|Factored| *6) *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|AlgebraicallyClosedField|)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|isDomain| *2 (|List| (|Fraction| *6))) (|isDomain| *1 (|RationalRicDE| *5 *6)))) (|ricDsolve| (*1 *2 *3) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *5 (|Fraction| *5))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|AlgebraicallyClosedField|)) (|ofCategory| *4 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|isDomain| *2 (|List| (|Fraction| *5))) (|isDomain| *1 (|RationalRicDE| *4 *5)))) (|ricDsolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| (|Fraction| *6))) (|isDomain| *4 (|Mapping| (|Factored| *6) *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|AlgebraicallyClosedField|)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|isDomain| *2 (|List| (|Fraction| *6))) (|isDomain| *1 (|RationalRicDE| *5 *6)))) (|ricDsolve| (*1 *2 *3) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| (|Fraction| *5))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|AlgebraicallyClosedField|)) (|ofCategory| *4 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|isDomain| *2 (|List| (|Fraction| *5))) (|isDomain| *1 (|RationalRicDE| *4 *5)))) (|polyRicDE| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| (|List| *5) *6)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|List| (|Record| (|:| |poly| *6) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| *6 (|Fraction| *6)))))) (|isDomain| *1 (|RationalRicDE| *5 *6)) (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *6 (|Fraction| *6))))) (|singRicDE| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| (|Factored| *6) *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |frac| (|Fraction| *6)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| *6 (|Fraction| *6)))))) (|isDomain| *1 (|RationalRicDE| *5 *6)) (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *6 (|Fraction| *6))))) (|ricDsolve| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *7 (|Fraction| *7))) (|isDomain| *4 (|Mapping| (|List| *6) *7)) (|isDomain| *5 (|Mapping| (|Factored| *7) *7)) (|ofCategory| *6 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|isDomain| *2 (|List| (|Fraction| *7))) (|isDomain| *1 (|RationalRicDE| *6 *7)))) (|ricDsolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *6 (|Fraction| *6))) (|isDomain| *4 (|Mapping| (|List| *5) *6)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|List| (|Fraction| *6))) (|isDomain| *1 (|RationalRicDE| *5 *6)))) (|ricDsolve| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| (|Fraction| *7))) (|isDomain| *4 (|Mapping| (|List| *6) *7)) (|isDomain| *5 (|Mapping| (|Factored| *7) *7)) (|ofCategory| *6 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|isDomain| *2 (|List| (|Fraction| *7))) (|isDomain| *1 (|RationalRicDE| *6 *7)))) (|ricDsolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| (|Fraction| *6))) (|isDomain| *4 (|Mapping| (|List| *5) *6)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|List| (|Fraction| *6))) (|isDomain| *1 (|RationalRicDE| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |ricDsolve| ((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|))) (SIGNATURE |ricDsolve| ((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|))) (SIGNATURE |ricDsolve| ((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|))) (SIGNATURE |ricDsolve| ((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|))) (SIGNATURE |singRicDE| ((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|))) (SIGNATURE |polyRicDE| ((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|))) (IF (|has| |#1| (|AlgebraicallyClosedField|)) (PROGN (SIGNATURE |ricDsolve| ((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)))) (SIGNATURE |ricDsolve| ((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|))) (SIGNATURE |ricDsolve| ((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)))) (SIGNATURE |ricDsolve| ((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)))) |noBranch|)) 
((|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) 86) (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) 14)) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) 92)) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) 45))) 
(((|SystemODESolver| |#1| |#2|) (CATEGORY |package| (SIGNATURE |triangulate| ((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |triangulate| ((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|))) (SIGNATURE |solveInField| ((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)))) (|Field|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|)) (T |SystemODESolver|)) 
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(CATEGORY |package| (SIGNATURE |triangulate| ((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |triangulate| ((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|))) (SIGNATURE |solveInField| ((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)))) 
((|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) 13) (((|Matrix| |#1|) (|List| |#1|)) 14)) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) 34)) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) 42))) 
(((|ODETools| |#1| |#2|) (CATEGORY |package| (SIGNATURE |wronskianMatrix| ((|Matrix| |#1|) (|List| |#1|))) (SIGNATURE |wronskianMatrix| ((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|))) (SIGNATURE |variationOfParameters| ((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|))) (SIGNATURE |particularSolution| ((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)))) (|Field|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|)) (T |ODETools|)) 
((|particularSolution| (*1 *2 *3 *2 *4 *5) (|partial| AND (|isDomain| *4 (|List| *2)) (|isDomain| *5 (|Mapping| *2 *2)) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|ODETools| *2 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2)))) (|variationOfParameters| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *5 (|List| *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|Vector| *4)) (|isDomain| *1 (|ODETools| *4 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4)))) (|wronskianMatrix| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Matrix| *5)) (|isDomain| *1 (|ODETools| *5 *6)) (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *5)))) (|wronskianMatrix| (*1 *2 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|ODETools| *4 *5)) (|ofCategory| *5 (|LinearOrdinaryDifferentialOperatorCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |wronskianMatrix| ((|Matrix| |#1|) (|List| |#1|))) (SIGNATURE |wronskianMatrix| ((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|))) (SIGNATURE |variationOfParameters| ((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|))) (SIGNATURE |particularSolution| ((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)))) 
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(|Finite|)))) (|qsetelt!| ((|#2| $ (|Integer|) |#2|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#2| $ (|Integer|)) NIL)) (|positive?| (((|Boolean|) $) NIL (|has| |#2| (|OrderedRing|)))) (|parts| (((|List| |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|one?| (((|Boolean|) $) NIL (|has| |#2| (|Monoid|)))) (|negative?| (((|Boolean|) $) NIL (|has| |#2| (|OrderedRing|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL (OR (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedRing|))))) (|members| (((|List| |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|maxIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (OR (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedRing|))))) (|map!| (($ (|Mapping| |#2| |#2|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#2| |#2|) $) NIL)) (|lookup| (((|PositiveInteger|) $) NIL (|has| |#2| (|Finite|)))) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| |#2| (|SetCategory|)))) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|index| (($ (|PositiveInteger|)) NIL (|has| |#2| (|Finite|)))) (|hash| (((|SingleInteger|) $) NIL (|has| |#2| (|SetCategory|)))) (|first| ((|#2| $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|fill!| (($ $ |#2|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#2|))) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|Equation| |#2|)) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ |#2| |#2|) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|List| |#2|) (|List| |#2|)) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|enumerate| (((|List| $)) NIL (|has| |#2| (|Finite|)))) (|entry?| (((|Boolean|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|entries| (((|List| |#2|) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#2| $ (|Integer|) |#2|) NIL) ((|#2| $ (|Integer|)) NIL)) (|dot| ((|#2| $ $) NIL (|has| |#2| (|Ring|)))) (|directProduct| (($ (|Vector| |#2|)) NIL)) (|dimension| (((|CardinalNumber|)) NIL (|has| |#2| (|Field|)))) (|differentiate| (($ $) NIL (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) (($ $ (|NonNegativeInteger|)) NIL (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) (($ $ (|Symbol|)) NIL (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#2| 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(|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|)))) (($ |#2|) NIL (|has| |#2| (|SetCategory|)))) (|characteristic| (((|NonNegativeInteger|)) NIL (|has| |#2| (|Ring|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|abs| (($ $) NIL (|has| |#2| (|OrderedRing|)))) (^ (($ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|Monoid|))) (($ $ (|PositiveInteger|)) NIL (|has| |#2| (|Monoid|)))) (|Zero| (($) NIL (|has| |#2| (|CancellationAbelianMonoid|)) CONST)) (|One| (($) NIL (|has| |#2| (|Monoid|)) CONST)) (D (($ $) NIL (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) (($ $ (|NonNegativeInteger|)) NIL (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) (($ $ (|Symbol|)) NIL (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND 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(($ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|Monoid|))) (($ $ (|PositiveInteger|)) NIL (|has| |#2| (|Monoid|)))) (* (($ (|Integer|) $) NIL (|has| |#2| (|Ring|))) (($ $ $) NIL (|has| |#2| (|Monoid|))) (($ $ |#2|) NIL (|has| |#2| (|Monoid|))) (($ |#2| $) NIL (|has| |#2| (|Monoid|))) (($ (|NonNegativeInteger|) $) NIL (|has| |#2| (|CancellationAbelianMonoid|))) (($ (|PositiveInteger|) $) NIL (|has| |#2| (|AbelianSemiGroup|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|OrderedDirectProduct| |#1| |#2| |#3|) (|DirectProductCategory| |#1| |#2|) (|NonNegativeInteger|) (|OrderedAbelianMonoidSup|) (|Mapping| (|Boolean|) (|Vector| |#2|) (|Vector| |#2|))) (T |OrderedDirectProduct|)) 
NIL 
(|DirectProductCategory| |#1| |#2|) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|weights| (((|List| (|NonNegativeInteger|)) $) NIL) (((|List| (|NonNegativeInteger|)) $ (|Symbol|)) NIL)) (|weight| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|Symbol|)) NIL)) (|variables| (((|List| (|OrderlyDifferentialVariable| (|Symbol|))) $) NIL)) (|univariate| (((|SparseUnivariatePolynomial| $) $ (|OrderlyDifferentialVariable| (|Symbol|))) NIL) (((|SparseUnivariatePolynomial| |#1|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|totalDegree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|List| (|OrderlyDifferentialVariable| (|Symbol|)))) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL (|has| |#1| (|GcdDomain|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#1| (|GcdDomain|)))) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|separant| (($ $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|OrderlyDifferentialVariable| (|Symbol|)) "failed") $) NIL) (((|Union| (|Symbol|) "failed") $) NIL) (((|Union| (|SparseMultivariatePolynomial| |#1| (|Symbol|)) "failed") $) NIL)) (|retract| ((|#1| $) NIL) (((|Fraction| (|Integer|)) $) NIL (|has| 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(|primitiveMonomials| (((|List| $) $) NIL)) (|prime?| (((|Boolean|) $) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|pomopo!| (($ $ |#1| (|IndexedExponents| (|OrderlyDifferentialVariable| (|Symbol|))) $) NIL)) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (AND (|has| (|OrderlyDifferentialVariable| (|Symbol|)) (|PatternMatchable| (|Float|))) (|has| |#1| (|PatternMatchable| (|Float|))))) (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (AND (|has| (|OrderlyDifferentialVariable| (|Symbol|)) (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Integer|)))))) (|order| (((|NonNegativeInteger|) $ (|Symbol|)) NIL) (((|NonNegativeInteger|) $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|numberOfMonomials| (((|NonNegativeInteger|) $) NIL)) (|multivariate| (($ (|SparseUnivariatePolynomial| |#1|) (|OrderlyDifferentialVariable| (|Symbol|))) NIL) (($ 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(|IndexedExponents| (|OrderlyDifferentialVariable| (|Symbol|)))) $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) (|Symbol|)) NIL) (((|Mapping| $ (|NonNegativeInteger|)) $) NIL (|has| |#1| (|DifferentialRing|)))) (|mainVariable| (((|Union| (|OrderlyDifferentialVariable| (|Symbol|)) "failed") $) NIL)) (|leadingMonomial| (($ $) NIL)) (|leadingCoefficient| ((|#1| $) NIL)) (|leader| (((|OrderlyDifferentialVariable| (|Symbol|)) $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| |#1| (|GcdDomain|)))) (|lcm| (($ (|List| $)) NIL (|has| |#1| (|GcdDomain|))) (($ $ $) NIL (|has| |#1| (|GcdDomain|)))) (|latex| (((|String|) $) NIL)) (|isobaric?| (((|Boolean|) $) NIL)) (|isTimes| (((|Union| (|List| $) "failed") $) NIL)) (|isPlus| (((|Union| (|List| $) "failed") $) NIL)) (|isExpt| (((|Union| (|Record| (|:| |var| (|OrderlyDifferentialVariable| (|Symbol|))) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) NIL)) (|initial| (($ $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|ground?| (((|Boolean|) $) NIL)) (|ground| ((|#1| $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|GcdDomain|)))) (|gcd| (($ (|List| $)) NIL (|has| |#1| (|GcdDomain|))) (($ $ $) NIL (|has| |#1| (|GcdDomain|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|exquo| (((|Union| $ "failed") $ |#1|) NIL (|has| |#1| (|IntegralDomain|))) (((|Union| $ "failed") $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|eval| (($ $ (|List| (|Equation| $))) NIL) (($ $ (|Equation| $)) NIL) (($ $ $ $) NIL) (($ $ (|List| $) (|List| $)) NIL) (($ $ (|OrderlyDifferentialVariable| (|Symbol|)) |#1|) NIL) (($ $ (|List| (|OrderlyDifferentialVariable| (|Symbol|))) (|List| |#1|)) NIL) (($ $ (|OrderlyDifferentialVariable| (|Symbol|)) $) NIL) (($ $ (|List| (|OrderlyDifferentialVariable| (|Symbol|))) (|List| $)) NIL) (($ $ (|Symbol|) $) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|List| (|Symbol|)) (|List| $)) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|Symbol|) |#1|) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|List| (|Symbol|)) (|List| |#1|)) NIL (|has| |#1| (|DifferentialRing|)))) (|discriminant| (($ $ (|OrderlyDifferentialVariable| (|Symbol|))) NIL (|has| |#1| (|CommutativeRing|)))) (|differentiate| (($ $ (|OrderlyDifferentialVariable| (|Symbol|))) NIL) (($ $ (|List| (|OrderlyDifferentialVariable| (|Symbol|)))) NIL) (($ $ (|OrderlyDifferentialVariable| (|Symbol|)) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderlyDifferentialVariable| (|Symbol|))) (|List| (|NonNegativeInteger|))) NIL) (($ $) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#1| |#1|)) NIL)) (|differentialVariables| (((|List| (|Symbol|)) $) NIL)) (|degree| (((|IndexedExponents| (|OrderlyDifferentialVariable| (|Symbol|))) $) NIL) (((|NonNegativeInteger|) $ (|OrderlyDifferentialVariable| (|Symbol|))) NIL) (((|List| (|NonNegativeInteger|)) $ (|List| (|OrderlyDifferentialVariable| (|Symbol|)))) NIL) (((|NonNegativeInteger|) $ (|Symbol|)) NIL)) (|convert| (((|Pattern| (|Float|)) $) NIL (AND (|has| (|OrderlyDifferentialVariable| (|Symbol|)) (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))))) (((|Pattern| (|Integer|)) $) NIL (AND (|has| (|OrderlyDifferentialVariable| (|Symbol|)) (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))))) (((|InputForm|) $) NIL (AND (|has| (|OrderlyDifferentialVariable| (|Symbol|)) (|ConvertibleTo| (|InputForm|))) (|has| |#1| (|ConvertibleTo| (|InputForm|)))))) (|content| ((|#1| $) NIL (|has| |#1| (|GcdDomain|))) (($ $ (|OrderlyDifferentialVariable| (|Symbol|))) NIL (|has| |#1| (|GcdDomain|)))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ |#1|) NIL) (($ (|OrderlyDifferentialVariable| (|Symbol|))) NIL) (($ (|Symbol|)) NIL) (($ (|SparseMultivariatePolynomial| |#1| (|Symbol|))) NIL) (($ (|Fraction| (|Integer|))) NIL (OR (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))))) (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|coefficients| (((|List| |#1|) $) NIL)) (|coefficient| ((|#1| $ (|IndexedExponents| (|OrderlyDifferentialVariable| (|Symbol|)))) NIL) (($ $ (|OrderlyDifferentialVariable| (|Symbol|)) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderlyDifferentialVariable| (|Symbol|))) (|List| (|NonNegativeInteger|))) NIL)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|CommutativeRing|)))) (|associates?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($ $ (|OrderlyDifferentialVariable| (|Symbol|))) NIL) (($ $ (|List| (|OrderlyDifferentialVariable| (|Symbol|)))) NIL) (($ $ (|OrderlyDifferentialVariable| (|Symbol|)) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|OrderlyDifferentialVariable| (|Symbol|))) (|List| (|NonNegativeInteger|))) NIL) (($ $) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#1| |#1|)) NIL)) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (/ (($ $ |#1|) NIL (|has| |#1| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ |#1| $) NIL) (($ $ |#1|) NIL))) 
(((|OrderlyDifferentialPolynomial| |#1|) (|Join| (|DifferentialPolynomialCategory| |#1| (|Symbol|) (|OrderlyDifferentialVariable| (|Symbol|)) (|IndexedExponents| (|OrderlyDifferentialVariable| (|Symbol|)))) (|RetractableTo| (|SparseMultivariatePolynomial| |#1| (|Symbol|)))) (|Ring|)) (T |OrderlyDifferentialPolynomial|)) 
NIL 
(|Join| (|DifferentialPolynomialCategory| |#1| (|Symbol|) (|OrderlyDifferentialVariable| (|Symbol|)) (|IndexedExponents| (|OrderlyDifferentialVariable| (|Symbol|)))) (|RetractableTo| (|SparseMultivariatePolynomial| |#1| (|Symbol|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#2| (|Field|)))) (|unitCanonical| (($ $) NIL (|has| |#2| (|Field|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#2| (|Field|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL (|has| |#2| (|Field|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#2| (|Field|)))) (|sizeLess?| (((|Boolean|) $ $) NIL (|has| |#2| (|Field|)))) (|sample| (($) NIL T CONST)) (|rem| (($ $ $) NIL (|has| |#2| (|Field|)))) (|recip| (((|Union| $ "failed") $) NIL)) (|quo| (($ $ $) NIL (|has| |#2| (|Field|)))) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL (|has| |#2| (|Field|)))) (|prime?| (((|Boolean|) $) NIL (|has| |#2| (|Field|)))) (|one?| (((|Boolean|) $) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#2| (|Field|)))) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| |#2| (|Field|)))) (|lcm| (($ (|List| $)) NIL (|has| |#2| (|Field|))) (($ $ $) NIL (|has| |#2| (|Field|)))) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 20 (|has| |#2| (|Field|)))) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|Field|)))) (|gcd| (($ (|List| $)) NIL (|has| |#2| (|Field|))) (($ $ $) NIL (|has| |#2| (|Field|)))) (|factor| (((|Factored| $) $) NIL (|has| |#2| (|Field|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL (|has| |#2| (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#2| (|Field|)))) (|exquo| (((|Union| $ "failed") $ $) NIL (|has| |#2| (|Field|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#2| (|Field|)))) (|euclideanSize| (((|NonNegativeInteger|) $) NIL (|has| |#2| (|Field|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#2| (|Field|)))) (|differentiate| (($ $ (|NonNegativeInteger|)) NIL) (($ $) 13)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ |#2|) 10) ((|#2| $) 11) (($ (|Fraction| (|Integer|))) NIL (|has| |#2| (|Field|))) (($ $) NIL (|has| |#2| (|Field|)))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|associates?| (((|Boolean|) $ $) NIL (|has| |#2| (|Field|)))) (^ (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|PositiveInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| |#2| (|Field|)))) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (= (((|Boolean|) $ $) NIL)) (/ (($ $ $) 15 (|has| |#2| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|PositiveInteger|)) NIL) (($ $ (|Integer|)) 18 (|has| |#2| (|Field|)))) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ $) NIL) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#2| (|Field|))) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#2| (|Field|))))) 
(((|OrdinaryDifferentialRing| |#1| |#2| |#3|) (|Join| (|BiModule| $ $) (|DifferentialRing|) (CATEGORY |domain| (IF (|has| |#2| (|Field|)) (ATTRIBUTE (|Field|)) |noBranch|) (SIGNATURE |coerce| ($ |#2|)) (SIGNATURE |coerce| (|#2| $)))) (|SetCategory|) (|PartialDifferentialRing| |#1|) |#1|) (T |OrdinaryDifferentialRing|)) 
((|coerce| (*1 *1 *2) (AND (|ofCategory| *3 (|SetCategory|)) (|ofType| *4 *3) (|isDomain| *1 (|OrdinaryDifferentialRing| *3 *2 *4)) (|ofCategory| *2 (|PartialDifferentialRing| *3)))) (|coerce| (*1 *2 *1) (AND (|ofCategory| *2 (|PartialDifferentialRing| *3)) (|isDomain| *1 (|OrdinaryDifferentialRing| *3 *2 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofType| *4 *3)))) 
(|Join| (|BiModule| $ $) (|DifferentialRing|) (CATEGORY |domain| (IF (|has| |#2| (|Field|)) (ATTRIBUTE (|Field|)) |noBranch|) (SIGNATURE |coerce| ($ |#2|)) (SIGNATURE |coerce| (|#2| $)))) 
((~= (((|Boolean|) $ $) NIL)) (|weight| (((|NonNegativeInteger|) $) NIL)) (|variable| ((|#1| $) 10)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL)) (|retract| ((|#1| $) NIL)) (|order| (((|NonNegativeInteger|) $) 11)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|makeVariable| (($ |#1| (|NonNegativeInteger|)) 9)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|differentiate| (($ $) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ |#1|) NIL)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) NIL))) 
(((|OrderlyDifferentialVariable| |#1|) (|DifferentialVariableCategory| |#1|) (|OrderedSet|)) (T |OrderlyDifferentialVariable|)) 
NIL 
(|DifferentialVariableCategory| |#1|) 
((~= (((|Boolean|) $ $) NIL)) (|varList| (((|List| |#1|) $) 34)) (|size| (((|NonNegativeInteger|) $) NIL)) (|sample| (($) NIL T CONST)) (|rquo| (((|Union| $ "failed") $ $) 21) (((|Union| $ "failed") $ |#1|) 19)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL)) (|retract| ((|#1| $) NIL)) (|rest| (($ $) 36)) (|recip| (((|Union| $ "failed") $) NIL)) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|nthFactor| ((|#1| $ (|Integer|)) NIL)) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) NIL)) (|mirror| (($ $) 40)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|lquo| (((|Union| $ "failed") $ $) 20) (((|Union| $ "failed") $ |#1|) 16)) (|lexico| (((|Boolean|) $ $) 38)) (|length| (((|NonNegativeInteger|) $) 30)) (|latex| (((|String|) $) NIL)) (|hcrf| (($ $ $) NIL)) (|hclf| (($ $ $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|first| ((|#1| $) 35)) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) NIL)) (|divide| (((|Union| (|Record| (|:| |lm| (|Union| $ "failed")) (|:| |rm| (|Union| $ "failed"))) "failed") $ $) 24)) (|coerce| (((|OutputForm|) $) NIL) (($ |#1|) NIL)) (^ (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|PositiveInteger|)) NIL)) (|One| (($) 14 T CONST)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 39)) (** (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|PositiveInteger|)) NIL) (($ |#1| (|NonNegativeInteger|)) NIL)) (* (($ $ $) NIL) (($ |#1| $) NIL) (($ $ |#1|) NIL))) 
(((|OrderedFreeMonoid| |#1|) (|Join| (|OrderedMonoid|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE * ($ |#1| $)) (SIGNATURE * ($ $ |#1|)) (SIGNATURE ** ($ |#1| (|NonNegativeInteger|))) (SIGNATURE |first| (|#1| $)) (SIGNATURE |rest| ($ $)) (SIGNATURE |mirror| ($ $)) (SIGNATURE |lexico| ((|Boolean|) $ $)) (SIGNATURE |hclf| ($ $ $)) (SIGNATURE |hcrf| ($ $ $)) (SIGNATURE |lquo| ((|Union| $ "failed") $ $)) (SIGNATURE |rquo| ((|Union| $ "failed") $ $)) (SIGNATURE |lquo| ((|Union| $ "failed") $ |#1|)) (SIGNATURE |rquo| ((|Union| $ "failed") $ |#1|)) (SIGNATURE |divide| ((|Union| (|Record| (|:| |lm| (|Union| $ "failed")) (|:| |rm| (|Union| $ "failed"))) "failed") $ $)) (SIGNATURE |overlap| ((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $)) (SIGNATURE |size| ((|NonNegativeInteger|) $)) (SIGNATURE |nthExpon| ((|NonNegativeInteger|) $ (|Integer|))) (SIGNATURE |nthFactor| (|#1| $ (|Integer|))) (SIGNATURE |factors| ((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |varList| ((|List| |#1|) $)))) (|OrderedSet|)) (T |OrderedFreeMonoid|)) 
((* (*1 *1 *2 *1) (AND (|isDomain| *1 (|OrderedFreeMonoid| *2)) (|ofCategory| *2 (|OrderedSet|)))) (* (*1 *1 *1 *2) (AND (|isDomain| *1 (|OrderedFreeMonoid| *2)) (|ofCategory| *2 (|OrderedSet|)))) (** (*1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|OrderedFreeMonoid| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|first| (*1 *2 *1) (AND (|isDomain| *1 (|OrderedFreeMonoid| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|rest| (*1 *1 *1) (AND (|isDomain| *1 (|OrderedFreeMonoid| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|mirror| (*1 *1 *1) (AND (|isDomain| *1 (|OrderedFreeMonoid| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|lexico| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OrderedFreeMonoid| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|hclf| (*1 *1 *1 *1) (AND (|isDomain| *1 (|OrderedFreeMonoid| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|hcrf| (*1 *1 *1 *1) (AND (|isDomain| *1 (|OrderedFreeMonoid| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|lquo| (*1 *1 *1 *1) (|partial| AND (|isDomain| *1 (|OrderedFreeMonoid| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|rquo| (*1 *1 *1 *1) (|partial| AND (|isDomain| *1 (|OrderedFreeMonoid| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|lquo| (*1 *1 *1 *2) (|partial| AND (|isDomain| *1 (|OrderedFreeMonoid| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|rquo| (*1 *1 *1 *2) (|partial| AND (|isDomain| *1 (|OrderedFreeMonoid| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|divide| (*1 *2 *1 *1) (|partial| AND (|isDomain| *2 (|Record| (|:| |lm| (|Union| (|OrderedFreeMonoid| *3) "failed")) (|:| |rm| (|Union| (|OrderedFreeMonoid| *3) "failed")))) (|isDomain| *1 (|OrderedFreeMonoid| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|overlap| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |lm| (|OrderedFreeMonoid| *3)) (|:| |mm| (|OrderedFreeMonoid| *3)) (|:| |rm| (|OrderedFreeMonoid| *3)))) (|isDomain| *1 (|OrderedFreeMonoid| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|size| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|OrderedFreeMonoid| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|nthExpon| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|OrderedFreeMonoid| *4)) (|ofCategory| *4 (|OrderedSet|)))) (|nthFactor| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|OrderedFreeMonoid| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|factors| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| (|NonNegativeInteger|))))) (|isDomain| *1 (|OrderedFreeMonoid| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|length| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|OrderedFreeMonoid| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|varList| (*1 *2 *1) (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|OrderedFreeMonoid| *3)) (|ofCategory| *3 (|OrderedSet|))))) 
(|Join| (|OrderedMonoid|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE * ($ |#1| $)) (SIGNATURE * ($ $ |#1|)) (SIGNATURE ** ($ |#1| (|NonNegativeInteger|))) (SIGNATURE |first| (|#1| $)) (SIGNATURE |rest| ($ $)) (SIGNATURE |mirror| ($ $)) (SIGNATURE |lexico| ((|Boolean|) $ $)) (SIGNATURE |hclf| ($ $ $)) (SIGNATURE |hcrf| ($ $ $)) (SIGNATURE |lquo| ((|Union| $ "failed") $ $)) (SIGNATURE |rquo| ((|Union| $ "failed") $ $)) (SIGNATURE |lquo| ((|Union| $ "failed") $ |#1|)) (SIGNATURE |rquo| ((|Union| $ "failed") $ |#1|)) (SIGNATURE |divide| ((|Union| (|Record| (|:| |lm| (|Union| $ "failed")) (|:| |rm| (|Union| $ "failed"))) "failed") $ $)) (SIGNATURE |overlap| ((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $)) (SIGNATURE |size| ((|NonNegativeInteger|) $)) (SIGNATURE |nthExpon| ((|NonNegativeInteger|) $ (|Integer|))) (SIGNATURE |nthFactor| (|#1| $ (|Integer|))) (SIGNATURE |factors| ((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |varList| ((|List| |#1|) $)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sign| (((|Integer|) $) 52)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|positive?| (((|Boolean|) $) 50)) (|one?| (((|Boolean|) $) 30)) (|negative?| (((|Boolean|) $) 51)) (|min| (($ $ $) 49)) (|max| (($ $ $) 48)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (|abs| (($ $) 53)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (>= (((|Boolean|) $ $) 46)) (> (((|Boolean|) $ $) 45)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 47)) (< (((|Boolean|) $ $) 44)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|OrderedIntegralDomain|) (|Category|)) (T |OrderedIntegralDomain|)) 
NIL 
(|Join| (|IntegralDomain|) (|OrderedRing|)) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|IntegralDomain|) . T) ((|LeftModule| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|OMmakeConn| (($ (|SingleInteger|)) 7)) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) 15)) (|OMconnOutDevice| (((|OpenMathDevice|) $) 12)) (|OMconnInDevice| (((|OpenMathDevice|) $) 11)) (|OMcloseConn| (((|Void|) $) 9)) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) 16))) 
(((|OpenMathConnection|) (CATEGORY |domain| (SIGNATURE |OMmakeConn| ($ (|SingleInteger|))) (SIGNATURE |OMcloseConn| ((|Void|) $)) (SIGNATURE |OMconnInDevice| ((|OpenMathDevice|) $)) (SIGNATURE |OMconnOutDevice| ((|OpenMathDevice|) $)) (SIGNATURE |OMconnectTCP| ((|Boolean|) $ (|String|) (|SingleInteger|))) (SIGNATURE |OMbindTCP| ((|Boolean|) $ (|SingleInteger|))))) (T |OpenMathConnection|)) 
((|OMbindTCP| (*1 *2 *1 *3) (AND (|isDomain| *3 (|SingleInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OpenMathConnection|)))) (|OMconnectTCP| (*1 *2 *1 *3 *4) (AND (|isDomain| *3 (|String|)) (|isDomain| *4 (|SingleInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OpenMathConnection|)))) (|OMconnOutDevice| (*1 *2 *1) (AND (|isDomain| *2 (|OpenMathDevice|)) (|isDomain| *1 (|OpenMathConnection|)))) (|OMconnInDevice| (*1 *2 *1) (AND (|isDomain| *2 (|OpenMathDevice|)) (|isDomain| *1 (|OpenMathConnection|)))) (|OMcloseConn| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathConnection|)))) (|OMmakeConn| (*1 *1 *2) (AND (|isDomain| *2 (|SingleInteger|)) (|isDomain| *1 (|OpenMathConnection|))))) 
(CATEGORY |domain| (SIGNATURE |OMmakeConn| ($ (|SingleInteger|))) (SIGNATURE |OMcloseConn| ((|Void|) $)) (SIGNATURE |OMconnInDevice| ((|OpenMathDevice|) $)) (SIGNATURE |OMconnOutDevice| ((|OpenMathDevice|) $)) (SIGNATURE |OMconnectTCP| ((|Boolean|) $ (|String|) (|SingleInteger|))) (SIGNATURE |OMbindTCP| ((|Boolean|) $ (|SingleInteger|)))) 
((|OMsetEncoding| (((|Void|) $ (|OpenMathEncoding|)) 12)) (|OMputVariable| (((|Void|) $ (|Symbol|)) 32)) (|OMputSymbol| (((|Void|) $ (|String|) (|String|)) 34)) (|OMputString| (((|Void|) $ (|String|)) 33)) (|OMputObject| (((|Void|) $) 19)) (|OMputInteger| (((|Void|) $ (|Integer|)) 28)) (|OMputFloat| (((|Void|) $ (|DoubleFloat|)) 30)) (|OMputError| (((|Void|) $) 18)) (|OMputEndObject| (((|Void|) $) 26)) (|OMputEndError| (((|Void|) $) 25)) (|OMputEndBind| (((|Void|) $) 23)) (|OMputEndBVar| (((|Void|) $) 24)) (|OMputEndAttr| (((|Void|) $) 22)) (|OMputEndAtp| (((|Void|) $) 21)) (|OMputEndApp| (((|Void|) $) 20)) (|OMputBind| (((|Void|) $) 16)) (|OMputBVar| (((|Void|) $) 17)) (|OMputAttr| (((|Void|) $) 15)) (|OMputAtp| (((|Void|) $) 14)) (|OMputApp| (((|Void|) $) 13)) (|OMopenString| (($ (|String|) (|OpenMathEncoding|)) 9)) (|OMopenFile| (($ (|String|) (|String|) (|OpenMathEncoding|)) 8)) (|OMgetVariable| (((|Symbol|) $) 51)) (|OMgetType| (((|Symbol|) $) 55)) (|OMgetSymbol| (((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $) 54)) (|OMgetString| (((|String|) $) 52)) (|OMgetObject| (((|Void|) $) 41)) (|OMgetInteger| (((|Integer|) $) 49)) (|OMgetFloat| (((|DoubleFloat|) $) 50)) (|OMgetError| (((|Void|) $) 40)) (|OMgetEndObject| (((|Void|) $) 48)) (|OMgetEndError| (((|Void|) $) 47)) (|OMgetEndBind| (((|Void|) $) 45)) (|OMgetEndBVar| (((|Void|) $) 46)) (|OMgetEndAttr| (((|Void|) $) 44)) (|OMgetEndAtp| (((|Void|) $) 43)) (|OMgetEndApp| (((|Void|) $) 42)) (|OMgetBind| (((|Void|) $) 38)) (|OMgetBVar| (((|Void|) $) 39)) (|OMgetAttr| (((|Void|) $) 37)) (|OMgetAtp| (((|Void|) $) 36)) (|OMgetApp| (((|Void|) $) 35)) (|OMclose| (((|Void|) $) 11))) 
(((|OpenMathDevice|) (CATEGORY |domain| (SIGNATURE |OMopenFile| ($ (|String|) (|String|) (|OpenMathEncoding|))) (SIGNATURE |OMopenString| ($ (|String|) (|OpenMathEncoding|))) (SIGNATURE |OMclose| ((|Void|) $)) (SIGNATURE |OMsetEncoding| ((|Void|) $ (|OpenMathEncoding|))) (SIGNATURE |OMputApp| ((|Void|) $)) (SIGNATURE |OMputAtp| ((|Void|) $)) (SIGNATURE |OMputAttr| ((|Void|) $)) (SIGNATURE |OMputBind| ((|Void|) $)) (SIGNATURE |OMputBVar| ((|Void|) $)) (SIGNATURE |OMputError| ((|Void|) $)) (SIGNATURE |OMputObject| ((|Void|) $)) (SIGNATURE |OMputEndApp| ((|Void|) $)) (SIGNATURE |OMputEndAtp| ((|Void|) $)) (SIGNATURE |OMputEndAttr| ((|Void|) $)) (SIGNATURE |OMputEndBind| ((|Void|) $)) (SIGNATURE |OMputEndBVar| ((|Void|) $)) (SIGNATURE |OMputEndError| ((|Void|) $)) (SIGNATURE |OMputEndObject| ((|Void|) $)) (SIGNATURE |OMputInteger| ((|Void|) $ (|Integer|))) (SIGNATURE |OMputFloat| ((|Void|) $ (|DoubleFloat|))) (SIGNATURE |OMputVariable| ((|Void|) $ (|Symbol|))) (SIGNATURE |OMputString| ((|Void|) $ (|String|))) (SIGNATURE |OMputSymbol| ((|Void|) $ (|String|) (|String|))) (SIGNATURE |OMgetApp| ((|Void|) $)) (SIGNATURE |OMgetAtp| ((|Void|) $)) (SIGNATURE |OMgetAttr| ((|Void|) $)) (SIGNATURE |OMgetBind| ((|Void|) $)) (SIGNATURE |OMgetBVar| ((|Void|) $)) (SIGNATURE |OMgetError| ((|Void|) $)) (SIGNATURE |OMgetObject| ((|Void|) $)) (SIGNATURE |OMgetEndApp| ((|Void|) $)) (SIGNATURE |OMgetEndAtp| ((|Void|) $)) (SIGNATURE |OMgetEndAttr| ((|Void|) $)) (SIGNATURE |OMgetEndBind| ((|Void|) $)) (SIGNATURE |OMgetEndBVar| ((|Void|) $)) (SIGNATURE |OMgetEndError| ((|Void|) $)) (SIGNATURE |OMgetEndObject| ((|Void|) $)) (SIGNATURE |OMgetInteger| ((|Integer|) $)) (SIGNATURE |OMgetFloat| ((|DoubleFloat|) $)) (SIGNATURE |OMgetVariable| ((|Symbol|) $)) (SIGNATURE |OMgetString| ((|String|) $)) (SIGNATURE |OMgetSymbol| ((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $)) (SIGNATURE |OMgetType| ((|Symbol|) $)))) (T |OpenMathDevice|)) 
((|OMgetType| (*1 *2 *1) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetSymbol| (*1 *2 *1) (AND (|isDomain| *2 (|Record| (|:| |cd| (|String|)) (|:| |name| (|String|)))) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetString| (*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetVariable| (*1 *2 *1) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetFloat| (*1 *2 *1) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetInteger| (*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetEndObject| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetEndError| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetEndBVar| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetEndBind| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetEndAttr| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetEndAtp| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetEndApp| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetObject| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetError| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetBVar| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetBind| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetAttr| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetAtp| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMgetApp| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputSymbol| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputString| (*1 *2 *1 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputVariable| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputFloat| (*1 *2 *1 *3) (AND (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputInteger| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputEndObject| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputEndError| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputEndBVar| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputEndBind| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputEndAttr| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputEndAtp| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputEndApp| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputObject| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputError| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputBVar| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputBind| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputAttr| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputAtp| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMputApp| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMsetEncoding| (*1 *2 *1 *3) (AND (|isDomain| *3 (|OpenMathEncoding|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMclose| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMopenString| (*1 *1 *2 *3) (AND (|isDomain| *2 (|String|)) (|isDomain| *3 (|OpenMathEncoding|)) (|isDomain| *1 (|OpenMathDevice|)))) (|OMopenFile| (*1 *1 *2 *2 *3) (AND (|isDomain| *2 (|String|)) (|isDomain| *3 (|OpenMathEncoding|)) (|isDomain| *1 (|OpenMathDevice|))))) 
(CATEGORY |domain| (SIGNATURE |OMopenFile| ($ (|String|) (|String|) (|OpenMathEncoding|))) (SIGNATURE |OMopenString| ($ (|String|) (|OpenMathEncoding|))) (SIGNATURE |OMclose| ((|Void|) $)) (SIGNATURE |OMsetEncoding| ((|Void|) $ (|OpenMathEncoding|))) (SIGNATURE |OMputApp| ((|Void|) $)) (SIGNATURE |OMputAtp| ((|Void|) $)) (SIGNATURE |OMputAttr| ((|Void|) $)) (SIGNATURE |OMputBind| ((|Void|) $)) (SIGNATURE |OMputBVar| ((|Void|) $)) (SIGNATURE |OMputError| ((|Void|) $)) (SIGNATURE |OMputObject| ((|Void|) $)) (SIGNATURE |OMputEndApp| ((|Void|) $)) (SIGNATURE |OMputEndAtp| ((|Void|) $)) (SIGNATURE |OMputEndAttr| ((|Void|) $)) (SIGNATURE |OMputEndBind| ((|Void|) $)) (SIGNATURE |OMputEndBVar| ((|Void|) $)) (SIGNATURE |OMputEndError| ((|Void|) $)) (SIGNATURE |OMputEndObject| ((|Void|) $)) (SIGNATURE |OMputInteger| ((|Void|) $ (|Integer|))) (SIGNATURE |OMputFloat| ((|Void|) $ (|DoubleFloat|))) (SIGNATURE |OMputVariable| ((|Void|) $ (|Symbol|))) (SIGNATURE |OMputString| ((|Void|) $ (|String|))) (SIGNATURE |OMputSymbol| ((|Void|) $ (|String|) (|String|))) (SIGNATURE |OMgetApp| ((|Void|) $)) (SIGNATURE |OMgetAtp| ((|Void|) $)) (SIGNATURE |OMgetAttr| ((|Void|) $)) (SIGNATURE |OMgetBind| ((|Void|) $)) (SIGNATURE |OMgetBVar| ((|Void|) $)) (SIGNATURE |OMgetError| ((|Void|) $)) (SIGNATURE |OMgetObject| ((|Void|) $)) (SIGNATURE |OMgetEndApp| ((|Void|) $)) (SIGNATURE |OMgetEndAtp| ((|Void|) $)) (SIGNATURE |OMgetEndAttr| ((|Void|) $)) (SIGNATURE |OMgetEndBind| ((|Void|) $)) (SIGNATURE |OMgetEndBVar| ((|Void|) $)) (SIGNATURE |OMgetEndError| ((|Void|) $)) (SIGNATURE |OMgetEndObject| ((|Void|) $)) (SIGNATURE |OMgetInteger| ((|Integer|) $)) (SIGNATURE |OMgetFloat| ((|DoubleFloat|) $)) (SIGNATURE |OMgetVariable| ((|Symbol|) $)) (SIGNATURE |OMgetString| ((|String|) $)) (SIGNATURE |OMgetSymbol| ((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $)) (SIGNATURE |OMgetType| ((|Symbol|) $))) 
((~= (((|Boolean|) $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 12)) (|OMencodingXML| (($) 15)) (|OMencodingUnknown| (($) 13)) (|OMencodingSGML| (($) 16)) (|OMencodingBinary| (($) 14)) (= (((|Boolean|) $ $) 8))) 
(((|OpenMathEncoding|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |OMencodingUnknown| ($)) (SIGNATURE |OMencodingXML| ($)) (SIGNATURE |OMencodingSGML| ($)) (SIGNATURE |OMencodingBinary| ($))))) (T |OpenMathEncoding|)) 
((|OMencodingUnknown| (*1 *1) (|isDomain| *1 (|OpenMathEncoding|))) (|OMencodingXML| (*1 *1) (|isDomain| *1 (|OpenMathEncoding|))) (|OMencodingSGML| (*1 *1) (|isDomain| *1 (|OpenMathEncoding|))) (|OMencodingBinary| (*1 *1) (|isDomain| *1 (|OpenMathEncoding|)))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |OMencodingUnknown| ($)) (SIGNATURE |OMencodingXML| ($)) (SIGNATURE |OMencodingSGML| ($)) (SIGNATURE |OMencodingBinary| ($)))) 
((~= (((|Boolean|) $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 21) (($ (|Symbol|)) 17)) (|OMUnknownSymbol?| (((|Boolean|) $) 10)) (|OMUnknownCD?| (((|Boolean|) $) 9)) (|OMReadError?| (((|Boolean|) $) 11)) (|OMParseError?| (((|Boolean|) $) 8)) (= (((|Boolean|) $ $) 19))) 
(((|OpenMathErrorKind|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Symbol|))) (SIGNATURE |OMParseError?| ((|Boolean|) $)) (SIGNATURE |OMUnknownCD?| ((|Boolean|) $)) (SIGNATURE |OMUnknownSymbol?| ((|Boolean|) $)) (SIGNATURE |OMReadError?| ((|Boolean|) $))))) (T |OpenMathErrorKind|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|OpenMathErrorKind|)))) (|OMParseError?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OpenMathErrorKind|)))) (|OMUnknownCD?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OpenMathErrorKind|)))) (|OMUnknownSymbol?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OpenMathErrorKind|)))) (|OMReadError?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OpenMathErrorKind|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Symbol|))) (SIGNATURE |OMParseError?| ((|Boolean|) $)) (SIGNATURE |OMUnknownCD?| ((|Boolean|) $)) (SIGNATURE |OMUnknownSymbol?| ((|Boolean|) $)) (SIGNATURE |OMReadError?| ((|Boolean|) $)))) 
((~= (((|Boolean|) $ $) NIL)) (|omError| (($ (|OpenMathErrorKind|) (|List| (|Symbol|))) 24)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|errorKind| (((|OpenMathErrorKind|) $) 25)) (|errorInfo| (((|List| (|Symbol|)) $) 26)) (|coerce| (((|OutputForm|) $) 23)) (= (((|Boolean|) $ $) NIL))) 
(((|OpenMathError|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |errorKind| ((|OpenMathErrorKind|) $)) (SIGNATURE |errorInfo| ((|List| (|Symbol|)) $)) (SIGNATURE |omError| ($ (|OpenMathErrorKind|) (|List| (|Symbol|))))))) (T |OpenMathError|)) 
((|errorKind| (*1 *2 *1) (AND (|isDomain| *2 (|OpenMathErrorKind|)) (|isDomain| *1 (|OpenMathError|)))) (|errorInfo| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *1 (|OpenMathError|)))) (|omError| (*1 *1 *2 *3) (AND (|isDomain| *2 (|OpenMathErrorKind|)) (|isDomain| *3 (|List| (|Symbol|))) (|isDomain| *1 (|OpenMathError|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |errorKind| ((|OpenMathErrorKind|) $)) (SIGNATURE |errorInfo| ((|List| (|Symbol|)) $)) (SIGNATURE |omError| ($ (|OpenMathErrorKind|) (|List| (|Symbol|)))))) 
((|OMwrite| (((|Void|) (|OpenMathDevice|) (|Expression| |#1|) (|Boolean|)) 22) (((|Void|) (|OpenMathDevice|) (|Expression| |#1|)) 76) (((|String|) (|Expression| |#1|) (|Boolean|)) 75) (((|String|) (|Expression| |#1|)) 74))) 
(((|ExpressionToOpenMath| |#1|) (CATEGORY |package| (SIGNATURE |OMwrite| ((|String|) (|Expression| |#1|))) (SIGNATURE |OMwrite| ((|String|) (|Expression| |#1|) (|Boolean|))) (SIGNATURE |OMwrite| ((|Void|) (|OpenMathDevice|) (|Expression| |#1|))) (SIGNATURE |OMwrite| ((|Void|) (|OpenMathDevice|) (|Expression| |#1|) (|Boolean|)))) (|Join| (|OpenMath|) (|OrderedSet|) (|Ring|))) (T |ExpressionToOpenMath|)) 
((|OMwrite| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|OpenMathDevice|)) (|isDomain| *4 (|Expression| *6)) (|isDomain| *5 (|Boolean|)) (|ofCategory| *6 (|Join| (|OpenMath|) (|OrderedSet|) (|Ring|))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ExpressionToOpenMath| *6)))) (|OMwrite| (*1 *2 *3 *4) (AND (|isDomain| *3 (|OpenMathDevice|)) (|isDomain| *4 (|Expression| *5)) (|ofCategory| *5 (|Join| (|OpenMath|) (|OrderedSet|) (|Ring|))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ExpressionToOpenMath| *5)))) (|OMwrite| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Expression| *5)) (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|OpenMath|) (|OrderedSet|) (|Ring|))) (|isDomain| *2 (|String|)) (|isDomain| *1 (|ExpressionToOpenMath| *5)))) (|OMwrite| (*1 *2 *3) (AND (|isDomain| *3 (|Expression| *4)) (|ofCategory| *4 (|Join| (|OpenMath|) (|OrderedSet|) (|Ring|))) (|isDomain| *2 (|String|)) (|isDomain| *1 (|ExpressionToOpenMath| *4))))) 
(CATEGORY |package| (SIGNATURE |OMwrite| ((|String|) (|Expression| |#1|))) (SIGNATURE |OMwrite| ((|String|) (|Expression| |#1|) (|Boolean|))) (SIGNATURE |OMwrite| ((|Void|) (|OpenMathDevice|) (|Expression| |#1|))) (SIGNATURE |OMwrite| ((|Void|) (|OpenMathDevice|) (|Expression| |#1|) (|Boolean|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|reductum| (($ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|po| ((|#1| $) 10)) (|op| (($ |#1|) 9)) (|one?| (((|Boolean|) $) NIL)) (|monomial| (($ |#2| (|NonNegativeInteger|)) NIL)) (|minimumDegree| (((|NonNegativeInteger|) $) NIL)) (|leadingCoefficient| ((|#2| $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|differentiate| (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|DifferentialRing|))) (($ $) NIL (|has| |#1| (|DifferentialRing|)))) (|degree| (((|NonNegativeInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 17) (($ (|Integer|)) NIL) (($ |#2|) NIL (|has| |#2| (|CommutativeRing|)))) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|DifferentialRing|))) (($ $) NIL (|has| |#1| (|DifferentialRing|)))) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 12) (($ $ |#2|) NIL) (($ |#2| $) NIL))) 
(((|OppositeMonogenicLinearOperator| |#1| |#2|) (|Join| (|MonogenicLinearOperator| |#2|) (CATEGORY |domain| (IF (|has| |#1| (|DifferentialRing|)) (ATTRIBUTE (|DifferentialRing|)) |noBranch|) (SIGNATURE |op| ($ |#1|)) (SIGNATURE |po| (|#1| $)))) (|MonogenicLinearOperator| |#2|) (|Ring|)) (T |OppositeMonogenicLinearOperator|)) 
((|op| (*1 *1 *2) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|OppositeMonogenicLinearOperator| *2 *3)) (|ofCategory| *2 (|MonogenicLinearOperator| *3)))) (|po| (*1 *2 *1) (AND (|ofCategory| *2 (|MonogenicLinearOperator| *3)) (|isDomain| *1 (|OppositeMonogenicLinearOperator| *2 *3)) (|ofCategory| *3 (|Ring|))))) 
(|Join| (|MonogenicLinearOperator| |#2|) (CATEGORY |domain| (IF (|has| |#1| (|DifferentialRing|)) (ATTRIBUTE (|DifferentialRing|)) |noBranch|) (SIGNATURE |op| ($ |#1|)) (SIGNATURE |po| (|#1| $)))) 
((|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) 9) (((|Void|) (|OpenMathDevice|) $) 8) (((|String|) $ (|Boolean|)) 7) (((|String|) $) 6))) 
(((|OpenMath|) (|Category|)) (T |OpenMath|)) 
((|OMwrite| (*1 *2 *3 *1 *4) (AND (|ofCategory| *1 (|OpenMath|)) (|isDomain| *3 (|OpenMathDevice|)) (|isDomain| *4 (|Boolean|)) (|isDomain| *2 (|Void|)))) (|OMwrite| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|OpenMath|)) (|isDomain| *3 (|OpenMathDevice|)) (|isDomain| *2 (|Void|)))) (|OMwrite| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|OpenMath|)) (|isDomain| *3 (|Boolean|)) (|isDomain| *2 (|String|)))) (|OMwrite| (*1 *2 *1) (AND (|ofCategory| *1 (|OpenMath|)) (|isDomain| *2 (|String|))))) 
(|Join| (CATEGORY |domain| (SIGNATURE |OMwrite| ((|String|) $)) (SIGNATURE |OMwrite| ((|String|) $ (|Boolean|))) (SIGNATURE |OMwrite| ((|Void|) (|OpenMathDevice|) $)) (SIGNATURE |OMwrite| ((|Void|) (|OpenMathDevice|) $ (|Boolean|))))) 
((|OMunhandledSymbol| (((|Exit|) (|String|) (|String|)) 12)) (|OMsupportsSymbol?| (((|Boolean|) (|String|) (|String|)) 33)) (|OMsupportsCD?| (((|Boolean|) (|String|)) 32)) (|OMreadStr| (((|Any|) (|String|)) 25)) (|OMreadFile| (((|Any|) (|String|)) 23)) (|OMread| (((|Any|) (|OpenMathDevice|)) 17)) (|OMlistSymbols| (((|List| (|String|)) (|String|)) 28)) (|OMlistCDs| (((|List| (|String|))) 27))) 
(((|OpenMathPackage|) (CATEGORY |package| (SIGNATURE |OMread| ((|Any|) (|OpenMathDevice|))) (SIGNATURE |OMreadFile| ((|Any|) (|String|))) (SIGNATURE |OMreadStr| ((|Any|) (|String|))) (SIGNATURE |OMlistCDs| ((|List| (|String|)))) (SIGNATURE |OMlistSymbols| ((|List| (|String|)) (|String|))) (SIGNATURE |OMsupportsCD?| ((|Boolean|) (|String|))) (SIGNATURE |OMsupportsSymbol?| ((|Boolean|) (|String|) (|String|))) (SIGNATURE |OMunhandledSymbol| ((|Exit|) (|String|) (|String|))))) (T |OpenMathPackage|)) 
((|OMunhandledSymbol| (*1 *2 *3 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Exit|)) (|isDomain| *1 (|OpenMathPackage|)))) (|OMsupportsSymbol?| (*1 *2 *3 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OpenMathPackage|)))) (|OMsupportsCD?| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OpenMathPackage|)))) (|OMlistSymbols| (*1 *2 *3) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|OpenMathPackage|)) (|isDomain| *3 (|String|)))) (|OMlistCDs| (*1 *2) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|OpenMathPackage|)))) (|OMreadStr| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|OpenMathPackage|)))) (|OMreadFile| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|OpenMathPackage|)))) (|OMread| (*1 *2 *3) (AND (|isDomain| *3 (|OpenMathDevice|)) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|OpenMathPackage|))))) 
(CATEGORY |package| (SIGNATURE |OMread| ((|Any|) (|OpenMathDevice|))) (SIGNATURE |OMreadFile| ((|Any|) (|String|))) (SIGNATURE |OMreadStr| ((|Any|) (|String|))) (SIGNATURE |OMlistCDs| ((|List| (|String|)))) (SIGNATURE |OMlistSymbols| ((|List| (|String|)) (|String|))) (SIGNATURE |OMsupportsCD?| ((|Boolean|) (|String|))) (SIGNATURE |OMsupportsSymbol?| ((|Boolean|) (|String|) (|String|))) (SIGNATURE |OMunhandledSymbol| ((|Exit|) (|String|) (|String|)))) 
((~= (((|Boolean|) $ $) 18)) (|union| (($ |#1| $) 72) (($ $ |#1|) 71) (($ $ $) 70)) (|symmetricDifference| (($ $ $) 68)) (|subset?| (((|Boolean|) $ $) 69)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|set| (($ (|List| |#1|)) 64) (($) 63)) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) 42 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 52 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) 7 T CONST)) (|removeDuplicates!| (($ $) 58)) (|removeDuplicates| (($ $) 55 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove!| (($ |#1| $) 44 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) |#1|) $) 43 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remove| (($ |#1| $) 54 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#1|) $) 51 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 53 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 50 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 49 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|min| ((|#1| $) 74)) (|merge!| (($ $ $) 77)) (|merge| (($ $ $) 76)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|max| ((|#1| $) 75)) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22)) (|intersect| (($ $ $) 65)) (|inspect| ((|#1| $) 36)) (|insert!| (($ |#1| $) 37) (($ |#1| $ (|NonNegativeInteger|)) 59)) (|hash| (((|SingleInteger|) $) 21)) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) 48)) (|extract!| ((|#1| $) 38)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) 57)) (|difference| (($ $ |#1|) 67) (($ $ $) 66)) (|dictionary| (($) 46) (($ (|List| |#1|)) 45)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|convert| (((|InputForm|) $) 56 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 47)) (|coerce| (((|OutputForm|) $) 20)) (|brace| (($ (|List| |#1|)) 62) (($) 61)) (|bag| (($ (|List| |#1|)) 39)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19)) (< (((|Boolean|) $ $) 60)) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|OrderedMultisetAggregate| |#1|) (|Category|) (|OrderedSet|)) (T |OrderedMultisetAggregate|)) 
((|min| (*1 *2 *1) (AND (|ofCategory| *1 (|OrderedMultisetAggregate| *2)) (|ofCategory| *2 (|OrderedSet|))))) 
(|Join| (|MultisetAggregate| |t#1|) (|PriorityQueueAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |min| (|t#1| $)))) 
(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|MultiDictionary| |#1|) . T) ((|MultisetAggregate| |#1|) . T) ((|PriorityQueueAggregate| |#1|) . T) ((|SetAggregate| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) 47)) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) 44)) (|OMreceive| (((|Any|) (|OpenMathConnection|)) 16))) 
(((|OpenMathServerPackage|) (CATEGORY |package| (SIGNATURE |OMreceive| ((|Any|) (|OpenMathConnection|))) (SIGNATURE |OMsend| ((|Void|) (|OpenMathConnection|) (|Any|))) (SIGNATURE |OMserve| ((|Void|) (|SingleInteger|) (|SingleInteger|))))) (T |OpenMathServerPackage|)) 
((|OMserve| (*1 *2 *3 *3) (AND (|isDomain| *3 (|SingleInteger|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathServerPackage|)))) (|OMsend| (*1 *2 *3 *4) (AND (|isDomain| *3 (|OpenMathConnection|)) (|isDomain| *4 (|Any|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OpenMathServerPackage|)))) (|OMreceive| (*1 *2 *3) (AND (|isDomain| *3 (|OpenMathConnection|)) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|OpenMathServerPackage|))))) 
(CATEGORY |package| (SIGNATURE |OMreceive| ((|Any|) (|OpenMathConnection|))) (SIGNATURE |OMsend| ((|Void|) (|OpenMathConnection|) (|Any|))) (SIGNATURE |OMserve| ((|Void|) (|SingleInteger|) (|SingleInteger|)))) 
((|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) 12) (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) 13))) 
(((|OnePointCompletionFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|))) (SIGNATURE |map| ((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)))) (|SetCategory|) (|SetCategory|)) (T |OnePointCompletionFunctions2|)) 
((|map| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|OnePointCompletion| *6)) (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|OnePointCompletion| *5)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|isDomain| *1 (|OnePointCompletionFunctions2| *5 *6)))) (|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|OnePointCompletion| *5)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|isDomain| *2 (|OnePointCompletion| *6)) (|isDomain| *1 (|OnePointCompletionFunctions2| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |map| ((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|))) (SIGNATURE |map| ((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL (|has| |#1| (|AbelianGroup|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|AbelianGroup|)))) (|sign| (((|Integer|) $) NIL (|has| |#1| (|OrderedRing|)))) (|sample| (($) NIL (|has| |#1| (|AbelianGroup|)) CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) 15)) (|retract| (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) 9)) (|recip| (((|Union| $ "failed") $) 40 (|has| |#1| (|OrderedRing|)))) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 48 (|has| |#1| (|IntegerNumberSystem|)))) (|rational?| (((|Boolean|) $) 43 (|has| |#1| (|IntegerNumberSystem|)))) (|rational| (((|Fraction| (|Integer|)) $) 45 (|has| |#1| (|IntegerNumberSystem|)))) (|positive?| (((|Boolean|) $) NIL (|has| |#1| (|OrderedRing|)))) (|one?| (((|Boolean|) $) NIL (|has| |#1| (|OrderedRing|)))) (|negative?| (((|Boolean|) $) NIL (|has| |#1| (|OrderedRing|)))) (|min| (($ $ $) NIL (|has| |#1| (|OrderedRing|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedRing|)))) (|latex| (((|String|) $) NIL)) (|infinity| (($) 13)) (|infinite?| (((|Boolean|) $) 12)) (|hash| (((|SingleInteger|) $) NIL)) (|finite?| (((|Boolean|) $) 11)) (|coerce| (((|OutputForm|) $) 18) (($ (|Fraction| (|Integer|))) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (($ |#1|) 8) (($ (|Integer|)) NIL (OR (|has| |#1| (|OrderedRing|)) (|has| |#1| (|RetractableTo| (|Integer|)))))) (|characteristic| (((|NonNegativeInteger|)) 34 (|has| |#1| (|OrderedRing|)))) (|abs| (($ $) NIL (|has| |#1| (|OrderedRing|)))) (^ (($ $ (|PositiveInteger|)) NIL (|has| |#1| (|OrderedRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|OrderedRing|)))) (|Zero| (($) 22 (|has| |#1| (|AbelianGroup|)) CONST)) (|One| (($) 31 (|has| |#1| (|OrderedRing|)) CONST)) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedRing|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedRing|)))) (= (((|Boolean|) $ $) 20)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedRing|)))) (< (((|Boolean|) $ $) 42 (|has| |#1| (|OrderedRing|)))) (- (($ $ $) NIL (|has| |#1| (|AbelianGroup|))) (($ $) 27 (|has| |#1| (|AbelianGroup|)))) (+ (($ $ $) 29 (|has| |#1| (|AbelianGroup|)))) (** (($ $ (|PositiveInteger|)) NIL (|has| |#1| (|OrderedRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|OrderedRing|)))) (* (($ $ $) 37 (|has| |#1| (|OrderedRing|))) (($ (|Integer|) $) 25 (|has| |#1| (|AbelianGroup|))) (($ (|NonNegativeInteger|) $) NIL (|has| |#1| (|AbelianGroup|))) (($ (|PositiveInteger|) $) NIL (|has| |#1| (|AbelianGroup|))))) 
(((|OnePointCompletion| |#1|) (|Join| (|SetCategory|) (|FullyRetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |infinity| ($)) (SIGNATURE |finite?| ((|Boolean|) $)) (SIGNATURE |infinite?| ((|Boolean|) $)) (IF (|has| |#1| (|AbelianGroup|)) (ATTRIBUTE (|AbelianGroup|)) |noBranch|) (IF (|has| |#1| (|OrderedRing|)) (ATTRIBUTE (|OrderedRing|)) |noBranch|) (IF (|has| |#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") $))) |noBranch|))) (|SetCategory|)) (T |OnePointCompletion|)) 
((|infinity| (*1 *1) (AND (|isDomain| *1 (|OnePointCompletion| *2)) (|ofCategory| *2 (|SetCategory|)))) (|finite?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OnePointCompletion| *3)) (|ofCategory| *3 (|SetCategory|)))) (|infinite?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OnePointCompletion| *3)) (|ofCategory| *3 (|SetCategory|)))) (|rational?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OnePointCompletion| *3)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|ofCategory| *3 (|SetCategory|)))) (|rational| (*1 *2 *1) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|OnePointCompletion| *3)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|ofCategory| *3 (|SetCategory|)))) (|rationalIfCan| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|OnePointCompletion| *3)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|ofCategory| *3 (|SetCategory|))))) 
(|Join| (|SetCategory|) (|FullyRetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |infinity| ($)) (SIGNATURE |finite?| ((|Boolean|) $)) (SIGNATURE |infinite?| ((|Boolean|) $)) (IF (|has| |#1| (|AbelianGroup|)) (ATTRIBUTE (|AbelianGroup|)) |noBranch|) (IF (|has| |#1| (|OrderedRing|)) (ATTRIBUTE (|OrderedRing|)) |noBranch|) (IF (|has| |#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") $))) |noBranch|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL) (((|Union| (|BasicOperator|) "failed") $) NIL)) (|retract| ((|#1| $) NIL) (((|BasicOperator|) $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|opeval| ((|#1| (|BasicOperator|) |#1|) NIL)) (|one?| (((|Boolean|) $) NIL)) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|evaluateInverse| (($ $ (|Mapping| |#1| |#1|)) NIL)) (|evaluate| (($ $ (|Mapping| |#1| |#1|)) NIL)) (|elt| ((|#1| $ |#1|) NIL)) (|conjug| ((|#1| |#1|) NIL (|has| |#1| (|CommutativeRing|)))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ |#1|) NIL) (($ (|BasicOperator|)) NIL)) (|charthRoot| (((|Union| $ "failed") $) NIL (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|adjoint| (($ $) NIL (|has| |#1| (|CommutativeRing|))) (($ $ $) NIL (|has| |#1| (|CommutativeRing|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ (|BasicOperator|) (|Integer|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ |#1| $) NIL (|has| |#1| (|CommutativeRing|))) (($ $ |#1|) NIL (|has| |#1| (|CommutativeRing|))))) 
(((|Operator| |#1|) (|Join| (|Ring|) (|RetractableTo| |#1|) (|RetractableTo| (|BasicOperator|)) (|Eltable| |#1| |#1|) (CATEGORY |domain| (IF (|has| |#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |noBranch|) (IF (|has| |#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (PROGN (ATTRIBUTE (|Algebra| |#1|)) (SIGNATURE |adjoint| ($ $)) (SIGNATURE |adjoint| ($ $ $)) (SIGNATURE |conjug| (|#1| |#1|))) |noBranch|) (SIGNATURE |evaluate| ($ $ (|Mapping| |#1| |#1|))) (SIGNATURE |evaluateInverse| ($ $ (|Mapping| |#1| |#1|))) (SIGNATURE ** ($ (|BasicOperator|) (|Integer|))) (SIGNATURE ** ($ $ (|Integer|))) (SIGNATURE |opeval| (|#1| (|BasicOperator|) |#1|)) (SIGNATURE |makeop| ($ |#1| (|FreeGroup| (|BasicOperator|)))))) (|Ring|)) (T |Operator|)) 
((|adjoint| (*1 *1 *1) (AND (|isDomain| *1 (|Operator| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|Ring|)))) (|adjoint| (*1 *1 *1 *1) (AND (|isDomain| *1 (|Operator| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|Ring|)))) (|conjug| (*1 *2 *2) (AND (|isDomain| *1 (|Operator| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|Ring|)))) (|evaluate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|Operator| *3)))) (|evaluateInverse| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|Operator| *3)))) (** (*1 *1 *2 *3) (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|Operator| *4)) (|ofCategory| *4 (|Ring|)))) (** (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Operator| *3)) (|ofCategory| *3 (|Ring|)))) (|opeval| (*1 *2 *3 *2) (AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *1 (|Operator| *2)) (|ofCategory| *2 (|Ring|)))) (|makeop| (*1 *1 *2 *3) (AND (|isDomain| *3 (|FreeGroup| (|BasicOperator|))) (|isDomain| *1 (|Operator| *2)) (|ofCategory| *2 (|Ring|))))) 
(|Join| (|Ring|) (|RetractableTo| |#1|) (|RetractableTo| (|BasicOperator|)) (|Eltable| |#1| |#1|) (CATEGORY |domain| (IF (|has| |#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |noBranch|) (IF (|has| |#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (PROGN (ATTRIBUTE (|Algebra| |#1|)) (SIGNATURE |adjoint| ($ $)) (SIGNATURE |adjoint| ($ $ $)) (SIGNATURE |conjug| (|#1| |#1|))) |noBranch|) (SIGNATURE |evaluate| ($ $ (|Mapping| |#1| |#1|))) (SIGNATURE |evaluateInverse| ($ $ (|Mapping| |#1| |#1|))) (SIGNATURE ** ($ (|BasicOperator|) (|Integer|))) (SIGNATURE ** ($ $ (|Integer|))) (SIGNATURE |opeval| (|#1| (|BasicOperator|) |#1|)) (SIGNATURE |makeop| ($ |#1| (|FreeGroup| (|BasicOperator|)))))) 
((|getDatabase| (((|Database| (|IndexCard|)) (|String|)) 8))) 
(((|OperationsQuery|) (CATEGORY |package| (SIGNATURE |getDatabase| ((|Database| (|IndexCard|)) (|String|))))) (T |OperationsQuery|)) 
((|getDatabase| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Database| (|IndexCard|))) (|isDomain| *1 (|OperationsQuery|))))) 
(CATEGORY |package| (SIGNATURE |getDatabase| ((|Database| (|IndexCard|)) (|String|)))) 
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((|goodnessOfFit| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Expression| (|Float|)))) (|isDomain| *4 (|List| (|Float|))) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaNumericalOptimizationPackage|)))) (|optimize| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Expression| (|Float|)))) (|isDomain| *4 (|List| (|Float|))) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaNumericalOptimizationPackage|)))) (|optimize| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Expression| (|Float|))) (|isDomain| *4 (|List| (|Float|))) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaNumericalOptimizationPackage|)))) (|optimize| (*1 *2 *3 *4 *5 *5) (AND (|isDomain| *3 (|Expression| (|Float|))) (|isDomain| *4 (|List| (|Float|))) (|isDomain| *5 (|List| (|OrderedCompletion| (|Float|)))) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaNumericalOptimizationPackage|)))) (|optimize| (*1 *2 *3 *4 *5 *6 *5) (AND (|isDomain| *4 (|List| (|Float|))) (|isDomain| *5 (|List| (|OrderedCompletion| (|Float|)))) (|isDomain| *6 (|List| (|Expression| (|Float|)))) (|isDomain| *3 (|Expression| (|Float|))) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaNumericalOptimizationPackage|)))) (|goodnessOfFit| (*1 *2 *3) (AND (|isDomain| *3 (|NumericalOptimizationProblem|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaNumericalOptimizationPackage|)))) (|optimize| (*1 *2 *3) (AND (|isDomain| *3 (|NumericalOptimizationProblem|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaNumericalOptimizationPackage|)))) (|optimize| (*1 *2 *3 *4) (AND (|isDomain| *3 (|NumericalOptimizationProblem|)) (|isDomain| *4 (|RoutinesTable|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaNumericalOptimizationPackage|)))) (|measure| (*1 *2 *3 *4) (AND (|isDomain| *3 (|NumericalOptimizationProblem|)) (|isDomain| *4 (|RoutinesTable|)) (|isDomain| *2 (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) (|isDomain| *1 (|AnnaNumericalOptimizationPackage|)))) (|measure| (*1 *2 *3) (AND (|isDomain| *3 (|NumericalOptimizationProblem|)) (|isDomain| *2 (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) (|isDomain| *1 (|AnnaNumericalOptimizationPackage|))))) 
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(CATEGORY |package| (SIGNATURE |map| ((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|))) (SIGNATURE |map| ((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL (|has| |#1| (|AbelianGroup|)))) (|whatInfinity| (((|SingleInteger|) $) 24)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|AbelianGroup|)))) (|sign| (((|Integer|) $) NIL (|has| |#1| (|OrderedRing|)))) (|sample| (($) NIL (|has| |#1| (|AbelianGroup|)) CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) 16)) (|retract| (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) 9)) (|recip| (((|Union| $ "failed") $) 47 (|has| |#1| (|OrderedRing|)))) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 54 (|has| |#1| (|IntegerNumberSystem|)))) (|rational?| (((|Boolean|) $) 49 (|has| |#1| (|IntegerNumberSystem|)))) (|rational| (((|Fraction| (|Integer|)) $) 52 (|has| |#1| (|IntegerNumberSystem|)))) (|positive?| (((|Boolean|) $) NIL (|has| |#1| (|OrderedRing|)))) (|plusInfinity| (($) 13)) (|one?| (((|Boolean|) $) NIL (|has| |#1| (|OrderedRing|)))) (|negative?| (((|Boolean|) $) NIL (|has| |#1| (|OrderedRing|)))) (|minusInfinity| (($) 14)) (|min| (($ $ $) NIL (|has| |#1| (|OrderedRing|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedRing|)))) (|latex| (((|String|) $) NIL)) (|infinite?| (((|Boolean|) $) 12)) (|hash| (((|SingleInteger|) $) NIL)) (|finite?| (((|Boolean|) $) 11)) (|coerce| (((|OutputForm|) $) 22) (($ (|Fraction| (|Integer|))) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (($ |#1|) 8) (($ (|Integer|)) NIL (OR (|has| |#1| (|OrderedRing|)) (|has| |#1| (|RetractableTo| (|Integer|)))))) (|characteristic| (((|NonNegativeInteger|)) 41 (|has| |#1| (|OrderedRing|)))) (|abs| (($ $) NIL (|has| |#1| (|OrderedRing|)))) (^ (($ $ (|PositiveInteger|)) NIL (|has| |#1| (|OrderedRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|OrderedRing|)))) (|Zero| (($) 29 (|has| |#1| (|AbelianGroup|)) CONST)) (|One| (($) 38 (|has| |#1| (|OrderedRing|)) CONST)) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedRing|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedRing|)))) (= (((|Boolean|) $ $) 27)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedRing|)))) (< (((|Boolean|) $ $) 48 (|has| |#1| (|OrderedRing|)))) (- (($ $ $) NIL (|has| |#1| (|AbelianGroup|))) (($ $) 34 (|has| |#1| (|AbelianGroup|)))) (+ (($ $ $) 36 (|has| |#1| (|AbelianGroup|)))) (** (($ $ (|PositiveInteger|)) NIL (|has| |#1| (|OrderedRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|OrderedRing|)))) (* (($ $ $) 44 (|has| |#1| (|OrderedRing|))) (($ (|Integer|) $) 32 (|has| |#1| (|AbelianGroup|))) (($ (|NonNegativeInteger|) $) NIL (|has| |#1| (|AbelianGroup|))) (($ (|PositiveInteger|) $) NIL (|has| |#1| (|AbelianGroup|))))) 
(((|OrderedCompletion| |#1|) (|Join| (|SetCategory|) (|FullyRetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |plusInfinity| ($)) (SIGNATURE |minusInfinity| ($)) (SIGNATURE |finite?| ((|Boolean|) $)) (SIGNATURE |infinite?| ((|Boolean|) $)) (SIGNATURE |whatInfinity| ((|SingleInteger|) $)) (IF (|has| |#1| (|AbelianGroup|)) (ATTRIBUTE (|AbelianGroup|)) |noBranch|) (IF (|has| |#1| (|OrderedRing|)) (ATTRIBUTE (|OrderedRing|)) |noBranch|) (IF (|has| |#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") $))) |noBranch|))) (|SetCategory|)) (T |OrderedCompletion|)) 
((|plusInfinity| (*1 *1) (AND (|isDomain| *1 (|OrderedCompletion| *2)) (|ofCategory| *2 (|SetCategory|)))) (|minusInfinity| (*1 *1) (AND (|isDomain| *1 (|OrderedCompletion| *2)) (|ofCategory| *2 (|SetCategory|)))) (|finite?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OrderedCompletion| *3)) (|ofCategory| *3 (|SetCategory|)))) (|infinite?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OrderedCompletion| *3)) (|ofCategory| *3 (|SetCategory|)))) (|whatInfinity| (*1 *2 *1) (AND (|isDomain| *2 (|SingleInteger|)) (|isDomain| *1 (|OrderedCompletion| *3)) (|ofCategory| *3 (|SetCategory|)))) (|rational?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OrderedCompletion| *3)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|ofCategory| *3 (|SetCategory|)))) (|rational| (*1 *2 *1) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|OrderedCompletion| *3)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|ofCategory| *3 (|SetCategory|)))) (|rationalIfCan| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|OrderedCompletion| *3)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|ofCategory| *3 (|SetCategory|))))) 
(|Join| (|SetCategory|) (|FullyRetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |plusInfinity| ($)) (SIGNATURE |minusInfinity| ($)) (SIGNATURE |finite?| ((|Boolean|) $)) (SIGNATURE |infinite?| ((|Boolean|) $)) (SIGNATURE |whatInfinity| ((|SingleInteger|) $)) (IF (|has| |#1| (|AbelianGroup|)) (ATTRIBUTE (|AbelianGroup|)) |noBranch|) (IF (|has| |#1| (|OrderedRing|)) (ATTRIBUTE (|OrderedRing|)) |noBranch|) (IF (|has| |#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") $))) |noBranch|))) 
((~= (((|Boolean|) $ $) 7)) (|size| (((|NonNegativeInteger|)) 19)) (|random| (($) 22)) (|min| (($ $ $) 12)) (|max| (($ $ $) 13)) (|lookup| (((|PositiveInteger|) $) 21)) (|latex| (((|String|) $) 9)) (|index| (($ (|PositiveInteger|)) 20)) (|hash| (((|SingleInteger|) $) 10)) (|enumerate| (((|List| $)) 23)) (|coerce| (((|OutputForm|) $) 11)) (>= (((|Boolean|) $ $) 15)) (> (((|Boolean|) $ $) 16)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 14)) (< (((|Boolean|) $ $) 17))) 
(((|OrderedFinite|) (|Category|)) (T |OrderedFinite|)) 
NIL 
(|Join| (|OrderedSet|) (|Finite|)) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Finite|) . T) ((|OrderedSet|) . T) ((|SetCategory|) . T)) 
((|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) 17)) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) 18)) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) 14))) 
(((|OrderingFunctions| |#1| |#2|) (CATEGORY |package| (SIGNATURE |pureLex| ((|Boolean|) (|Vector| |#2|) (|Vector| |#2|))) (SIGNATURE |totalLex| ((|Boolean|) (|Vector| |#2|) (|Vector| |#2|))) (SIGNATURE |reverseLex| ((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)))) (|NonNegativeInteger|) (|OrderedAbelianMonoid|)) (T |OrderingFunctions|)) 
((|reverseLex| (*1 *2 *3 *3) (AND (|isDomain| *3 (|Vector| *5)) (|ofCategory| *5 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OrderingFunctions| *4 *5)) (|ofType| *4 (|NonNegativeInteger|)))) (|totalLex| (*1 *2 *3 *3) (AND (|isDomain| *3 (|Vector| *5)) (|ofCategory| *5 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OrderingFunctions| *4 *5)) (|ofType| *4 (|NonNegativeInteger|)))) (|pureLex| (*1 *2 *3 *3) (AND (|isDomain| *3 (|Vector| *5)) (|ofCategory| *5 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OrderingFunctions| *4 *5)) (|ofType| *4 (|NonNegativeInteger|))))) 
(CATEGORY |package| (SIGNATURE |pureLex| ((|Boolean|) (|Vector| |#2|) (|Vector| |#2|))) (SIGNATURE |totalLex| ((|Boolean|) (|Vector| |#2|) (|Vector| |#2|))) (SIGNATURE |reverseLex| ((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)))) 
((~= (((|Boolean|) $ $) 7)) (|sample| (($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 27)) (|one?| (((|Boolean|) $) 24)) (|min| (($ $ $) 12)) (|max| (($ $ $) 13)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (^ (($ $ (|NonNegativeInteger|)) 26) (($ $ (|PositiveInteger|)) 21)) (|One| (($) 22 T CONST)) (>= (((|Boolean|) $ $) 15)) (> (((|Boolean|) $ $) 16)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 14)) (< (((|Boolean|) $ $) 17)) (** (($ $ (|NonNegativeInteger|)) 25) (($ $ (|PositiveInteger|)) 20)) (* (($ $ $) 19))) 
(((|OrderedMonoid|) (|Category|)) (T |OrderedMonoid|)) 
NIL 
(|Join| (|OrderedSet|) (|Monoid|)) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Monoid|) . T) ((|OrderedSet|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|sign| (((|Integer|) $) 17)) (|positive?| (((|Boolean|) $) 10)) (|negative?| (((|Boolean|) $) 11)) (|abs| (($ $) 19))) 
(((|OrderedRing&| |#1|) (CATEGORY |domain| (SIGNATURE |abs| (|#1| |#1|)) (SIGNATURE |sign| ((|Integer|) |#1|)) (SIGNATURE |negative?| ((|Boolean|) |#1|)) (SIGNATURE |positive?| ((|Boolean|) |#1|))) (|OrderedRing|)) (T |OrderedRing&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |abs| (|#1| |#1|)) (SIGNATURE |sign| ((|Integer|) |#1|)) (SIGNATURE |negative?| ((|Boolean|) |#1|)) (SIGNATURE |positive?| ((|Boolean|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 23)) (|subtractIfCan| (((|Union| $ "failed") $ $) 25)) (|sign| (((|Integer|) $) 32)) (|sample| (($) 22 T CONST)) (|recip| (((|Union| $ "failed") $) 38)) (|positive?| (((|Boolean|) $) 34)) (|one?| (((|Boolean|) $) 41)) (|negative?| (((|Boolean|) $) 33)) (|min| (($ $ $) 12)) (|max| (($ $ $) 13)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 44)) (|characteristic| (((|NonNegativeInteger|)) 43)) (|abs| (($ $) 31)) (^ (($ $ (|NonNegativeInteger|)) 39) (($ $ (|PositiveInteger|)) 35)) (|Zero| (($) 21 T CONST)) (|One| (($) 42 T CONST)) (>= (((|Boolean|) $ $) 15)) (> (((|Boolean|) $ $) 16)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 14)) (< (((|Boolean|) $ $) 17)) (- (($ $ $) 27) (($ $) 26)) (+ (($ $ $) 19)) (** (($ $ (|NonNegativeInteger|)) 40) (($ $ (|PositiveInteger|)) 36)) (* (($ (|PositiveInteger|) $) 20) (($ (|NonNegativeInteger|) $) 24) (($ (|Integer|) $) 28) (($ $ $) 37))) 
(((|OrderedRing|) (|Category|)) (T |OrderedRing|)) 
((|positive?| (*1 *2 *1) (AND (|ofCategory| *1 (|OrderedRing|)) (|isDomain| *2 (|Boolean|)))) (|negative?| (*1 *2 *1) (AND (|ofCategory| *1 (|OrderedRing|)) (|isDomain| *2 (|Boolean|)))) (|sign| (*1 *2 *1) (AND (|ofCategory| *1 (|OrderedRing|)) (|isDomain| *2 (|Integer|)))) (|abs| (*1 *1 *1) (|ofCategory| *1 (|OrderedRing|)))) 
(|Join| (|OrderedAbelianGroup|) (|Ring|) (|Monoid|) (CATEGORY |domain| (SIGNATURE |positive?| ((|Boolean|) $)) (SIGNATURE |negative?| ((|Boolean|) $)) (SIGNATURE |sign| ((|Integer|) $)) (SIGNATURE |abs| ($ $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedSet|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|min| (($ $ $) 10)) (|max| (($ $ $) 9)) (>= (((|Boolean|) $ $) 12)) (> (((|Boolean|) $ $) 11)) (<= (((|Boolean|) $ $) 13))) 
(((|OrderedSet&| |#1|) (CATEGORY |domain| (SIGNATURE |min| (|#1| |#1| |#1|)) (SIGNATURE |max| (|#1| |#1| |#1|)) (SIGNATURE <= ((|Boolean|) |#1| |#1|)) (SIGNATURE >= ((|Boolean|) |#1| |#1|)) (SIGNATURE > ((|Boolean|) |#1| |#1|))) (|OrderedSet|)) (T |OrderedSet&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |min| (|#1| |#1| |#1|)) (SIGNATURE |max| (|#1| |#1| |#1|)) (SIGNATURE <= ((|Boolean|) |#1| |#1|)) (SIGNATURE >= ((|Boolean|) |#1| |#1|)) (SIGNATURE > ((|Boolean|) |#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|min| (($ $ $) 12)) (|max| (($ $ $) 13)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (>= (((|Boolean|) $ $) 15)) (> (((|Boolean|) $ $) 16)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 14)) (< (((|Boolean|) $ $) 17))) 
(((|OrderedSet|) (|Category|)) (T |OrderedSet|)) 
((< (*1 *2 *1 *1) (AND (|ofCategory| *1 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (> (*1 *2 *1 *1) (AND (|ofCategory| *1 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (>= (*1 *2 *1 *1) (AND (|ofCategory| *1 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (<= (*1 *2 *1 *1) (AND (|ofCategory| *1 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|max| (*1 *1 *1 *1) (|ofCategory| *1 (|OrderedSet|))) (|min| (*1 *1 *1 *1) (|ofCategory| *1 (|OrderedSet|)))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE < ((|Boolean|) $ $)) (SIGNATURE > ((|Boolean|) $ $)) (SIGNATURE >= ((|Boolean|) $ $)) (SIGNATURE <= ((|Boolean|) $ $)) (SIGNATURE |max| ($ $ $)) (SIGNATURE |min| ($ $ $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((|rightRemainder| (($ $ $) 45)) (|rightQuotient| (($ $ $) 44)) (|rightLcm| (($ $ $) 42)) (|rightGcd| (($ $ $) 51)) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 46)) (|rightExactQuotient| (((|Union| $ "failed") $ $) 49)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL) (((|Union| |#2| "failed") $) 25)) (|primitivePart| (($ $) 35)) (|leftRemainder| (($ $ $) 39)) (|leftQuotient| (($ $ $) 38)) (|leftLcm| (($ $ $) 47)) (|leftGcd| (($ $ $) 53)) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 41)) (|leftExactQuotient| (((|Union| $ "failed") $ $) 48)) (|exquo| (((|Union| $ "failed") $ |#2|) 28)) (|content| ((|#2| $) 32)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ |#2|) 12)) (|coefficients| (((|List| |#2|) $) 18)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ |#2|) NIL) (($ |#2| $) 22))) 
(((|UnivariateSkewPolynomialCategory&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |leftLcm| (|#1| |#1| |#1|)) (SIGNATURE |rightExtendedGcd| ((|Record| (|:| |coef1| |#1|) (|:| |coef2| |#1|) (|:| |generator| |#1|)) |#1| |#1|)) (SIGNATURE |rightGcd| (|#1| |#1| |#1|)) (SIGNATURE |rightExactQuotient| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE |rightRemainder| (|#1| |#1| |#1|)) (SIGNATURE |rightQuotient| (|#1| |#1| |#1|)) (SIGNATURE |rightLcm| (|#1| |#1| |#1|)) (SIGNATURE |leftExtendedGcd| ((|Record| (|:| |coef1| |#1|) (|:| |coef2| |#1|) (|:| |generator| |#1|)) |#1| |#1|)) (SIGNATURE |leftGcd| (|#1| |#1| |#1|)) (SIGNATURE |leftExactQuotient| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE |leftRemainder| (|#1| |#1| |#1|)) (SIGNATURE |leftQuotient| (|#1| |#1| |#1|)) (SIGNATURE |primitivePart| (|#1| |#1|)) (SIGNATURE |content| (|#2| |#1|)) (SIGNATURE |exquo| ((|Union| |#1| "failed") |#1| |#2|)) (SIGNATURE |coefficients| ((|List| |#2|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|UnivariateSkewPolynomialCategory| |#2|) (|Ring|)) (T |UnivariateSkewPolynomialCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |leftLcm| (|#1| |#1| |#1|)) (SIGNATURE |rightExtendedGcd| ((|Record| (|:| |coef1| |#1|) (|:| |coef2| |#1|) (|:| |generator| |#1|)) |#1| |#1|)) (SIGNATURE |rightGcd| (|#1| |#1| |#1|)) (SIGNATURE |rightExactQuotient| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE |rightRemainder| (|#1| |#1| |#1|)) (SIGNATURE |rightQuotient| (|#1| |#1| |#1|)) (SIGNATURE |rightLcm| (|#1| |#1| |#1|)) (SIGNATURE |leftExtendedGcd| ((|Record| (|:| |coef1| |#1|) (|:| |coef2| |#1|) (|:| |generator| |#1|)) |#1| |#1|)) (SIGNATURE |leftGcd| (|#1| |#1| |#1|)) (SIGNATURE |leftExactQuotient| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE |leftRemainder| (|#1| |#1| |#1|)) (SIGNATURE |leftQuotient| (|#1| |#1| |#1|)) (SIGNATURE |primitivePart| (|#1| |#1|)) (SIGNATURE |content| (|#2| |#1|)) (SIGNATURE |exquo| ((|Union| |#1| "failed") |#1| |#2|)) (SIGNATURE |coefficients| ((|List| |#2|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|rightRemainder| (($ $ $) 44 (|has| |#1| (|Field|)))) (|rightQuotient| (($ $ $) 45 (|has| |#1| (|Field|)))) (|rightLcm| (($ $ $) 47 (|has| |#1| (|Field|)))) (|rightGcd| (($ $ $) 42 (|has| |#1| (|Field|)))) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 41 (|has| |#1| (|Field|)))) (|rightExactQuotient| (((|Union| $ "failed") $ $) 43 (|has| |#1| (|Field|)))) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 46 (|has| |#1| (|Field|)))) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 73 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) 71 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) 68)) (|retract| (((|Integer|) $) 74 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) 72 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) 67)) (|reductum| (($ $) 63)) (|recip| (((|Union| $ "failed") $) 33)) (|primitivePart| (($ $) 54 (|has| |#1| (|GcdDomain|)))) (|one?| (((|Boolean|) $) 30)) (|monomial| (($ |#1| (|NonNegativeInteger|)) 61)) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 56 (|has| |#1| (|IntegralDomain|)))) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 57 (|has| |#1| (|IntegralDomain|)))) (|minimumDegree| (((|NonNegativeInteger|) $) 65)) (|leftRemainder| (($ $ $) 51 (|has| |#1| (|Field|)))) (|leftQuotient| (($ $ $) 52 (|has| |#1| (|Field|)))) (|leftLcm| (($ $ $) 40 (|has| |#1| (|Field|)))) (|leftGcd| (($ $ $) 49 (|has| |#1| (|Field|)))) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 48 (|has| |#1| (|Field|)))) (|leftExactQuotient| (((|Union| $ "failed") $ $) 50 (|has| |#1| (|Field|)))) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 53 (|has| |#1| (|Field|)))) (|leadingCoefficient| ((|#1| $) 64)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|exquo| (((|Union| $ "failed") $ |#1|) 58 (|has| |#1| (|IntegralDomain|)))) (|degree| (((|NonNegativeInteger|) $) 66)) (|content| ((|#1| $) 55 (|has| |#1| (|GcdDomain|)))) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ (|Fraction| (|Integer|))) 70 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (($ |#1|) 69)) (|coefficients| (((|List| |#1|) $) 60)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) 62)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|apply| ((|#1| $ |#1| |#1|) 59)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 76) (($ |#1| $) 75))) 
(((|UnivariateSkewPolynomialCategory| |#1|) (|Category|) (|Ring|)) (T |UnivariateSkewPolynomialCategory|)) 
((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|minimumDegree| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|reductum| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|coefficient| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|monomial| (*1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|coefficients| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|List| *3)))) (|apply| (*1 *2 *1 *2 *2) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|exquo| (*1 *1 *1 *2) (|partial| AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|IntegralDomain|)))) (|monicLeftDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|monicRightDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|content| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|GcdDomain|)))) (|primitivePart| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|GcdDomain|)))) (|leftDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|leftQuotient| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|leftRemainder| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|leftExactQuotient| (*1 *1 *1 *1) (|partial| AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|leftGcd| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|leftExtendedGcd| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |coef1| *1) (|:| |coef2| *1) (|:| |generator| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|rightLcm| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|rightDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|rightQuotient| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|rightRemainder| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|rightExactQuotient| (*1 *1 *1 *1) (|partial| AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|rightGcd| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|rightExtendedGcd| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |coef1| *1) (|:| |coef2| *1) (|:| |generator| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|leftLcm| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) 
(|Join| (|Ring|) (|BiModule| |t#1| |t#1|) (|FullyRetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |minimumDegree| ((|NonNegativeInteger|) $)) (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |coefficient| (|t#1| $ (|NonNegativeInteger|))) (SIGNATURE |monomial| ($ |t#1| (|NonNegativeInteger|))) (SIGNATURE |coefficients| ((|List| |t#1|) $)) (SIGNATURE |apply| (|t#1| $ |t#1| |t#1|)) (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |t#1|)) |noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |exquo| ((|Union| $ "failed") $ |t#1|)) (SIGNATURE |monicLeftDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |monicRightDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $))) |noBranch|) (IF (|has| |t#1| (|GcdDomain|)) (PROGN (SIGNATURE |content| (|t#1| $)) (SIGNATURE |primitivePart| ($ $))) |noBranch|) (IF (|has| |t#1| (|Field|)) (PROGN (SIGNATURE |leftDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |leftQuotient| ($ $ $)) (SIGNATURE |leftRemainder| ($ $ $)) (SIGNATURE |leftExactQuotient| ((|Union| $ "failed") $ $)) (SIGNATURE |leftGcd| ($ $ $)) (SIGNATURE |leftExtendedGcd| ((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $)) (SIGNATURE |rightLcm| ($ $ $)) (SIGNATURE |rightDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |rightQuotient| ($ $ $)) (SIGNATURE |rightRemainder| ($ $ $)) (SIGNATURE |rightExactQuotient| ((|Union| $ "failed") $ $)) (SIGNATURE |rightGcd| ($ $ $)) (SIGNATURE |rightExtendedGcd| ((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $)) (SIGNATURE |leftLcm| ($ $ $))) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|FullyRetractableTo| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) 20)) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) 43 (|has| |#1| (|Field|)))) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) 40 (|has| |#1| (|IntegralDomain|)))) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) 39 (|has| |#1| (|IntegralDomain|)))) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) 42 (|has| |#1| (|Field|)))) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) 31))) 
(((|UnivariateSkewPolynomialCategoryOps| |#1| |#2|) (CATEGORY |package| (SIGNATURE |times| (|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|))) (SIGNATURE |apply| (|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|))) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |monicLeftDivide| ((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|))) (SIGNATURE |monicRightDivide| ((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)))) |noBranch|) (IF (|has| |#1| (|Field|)) (PROGN (SIGNATURE |leftDivide| ((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|))) (SIGNATURE |rightDivide| ((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)))) |noBranch|)) (|Ring|) (|UnivariateSkewPolynomialCategory| |#1|)) (T |UnivariateSkewPolynomialCategoryOps|)) 
((|rightDivide| (*1 *2 *3 *3 *4) (AND (|isDomain| *4 (|Automorphism| *5)) (|ofCategory| *5 (|Field|)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *5 *3)) (|ofCategory| *3 (|UnivariateSkewPolynomialCategory| *5)))) (|leftDivide| (*1 *2 *3 *3 *4) (AND (|isDomain| *4 (|Automorphism| *5)) (|ofCategory| *5 (|Field|)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *5 *3)) (|ofCategory| *3 (|UnivariateSkewPolynomialCategory| *5)))) (|monicRightDivide| (*1 *2 *3 *3 *4) (AND (|isDomain| *4 (|Automorphism| *5)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *5 *3)) (|ofCategory| *3 (|UnivariateSkewPolynomialCategory| *5)))) (|monicLeftDivide| (*1 *2 *3 *3 *4) (AND (|isDomain| *4 (|Automorphism| *5)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *5 *3)) (|ofCategory| *3 (|UnivariateSkewPolynomialCategory| *5)))) (|apply| (*1 *2 *3 *2 *2 *4 *5) (AND (|isDomain| *4 (|Automorphism| *2)) (|isDomain| *5 (|Mapping| *2 *2)) (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *2 *3)) (|ofCategory| *3 (|UnivariateSkewPolynomialCategory| *2)))) (|times| (*1 *2 *2 *2 *3 *4) (AND (|isDomain| *3 (|Automorphism| *5)) (|isDomain| *4 (|Mapping| *5 *5)) (|ofCategory| *5 (|Ring|)) (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *5 *2)) (|ofCategory| *2 (|UnivariateSkewPolynomialCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |times| (|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|))) (SIGNATURE |apply| (|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|))) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |monicLeftDivide| ((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|))) (SIGNATURE |monicRightDivide| ((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)))) |noBranch|) (IF (|has| |#1| (|Field|)) (PROGN (SIGNATURE |leftDivide| ((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|))) (SIGNATURE |rightDivide| ((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)))) |noBranch|)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|rightRemainder| (($ $ $) NIL (|has| |#1| (|Field|)))) (|rightQuotient| (($ $ $) NIL (|has| |#1| (|Field|)))) (|rightLcm| (($ $ $) NIL (|has| |#1| (|Field|)))) (|rightGcd| (($ $ $) NIL (|has| |#1| (|Field|)))) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|rightExactQuotient| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|Field|)))) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 25 (|has| |#1| (|Field|)))) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) NIL)) (|retract| (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) NIL)) (|reductum| (($ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|primitivePart| (($ $) NIL (|has| |#1| (|GcdDomain|)))) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) NIL)) (|one?| (((|Boolean|) $) NIL)) (|monomial| (($ |#1| (|NonNegativeInteger|)) NIL)) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 21 (|has| |#1| (|IntegralDomain|)))) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 19 (|has| |#1| (|IntegralDomain|)))) (|minimumDegree| (((|NonNegativeInteger|) $) NIL)) (|leftRemainder| (($ $ $) NIL (|has| |#1| (|Field|)))) (|leftQuotient| (($ $ $) NIL (|has| |#1| (|Field|)))) (|leftLcm| (($ $ $) NIL (|has| |#1| (|Field|)))) (|leftGcd| (($ $ $) NIL (|has| |#1| (|Field|)))) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|leftExactQuotient| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|Field|)))) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 23 (|has| |#1| (|Field|)))) (|leadingCoefficient| ((|#1| $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|exquo| (((|Union| $ "failed") $ |#1|) NIL (|has| |#1| (|IntegralDomain|)))) (|degree| (((|NonNegativeInteger|) $) NIL)) (|content| ((|#1| $) NIL (|has| |#1| (|GcdDomain|)))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ (|Fraction| (|Integer|))) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (($ |#1|) NIL)) (|coefficients| (((|List| |#1|) $) NIL)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|apply| ((|#1| $ |#1| |#1|) 15)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 13) (($ $ |#1|) NIL) (($ |#1| $) NIL))) 
(((|SparseUnivariateSkewPolynomial| |#1| |#2| |#3|) (|Join| (|UnivariateSkewPolynomialCategory| |#1|) (CATEGORY |domain| (SIGNATURE |outputForm| ((|OutputForm|) $ (|OutputForm|))))) (|Ring|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) (T |SparseUnivariateSkewPolynomial|)) 
((|outputForm| (*1 *2 *1 *2) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|SparseUnivariateSkewPolynomial| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|Automorphism| *3)) (|ofType| *5 (|Mapping| *3 *3))))) 
(|Join| (|UnivariateSkewPolynomialCategory| |#1|) (CATEGORY |domain| (SIGNATURE |outputForm| ((|OutputForm|) $ (|OutputForm|))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|rightRemainder| (($ $ $) NIL (|has| |#2| (|Field|)))) (|rightQuotient| (($ $ $) NIL (|has| |#2| (|Field|)))) (|rightLcm| (($ $ $) NIL (|has| |#2| (|Field|)))) (|rightGcd| (($ $ $) NIL (|has| |#2| (|Field|)))) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#2| (|Field|)))) (|rightExactQuotient| (((|Union| $ "failed") $ $) NIL (|has| |#2| (|Field|)))) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#2| (|Field|)))) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (|has| |#2| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#2| "failed") $) NIL)) (|retract| (((|Integer|) $) NIL (|has| |#2| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) NIL (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#2| $) NIL)) (|reductum| (($ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|primitivePart| (($ $) NIL (|has| |#2| (|GcdDomain|)))) (|one?| (((|Boolean|) $) NIL)) (|monomial| (($ |#2| (|NonNegativeInteger|)) 16)) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#2| (|IntegralDomain|)))) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#2| (|IntegralDomain|)))) (|minimumDegree| (((|NonNegativeInteger|) $) NIL)) (|leftRemainder| (($ $ $) NIL (|has| |#2| (|Field|)))) (|leftQuotient| (($ $ $) NIL (|has| |#2| (|Field|)))) (|leftLcm| (($ $ $) NIL (|has| |#2| (|Field|)))) (|leftGcd| (($ $ $) NIL (|has| |#2| (|Field|)))) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#2| (|Field|)))) (|leftExactQuotient| (((|Union| $ "failed") $ $) NIL (|has| |#2| (|Field|)))) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#2| (|Field|)))) (|leadingCoefficient| ((|#2| $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|exquo| (((|Union| $ "failed") $ |#2|) NIL (|has| |#2| (|IntegralDomain|)))) (|degree| (((|NonNegativeInteger|) $) NIL)) (|content| ((|#2| $) NIL (|has| |#2| (|GcdDomain|)))) (|coerce| (((|OutputForm|) $) 23) (($ (|Integer|)) NIL) (($ (|Fraction| (|Integer|))) NIL (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|))))) (($ |#2|) NIL) (($ (|Variable| |#1|)) 18)) (|coefficients| (((|List| |#2|) $) NIL)) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|apply| ((|#2| $ |#2| |#2|) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) 13 T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ |#2|) NIL) (($ |#2| $) NIL))) 
(((|UnivariateSkewPolynomial| |#1| |#2| |#3| |#4|) (|Join| (|UnivariateSkewPolynomialCategory| |#2|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Variable| |#1|))))) (|Symbol|) (|Ring|) (|Automorphism| |#2|) (|Mapping| |#2| |#2|)) (T |UnivariateSkewPolynomial|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Variable| *3)) (|ofType| *3 (|Symbol|)) (|isDomain| *1 (|UnivariateSkewPolynomial| *3 *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofType| *5 (|Automorphism| *4)) (|ofType| *6 (|Mapping| *4 *4))))) 
(|Join| (|UnivariateSkewPolynomialCategory| |#2|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Variable| |#1|))))) 
((|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) 35 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) 27) ((|#1| (|NonNegativeInteger|) |#1|) 20)) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) 31)) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) 29)) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) 28))) 
(((|OrthogonalPolynomialFunctions| |#1|) (CATEGORY |package| (SIGNATURE |chebyshevT| (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE |chebyshevU| (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE |hermiteH| (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE |laguerreL| (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE |laguerreL| (|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |legendreP| (|#1| (|NonNegativeInteger|) |#1|)) |noBranch|)) (|CommutativeRing|)) (T |OrthogonalPolynomialFunctions|)) 
((|legendreP| (*1 *2 *3 *2) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|OrthogonalPolynomialFunctions| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|CommutativeRing|)))) (|laguerreL| (*1 *2 *3 *3 *2) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|OrthogonalPolynomialFunctions| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|laguerreL| (*1 *2 *3 *2) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|OrthogonalPolynomialFunctions| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|hermiteH| (*1 *2 *3 *2) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|OrthogonalPolynomialFunctions| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|chebyshevU| (*1 *2 *3 *2) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|OrthogonalPolynomialFunctions| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|chebyshevT| (*1 *2 *3 *2) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|OrthogonalPolynomialFunctions| *2)) (|ofCategory| *2 (|CommutativeRing|))))) 
(CATEGORY |package| (SIGNATURE |chebyshevT| (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE |chebyshevU| (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE |hermiteH| (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE |laguerreL| (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE |laguerreL| (|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |legendreP| (|#1| (|NonNegativeInteger|) |#1|)) |noBranch|)) 
((~= (((|Boolean|) $ $) NIL)) (|value| (((|Integer|) $) 12)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 18) (($ (|Integer|)) 11)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 8)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 9))) 
(((|OrdSetInts|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Integer|))) (SIGNATURE |value| ((|Integer|) $))))) (T |OrdSetInts|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OrdSetInts|)))) (|value| (*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OrdSetInts|))))) 
(|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Integer|))) (SIGNATURE |value| ((|Integer|) $)))) 
((~= (((|Boolean|) $ $) NIL)) (|zag| (($ $ $) 115)) (|width| (((|Integer|) $) 30) (((|Integer|)) 35)) (|vspace| (($ (|Integer|)) 44)) (|vconcat| (($ $ $) 45) (($ (|List| $)) 76)) (|supersub| (($ $ (|List| $)) 74)) (|superHeight| (((|Integer|) $) 33)) (|super| (($ $ $) 63)) (|sum| (($ $) 128) (($ $ $) 129) (($ $ $ $) 130)) (|subHeight| (((|Integer|) $) 32)) (|sub| (($ $ $) 62)) (|string| (($ $) 105)) (|slash| (($ $ $) 119)) (|semicolonSeparate| (($ (|List| $)) 52)) (|scripts| (($ $ (|List| $)) 69)) (|rspace| (($ (|Integer|) (|Integer|)) 46)) (|root| (($ $) 116) (($ $ $) 117)) (|right| (($ $ (|Integer|)) 40) (($ $) 43)) (|rem| (($ $ $) 89)) (|rarrow| (($ $ $) 122)) (|quote| (($ $) 106)) (|quo| (($ $ $) 90)) (|prod| (($ $) 131) (($ $ $) 132) (($ $ $ $) 133)) (|print| (((|Void|) $) 8)) (|prime| (($ $) 109) (($ $ (|NonNegativeInteger|)) 112)) (|presuper| (($ $ $) 65)) (|presub| (($ $ $) 64)) (|prefix| (($ $ (|List| $)) 100)) (|postfix| (($ $ $) 104)) (|pile| (($ (|List| $)) 50)) (|paren| (($ $) 60) (($ (|List| $)) 61)) (|overlabel| (($ $ $) 113)) (|overbar| (($ $) 107)) (|over| (($ $ $) 118)) (|outputForm| (($ (|Integer|)) 20) (($ (|Symbol|)) 22) (($ (|String|)) 29) (($ (|DoubleFloat|)) 24)) (|or| (($ $ $) 93)) (|not| (($ $) 94)) (|messagePrint| (((|Void|) (|String|)) 14)) (|message| (($ (|String|)) 13)) (|matrix| (($ (|List| (|List| $))) 48)) (|left| (($ $ (|Integer|)) 39) (($ $) 42)) (|latex| (((|String|) $) NIL)) (|label| (($ $ $) 121)) (|int| (($ $) 134) (($ $ $) 135) (($ $ $ $) 136)) (|infix?| (((|Boolean|) $) 98)) (|infix| (($ $ (|List| $)) 102) (($ $ $ $) 103)) (|hspace| (($ (|Integer|)) 36)) (|height| (((|Integer|) $) 31) (((|Integer|)) 34)) (|hconcat| (($ $ $) 37) (($ (|List| $)) 75)) (|hash| (((|SingleInteger|) $) NIL)) (|exquo| (($ $ $) 91)) (|empty| (($) 12)) (|elt| (($ $ (|List| $)) 99)) (|dot| (($ $) 108) (($ $ (|NonNegativeInteger|)) 111)) (|div| (($ $ $) 88)) (|differentiate| (($ $ (|NonNegativeInteger|)) 127)) (|commaSeparate| (($ (|List| $)) 51)) (|coerce| (((|OutputForm|) $) 18)) (|center| (($ $ (|Integer|)) 38) (($ $) 41)) (|bracket| (($ $) 58) (($ (|List| $)) 59)) (|brace| (($ $) 56) (($ (|List| $)) 57)) (|box| (($ $) 114)) (|blankSeparate| (($ (|List| $)) 55)) (|binomial| (($ $ $) 97)) (|assign| (($ $ $) 120)) (|and| (($ $ $) 92)) (^= (($ $ $) 77)) (SEGMENT (($ $ $) 95) (($ $) 96)) (>= (($ $ $) 81)) (> (($ $ $) 79)) (= (((|Boolean|) $ $) 15) (($ $ $) 16)) (<= (($ $ $) 80)) (< (($ $ $) 78)) (/ (($ $ $) 86)) (- (($ $ $) 83) (($ $) 84)) (+ (($ $ $) 82)) (** (($ $ $) 87)) (* (($ $ $) 85))) 
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((|outputList| (((|Void|) (|List| (|Any|))) 24)) (|output| (((|Void|) (|String|) (|OutputForm|)) 14) (((|Void|) (|OutputForm|)) 9) (((|Void|) (|String|)) 11))) 
(((|OutputPackage|) (CATEGORY |package| (SIGNATURE |output| ((|Void|) (|String|))) (SIGNATURE |output| ((|Void|) (|OutputForm|))) (SIGNATURE |output| ((|Void|) (|String|) (|OutputForm|))) (SIGNATURE |outputList| ((|Void|) (|List| (|Any|)))))) (T |OutputPackage|)) 
((|outputList| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Any|))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OutputPackage|)))) (|output| (*1 *2 *3 *4) (AND (|isDomain| *3 (|String|)) (|isDomain| *4 (|OutputForm|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OutputPackage|)))) (|output| (*1 *2 *3) (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OutputPackage|)))) (|output| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OutputPackage|))))) 
(CATEGORY |package| (SIGNATURE |output| ((|Void|) (|String|))) (SIGNATURE |output| ((|Void|) (|OutputForm|))) (SIGNATURE |output| ((|Void|) (|String|) (|OutputForm|))) (SIGNATURE |outputList| ((|Void|) (|List| (|Any|))))) 
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((|variable| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|OrderedVariableList| *3)) (|ofType| *3 (|List| *2))))) 
(|Join| (|OrderedFinite|) (|ConvertibleTo| (|Symbol|)) (|ConvertibleTo| (|InputForm|)) (|ConvertibleTo| (|Pattern| (|Float|))) (|ConvertibleTo| (|Pattern| (|Integer|))) (CATEGORY |domain| (SIGNATURE |variable| ((|Union| $ "failed") (|Symbol|))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (((|Polynomial| |#1|) $) NIL) (($ (|Polynomial| |#1|)) NIL) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (= (((|Boolean|) $ $) NIL)) (/ (((|Union| $ "failed") $ $) NIL (|has| |#1| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ |#1| $) NIL (|has| |#1| (|CommutativeRing|))) (($ $ |#1|) NIL (|has| |#1| (|CommutativeRing|))))) 
(((|OrdinaryWeightedPolynomials| |#1| |#2| |#3| |#4|) (|Join| (|Ring|) (CATEGORY |domain| (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |#1|)) |noBranch|) (SIGNATURE |coerce| ((|Polynomial| |#1|) $)) (SIGNATURE |coerce| ($ (|Polynomial| |#1|))) (IF (|has| |#1| (|Field|)) (SIGNATURE / ((|Union| $ "failed") $ $)) |noBranch|) (SIGNATURE |changeWeightLevel| ((|Void|) (|NonNegativeInteger|))))) (|Ring|) (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) (T |OrdinaryWeightedPolynomials|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Polynomial| *3)) (|isDomain| *1 (|OrdinaryWeightedPolynomials| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|List| (|Symbol|))) (|ofType| *5 (|List| (|NonNegativeInteger|))) (|ofType| *6 (|NonNegativeInteger|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|OrdinaryWeightedPolynomials| *3 *4 *5 *6)) (|ofType| *4 (|List| (|Symbol|))) (|ofType| *5 (|List| (|NonNegativeInteger|))) (|ofType| *6 (|NonNegativeInteger|)))) (/ (*1 *1 *1 *1) (|partial| AND (|isDomain| *1 (|OrdinaryWeightedPolynomials| *2 *3 *4 *5)) (|ofCategory| *2 (|Field|)) (|ofCategory| *2 (|Ring|)) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|List| (|NonNegativeInteger|))) (|ofType| *5 (|NonNegativeInteger|)))) (|changeWeightLevel| (*1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OrdinaryWeightedPolynomials| *4 *5 *6 *7)) (|ofCategory| *4 (|Ring|)) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|List| *3)) (|ofType| *7 *3)))) 
(|Join| (|Ring|) (CATEGORY |domain| (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |#1|)) |noBranch|) (SIGNATURE |coerce| ((|Polynomial| |#1|) $)) (SIGNATURE |coerce| ($ (|Polynomial| |#1|))) (IF (|has| |#1| (|Field|)) (SIGNATURE / ((|Union| $ "failed") $ $)) |noBranch|) (SIGNATURE |changeWeightLevel| ((|Void|) (|NonNegativeInteger|))))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|vectorise| (((|Vector| $) $ $) 80)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|transcendent?| (((|Boolean|) $) 113)) (|transcendenceDegree| (((|NonNegativeInteger|)) 117)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 73)) (|squareFree| (((|Factored| $) $) 72)) (|sizeLess?| (((|Boolean|) $ $) 58)) (|setTower!| (((|Void|) $) 76)) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 124) (((|Union| (|Fraction| (|Integer|)) "failed") $) 121) (((|Union| (|Fraction| (|Integer|)) "failed") $) 106) (((|Union| (|PseudoAlgebraicClosureOfRationalNumber|) "failed") $) 138) (((|Union| (|PseudoAlgebraicClosureOfRationalNumber|) "failed") $) 132)) (|retract| (((|Integer|) $) 123) (((|Fraction| (|Integer|)) $) 120) (((|Fraction| (|Integer|)) $) 107) (((|PseudoAlgebraicClosureOfRationalNumber|) $) 137) (((|PseudoAlgebraicClosureOfRationalNumber|) $) 133)) (|rem| (($ $ $) 54)) (|reduce| (($ (|SparseUnivariatePolynomial| $)) 86)) (|recip| (((|Union| $ "failed") $) 33)) (|quo| (($ $ $) 55)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 50)) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) 104 (OR (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|CharacteristicNonZero|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|Finite|)) (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|)))) (($ $) 103 (OR (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|CharacteristicNonZero|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|Finite|)) (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|))))) (|prime?| (((|Boolean|) $) 71)) (|previousTower| (($ $) 81)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 101 (OR (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|CharacteristicNonZero|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|Finite|)) (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|))))) (|one?| (((|Boolean|) $) 30)) (|newElement| (($ (|SparseUnivariatePolynomial| $) $ (|Symbol|)) 78) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 77)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 51)) (|maxTower| (($ (|List| $)) 83)) (|lift| (((|SparseUnivariatePolynomial| $) $) 88) (((|SparseUnivariatePolynomial| $) $ $) 87)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 70)) (|inGroundField?| (((|Boolean|) $) 114)) (|hash| (((|SingleInteger|) $) 10)) (|ground?| (((|Boolean|) $) 84)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|fullOutput| (((|OutputForm|) $) 75)) (|factor| (((|Factored| $) $) 74)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) 116)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 53) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 52)) (|extDegree| (((|PositiveInteger|) $) 82)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 49)) (|euclideanSize| (((|NonNegativeInteger|) $) 57)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 56)) (|distinguishedRootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) $) 85)) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) 102 (OR (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|CharacteristicNonZero|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|Finite|)) (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|))))) (|dimension| (((|CardinalNumber|)) 108)) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) 115)) (|definingPolynomial| (((|SparseUnivariatePolynomial| $)) 90) (((|SparseUnivariatePolynomial| $) $) 89)) (|conjugate| (($ $) 79)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42) (($ (|Fraction| (|Integer|))) 65) (($ (|Integer|)) 125) (($ (|Fraction| (|Integer|))) 122) (($ (|Fraction| (|Integer|))) 105) (($ (|PseudoAlgebraicClosureOfRationalNumber|)) 139) (($ (|PseudoAlgebraicClosureOfRationalNumber|)) 131)) (|charthRoot| (((|Union| $ "failed") $) 100 (OR (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|CharacteristicNonZero|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|Finite|)) (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|))))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (|algebraic?| (((|Boolean|) $) 112)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 69)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (|Frobenius| (($ $ (|NonNegativeInteger|)) 119 (OR (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|Finite|)) (|has| (|Fraction| (|Integer|)) (|Finite|)))) (($ $) 118 (OR (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|Finite|)) (|has| (|Fraction| (|Integer|)) (|Finite|))))) (= (((|Boolean|) $ $) 6)) (/ (($ $ $) 64) (($ $ (|Fraction| (|Integer|))) 109) (($ $ (|PseudoAlgebraicClosureOfRationalNumber|)) 134)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 68)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ (|Fraction| (|Integer|))) 67) (($ (|Fraction| (|Integer|)) $) 66) (($ (|Fraction| (|Integer|)) $) 111) (($ $ (|Fraction| (|Integer|))) 110) (($ (|PseudoAlgebraicClosureOfRationalNumber|) $) 136) (($ $ (|PseudoAlgebraicClosureOfRationalNumber|)) 135))) 
(((|PseudoAlgebraicClosureOfAlgExtOfRationalNumberCategory|) (|Category|)) (T |PseudoAlgebraicClosureOfAlgExtOfRationalNumberCategory|)) 
NIL 
(|Join| (|PseudoAlgebraicClosureOfRationalNumberCategory|) (|RetractableTo| (|PseudoAlgebraicClosureOfRationalNumber|)) (|ExtensionField| (|PseudoAlgebraicClosureOfRationalNumber|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) . T) ((|BiModule| (|PseudoAlgebraicClosureOfRationalNumber|) (|PseudoAlgebraicClosureOfRationalNumber|)) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|Finite|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|)) (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|))) ((|CharacteristicZero|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|ExtensionField| (|Fraction| (|Integer|))) . T) ((|ExtensionField| (|PseudoAlgebraicClosureOfRationalNumber|)) . T) ((|Field|) . T) ((|FieldOfPrimeCharacteristic|) OR (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|Finite|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|)) (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|))) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| (|Fraction| (|Integer|))) . T) ((|LeftModule| (|PseudoAlgebraicClosureOfRationalNumber|)) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| (|Fraction| (|Integer|))) . T) ((|Module| (|PseudoAlgebraicClosureOfRationalNumber|)) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|PseudoAlgebraicClosureOfPerfectFieldCategory|) . T) ((|PseudoAlgebraicClosureOfRationalNumberCategory|) . T) ((|RetractableTo| (|Fraction| (|Integer|))) . T) ((|RetractableTo| (|Integer|)) . T) ((|RetractableTo| (|PseudoAlgebraicClosureOfRationalNumber|)) . T) ((|RightModule| (|Fraction| (|Integer|))) . T) ((|RightModule| (|PseudoAlgebraicClosureOfRationalNumber|)) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|UniqueFactorizationDomain|) . T) ((|VectorSpace| (|Fraction| (|Integer|))) . T) ((|VectorSpace| (|PseudoAlgebraicClosureOfRationalNumber|)) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 47)) (|vectorise| (((|Vector| $) $ $) 69)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|transcendent?| (((|Boolean|) $) NIL)) (|transcendenceDegree| (((|NonNegativeInteger|)) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|setTower!| (((|Void|) $) 78)) (|sample| (($) NIL T CONST)) (|retractToGrn| (((|PseudoAlgebraicClosureOfRationalNumber|) $) 17)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 75) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL) (((|Union| (|PseudoAlgebraicClosureOfRationalNumber|) "failed") $) 72) (((|Union| (|PseudoAlgebraicClosureOfRationalNumber|) "failed") $) 72)) (|retract| (((|Integer|) $) NIL) (((|Fraction| (|Integer|)) $) NIL) (((|Fraction| (|Integer|)) $) NIL) (((|PseudoAlgebraicClosureOfRationalNumber|) $) 111) (((|PseudoAlgebraicClosureOfRationalNumber|) $) 111)) (|rem| (($ $ $) NIL)) (|reduce| (($ (|SparseUnivariatePolynomial| $)) 59)) (|recip| (((|Union| $ "failed") $) NIL)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) NIL (OR (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|CharacteristicNonZero|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|Finite|)))) (($ $) NIL (OR (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|CharacteristicNonZero|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|Finite|))))) (|prime?| (((|Boolean|) $) NIL)) (|previousTower| (($ $) 63)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL (OR (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|CharacteristicNonZero|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|Finite|))))) (|one?| (((|Boolean|) $) 117)) (|newElement| (($ (|SparseUnivariatePolynomial| $) $ (|Symbol|)) 41) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 94)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|maxTower| (($ (|List| $)) 61)) (|lift| (((|SparseUnivariatePolynomial| $) $) 55) (((|SparseUnivariatePolynomial| $) $ $) 56)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 101)) (|inGroundField?| (((|Boolean|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|ground?| (((|Boolean|) $) 62)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|fullOutput| (((|OutputForm|) $) 124)) (|factor| (((|Factored| $) $) NIL)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|extDegree| (((|PositiveInteger|) $) 37)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|distinguishedRootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) $) 96)) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) NIL (OR (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|CharacteristicNonZero|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|Finite|))))) (|dimension| (((|CardinalNumber|)) NIL)) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL)) (|definingPolynomial| (((|SparseUnivariatePolynomial| $)) 79) (((|SparseUnivariatePolynomial| $) $) 64)) (|conjugate| (($ $) NIL)) (|coerce| (((|OutputForm|) $) 123) (($ (|Integer|)) 44) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ (|Integer|)) 44) (($ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ (|PseudoAlgebraicClosureOfRationalNumber|)) 118) (($ (|PseudoAlgebraicClosureOfRationalNumber|)) 118)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|CharacteristicNonZero|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|Finite|))))) (|characteristic| (((|NonNegativeInteger|)) 126)) (|associates?| (((|Boolean|) $ $) NIL)) (|algebraic?| (((|Boolean|) $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) 48 T CONST)) (|One| (($) 38 T CONST)) (|Frobenius| (($ $ (|NonNegativeInteger|)) NIL (OR (|has| (|Fraction| (|Integer|)) (|Finite|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|Finite|)))) (($ $) NIL (OR (|has| (|Fraction| (|Integer|)) (|Finite|)) (|has| (|PseudoAlgebraicClosureOfRationalNumber|) (|Finite|))))) (= (((|Boolean|) $ $) 114)) (/ (($ $ $) 102) (($ $ (|Fraction| (|Integer|))) NIL) (($ $ (|PseudoAlgebraicClosureOfRationalNumber|)) NIL)) (- (($ $) 35) (($ $ $) 105)) (+ (($ $ $) 81)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 53) (($ $ $) 31) (($ $ (|Fraction| (|Integer|))) 109) (($ (|Fraction| (|Integer|)) $) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ $ (|Fraction| (|Integer|))) 109) (($ (|PseudoAlgebraicClosureOfRationalNumber|) $) 103) (($ $ (|PseudoAlgebraicClosureOfRationalNumber|)) 104))) 
(((|PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |#1|) (|Join| (|PseudoAlgebraicClosureOfAlgExtOfRationalNumberCategory|) (CATEGORY |domain| (SIGNATURE |fullOutput| ((|OutputForm|) $)) (SIGNATURE |retractToGrn| ((|PseudoAlgebraicClosureOfRationalNumber|) $)))) (|PseudoAlgebraicClosureOfRationalNumber|)) (T |PseudoAlgebraicClosureOfAlgExtOfRationalNumber|)) 
((|fullOutput| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|PseudoAlgebraicClosureOfAlgExtOfRationalNumber| *3)) (|ofType| *3 (|PseudoAlgebraicClosureOfRationalNumber|)))) (|retractToGrn| (*1 *2 *1) (AND (|isDomain| *2 (|PseudoAlgebraicClosureOfRationalNumber|)) (|isDomain| *1 (|PseudoAlgebraicClosureOfAlgExtOfRationalNumber| *3)) (|ofType| *3 *2)))) 
(|Join| (|PseudoAlgebraicClosureOfAlgExtOfRationalNumberCategory|) (CATEGORY |domain| (SIGNATURE |fullOutput| ((|OutputForm|) $)) (SIGNATURE |retractToGrn| ((|PseudoAlgebraicClosureOfRationalNumber|) $)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|vectorise| (((|Vector| $) $ $) 116)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) 90)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 73)) (|squareFree| (((|Factored| $) $) 72)) (|sizeLess?| (((|Boolean|) $ $) 58)) (|size| (((|NonNegativeInteger|)) 100)) (|setTower!| (((|Void|) $) 120)) (|sample| (($) 16 T CONST)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 84)) (|rem| (($ $ $) 54)) (|reduce| (($ (|SparseUnivariatePolynomial| $)) 110)) (|recip| (((|Union| $ "failed") $) 33)) (|random| (($) 103)) (|quo| (($ $ $) 55)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 50)) (|primitiveElement| (($) 88)) (|primitive?| (((|Boolean|) $) 87)) (|primeFrobenius| (($ $) 77) (($ $ (|NonNegativeInteger|)) 76)) (|prime?| (((|Boolean|) $) 71)) (|previousTower| (($ $) 115)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 79) (((|PositiveInteger|) $) 85)) (|one?| (((|Boolean|) $) 30)) (|nextItem| (((|Union| $ "failed") $) 99)) (|newElement| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 119) (($ (|SparseUnivariatePolynomial| $) $ (|Symbol|)) 118)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 51)) (|maxTower| (($ (|List| $)) 113)) (|lookup| (((|PositiveInteger|) $) 102)) (|lift| (((|SparseUnivariatePolynomial| $) $ $) 109) (((|SparseUnivariatePolynomial| $) $) 108)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 70)) (|init| (($) 98 T CONST)) (|index| (($ (|PositiveInteger|)) 101)) (|hash| (((|SingleInteger|) $) 10)) (|ground?| (((|Boolean|) $) 112)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|fullOutput| (((|OutputForm|) $) 121)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) 91)) (|factor| (((|Factored| $) $) 74)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 53) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 52)) (|extDegree| (((|PositiveInteger|) $) 114)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 49)) (|euclideanSize| (((|NonNegativeInteger|) $) 57)) (|enumerate| (((|List| $)) 104)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 56)) (|distinguishedRootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) $) 111)) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) 78) (((|NonNegativeInteger|) $) 86)) (|differentiate| (($ $ (|NonNegativeInteger|)) 96) (($ $) 94)) (|definingPolynomial| (((|SparseUnivariatePolynomial| $) $) 107) (((|SparseUnivariatePolynomial| $)) 106)) (|createPrimitiveElement| (($) 89)) (|conjugate| (($ $) 117)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 92)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42) (($ (|Fraction| (|Integer|))) 65)) (|charthRoot| (((|Union| $ "failed") $) 80) (($ $) 93)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 69)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $ (|NonNegativeInteger|)) 97) (($ $) 95)) (= (((|Boolean|) $ $) 6)) (/ (($ $ $) 64)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 68)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ (|Fraction| (|Integer|))) 67) (($ (|Fraction| (|Integer|)) $) 66))) 
(((|PseudoAlgebraicClosureOfFiniteFieldCategory|) (|Category|)) (T |PseudoAlgebraicClosureOfFiniteFieldCategory|)) 
NIL 
(|Join| (|FiniteFieldCategory|) (|PseudoAlgebraicClosureOfPerfectFieldCategory|)) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DifferentialRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|FieldOfPrimeCharacteristic|) . T) ((|Finite|) . T) ((|FiniteFieldCategory|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| (|Fraction| (|Integer|))) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| (|Fraction| (|Integer|))) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|PseudoAlgebraicClosureOfPerfectFieldCategory|) . T) ((|RightModule| (|Fraction| (|Integer|))) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|StepThrough|) . T) ((|UniqueFactorizationDomain|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 29)) (|vectorise| (((|Vector| $) $ $) 48)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 39)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|transcendent?| (((|Boolean|) $) NIL)) (|transcendenceDegree| (((|NonNegativeInteger|)) NIL)) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|size| (((|NonNegativeInteger|)) 52)) (|setTower!| (((|Void|) $) 56)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 126)) (|retract| ((|#1| $) 85)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 139)) (|rem| (($ $ $) NIL)) (|reduce| (($ (|SparseUnivariatePolynomial| $)) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) 82)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|primitiveElement| (($) NIL)) (|primitive?| (((|Boolean|) $) NIL)) (|primeFrobenius| (($ $) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|previousTower| (($ $) 41)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL) (((|PositiveInteger|) $) NIL)) (|one?| (((|Boolean|) $) 123)) (|nextItem| (((|Union| $ "failed") $) NIL)) (|newElement| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 79) (($ (|SparseUnivariatePolynomial| $) $ (|Symbol|)) 99)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|maxTower| (($ (|List| $)) 104)) (|lookup| (((|PositiveInteger|) $) 134)) (|lift| (((|SparseUnivariatePolynomial| $) $ $) NIL) (((|SparseUnivariatePolynomial| $) $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 27)) (|init| (($) NIL T CONST)) (|index| (($ (|PositiveInteger|)) 136)) (|inGroundField?| (((|Boolean|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|ground?| (((|Boolean|) $) 40)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|fullOutput| (((|OutputForm|) $) 132)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) NIL)) (|factor| (((|Factored| $) $) NIL)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|extDegree| (((|PositiveInteger|) $) 14)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|enumerate| (((|List| $)) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|distinguishedRootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) $) 81)) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) NIL) (((|NonNegativeInteger|) $) NIL)) (|dimension| (((|CardinalNumber|)) NIL)) (|differentiate| (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) 17)) (|definingPolynomial| (((|SparseUnivariatePolynomial| $) $) 20) (((|SparseUnivariatePolynomial| $)) NIL)) (|createPrimitiveElement| (($) NIL)) (|conjugate| (($ $) 90)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL)) (|coerce| (((|OutputForm|) $) 131) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ |#1|) 124)) (|charthRoot| (((|Union| $ "failed") $) NIL) (($ $) 89)) (|characteristic| (((|NonNegativeInteger|)) 140)) (|associates?| (((|Boolean|) $ $) NIL)) (|algebraic?| (((|Boolean|) $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) 30 T CONST)) (|One| (($) 21 T CONST)) (|Frobenius| (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|))) (($ $) NIL (|has| |#1| (|Finite|)))) (D (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (= (((|Boolean|) $ $) 120)) (/ (($ $ $) 96) (($ $ |#1|) NIL)) (- (($ $) 97) (($ $ $) 107)) (+ (($ $ $) 63)) (** (($ $ (|PositiveInteger|)) 33) (($ $ (|NonNegativeInteger|)) 34) (($ $ (|Integer|)) 37)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 111) (($ $ $) 65) (($ $ (|Fraction| (|Integer|))) 112) (($ (|Fraction| (|Integer|)) $) NIL) (($ |#1| $) 105) (($ $ |#1|) 106))) 
(((|PseudoAlgebraicClosureOfFiniteField| |#1|) (|Join| (|PseudoAlgebraicClosureOfFiniteFieldCategory|) (|ExtensionField| |#1|) (CATEGORY |domain| (SIGNATURE |fullOutput| ((|OutputForm|) $)))) (|FiniteFieldCategory|)) (T |PseudoAlgebraicClosureOfFiniteField|)) 
((|fullOutput| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|PseudoAlgebraicClosureOfFiniteField| *3)) (|ofCategory| *3 (|FiniteFieldCategory|))))) 
(|Join| (|PseudoAlgebraicClosureOfFiniteFieldCategory|) (|ExtensionField| |#1|) (CATEGORY |domain| (SIGNATURE |fullOutput| ((|OutputForm|) $)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|vectorise| (((|Vector| $) $ $) 80)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 73)) (|squareFree| (((|Factored| $) $) 72)) (|sizeLess?| (((|Boolean|) $ $) 58)) (|setTower!| (((|Void|) $) 76)) (|sample| (($) 16 T CONST)) (|rem| (($ $ $) 54)) (|reduce| (($ (|SparseUnivariatePolynomial| $)) 86)) (|recip| (((|Union| $ "failed") $) 33)) (|quo| (($ $ $) 55)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 50)) (|prime?| (((|Boolean|) $) 71)) (|previousTower| (($ $) 81)) (|one?| (((|Boolean|) $) 30)) (|newElement| (($ (|SparseUnivariatePolynomial| $) $ (|Symbol|)) 78) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 77)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 51)) (|maxTower| (($ (|List| $)) 83)) (|lift| (((|SparseUnivariatePolynomial| $) $) 88) (((|SparseUnivariatePolynomial| $) $ $) 87)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 70)) (|hash| (((|SingleInteger|) $) 10)) (|ground?| (((|Boolean|) $) 84)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|fullOutput| (((|OutputForm|) $) 75)) (|factor| (((|Factored| $) $) 74)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 53) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 52)) (|extDegree| (((|PositiveInteger|) $) 82)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 49)) (|euclideanSize| (((|NonNegativeInteger|) $) 57)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 56)) (|distinguishedRootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) $) 85)) (|definingPolynomial| (((|SparseUnivariatePolynomial| $)) 90) (((|SparseUnivariatePolynomial| $) $) 89)) (|conjugate| (($ $) 79)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42) (($ (|Fraction| (|Integer|))) 65)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 69)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (/ (($ $ $) 64)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 68)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ (|Fraction| (|Integer|))) 67) (($ (|Fraction| (|Integer|)) $) 66))) 
(((|PseudoAlgebraicClosureOfPerfectFieldCategory|) (|Category|)) (T |PseudoAlgebraicClosureOfPerfectFieldCategory|)) 
((|definingPolynomial| (*1 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|PseudoAlgebraicClosureOfPerfectFieldCategory|)))) (|definingPolynomial| (*1 *2 *1) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|PseudoAlgebraicClosureOfPerfectFieldCategory|)))) (|lift| (*1 *2 *1) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|PseudoAlgebraicClosureOfPerfectFieldCategory|)))) (|lift| (*1 *2 *1 *1) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|PseudoAlgebraicClosureOfPerfectFieldCategory|)))) (|reduce| (*1 *1 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|PseudoAlgebraicClosureOfPerfectFieldCategory|)))) (|distinguishedRootsOf| (*1 *2 *3 *1) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|PseudoAlgebraicClosureOfPerfectFieldCategory|)) (|isDomain| *2 (|List| *1)))) (|ground?| (*1 *2 *1) (AND (|ofCategory| *1 (|PseudoAlgebraicClosureOfPerfectFieldCategory|)) (|isDomain| *2 (|Boolean|)))) (|maxTower| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|PseudoAlgebraicClosureOfPerfectFieldCategory|)))) (|extDegree| (*1 *2 *1) (AND (|ofCategory| *1 (|PseudoAlgebraicClosureOfPerfectFieldCategory|)) (|isDomain| *2 (|PositiveInteger|)))) (|previousTower| (*1 *1 *1) (|ofCategory| *1 (|PseudoAlgebraicClosureOfPerfectFieldCategory|))) (|vectorise| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|PseudoAlgebraicClosureOfPerfectFieldCategory|)))) (|conjugate| (*1 *1 *1) (|ofCategory| *1 (|PseudoAlgebraicClosureOfPerfectFieldCategory|))) (|newElement| (*1 *1 *2 *1 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|isDomain| *3 (|Symbol|)) (|ofCategory| *1 (|PseudoAlgebraicClosureOfPerfectFieldCategory|)))) (|newElement| (*1 *1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|isDomain| *3 (|Symbol|)) (|ofCategory| *1 (|PseudoAlgebraicClosureOfPerfectFieldCategory|)))) (|setTower!| (*1 *2 *1) (AND (|ofCategory| *1 (|PseudoAlgebraicClosureOfPerfectFieldCategory|)) (|isDomain| *2 (|Void|)))) (|fullOutput| (*1 *2 *1) (AND (|ofCategory| *1 (|PseudoAlgebraicClosureOfPerfectFieldCategory|)) (|isDomain| *2 (|OutputForm|))))) 
(|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |definingPolynomial| ((|SparseUnivariatePolynomial| $))) (SIGNATURE |definingPolynomial| ((|SparseUnivariatePolynomial| $) $)) (SIGNATURE |lift| ((|SparseUnivariatePolynomial| $) $)) (SIGNATURE |lift| ((|SparseUnivariatePolynomial| $) $ $)) (SIGNATURE |reduce| ($ (|SparseUnivariatePolynomial| $))) (SIGNATURE |distinguishedRootsOf| ((|List| $) (|SparseUnivariatePolynomial| $) $)) (SIGNATURE |ground?| ((|Boolean|) $)) (SIGNATURE |maxTower| ($ (|List| $))) (SIGNATURE |extDegree| ((|PositiveInteger|) $)) (SIGNATURE |previousTower| ($ $)) (SIGNATURE |vectorise| ((|Vector| $) $ $)) (SIGNATURE |conjugate| ($ $)) (SIGNATURE |newElement| ($ (|SparseUnivariatePolynomial| $) $ (|Symbol|))) (SIGNATURE |newElement| ($ (|SparseUnivariatePolynomial| $) (|Symbol|))) (SIGNATURE |setTower!| ((|Void|) $)) (SIGNATURE |fullOutput| ((|OutputForm|) $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| (|Fraction| (|Integer|))) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| (|Fraction| (|Integer|))) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightModule| (|Fraction| (|Integer|))) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|UniqueFactorizationDomain|) . T)) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|vectorise| (((|Vector| $) $ $) 80)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|transcendent?| (((|Boolean|) $) 113)) (|transcendenceDegree| (((|NonNegativeInteger|)) 117)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 73)) (|squareFree| (((|Factored| $) $) 72)) (|sizeLess?| (((|Boolean|) $ $) 58)) (|setTower!| (((|Void|) $) 76)) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 124) (((|Union| (|Fraction| (|Integer|)) "failed") $) 121) (((|Union| (|Fraction| (|Integer|)) "failed") $) 106)) (|retract| (((|Integer|) $) 123) (((|Fraction| (|Integer|)) $) 120) (((|Fraction| (|Integer|)) $) 107)) (|rem| (($ $ $) 54)) (|reduce| (($ (|SparseUnivariatePolynomial| $)) 86)) (|recip| (((|Union| $ "failed") $) 33)) (|quo| (($ $ $) 55)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 50)) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) 104 (OR (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|)))) (($ $) 103 (OR (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|))))) (|prime?| (((|Boolean|) $) 71)) (|previousTower| (($ $) 81)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 101 (OR (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|))))) (|one?| (((|Boolean|) $) 30)) (|newElement| (($ (|SparseUnivariatePolynomial| $) $ (|Symbol|)) 78) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 77)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 51)) (|maxTower| (($ (|List| $)) 83)) (|lift| (((|SparseUnivariatePolynomial| $) $) 88) (((|SparseUnivariatePolynomial| $) $ $) 87)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 70)) (|inGroundField?| (((|Boolean|) $) 114)) (|hash| (((|SingleInteger|) $) 10)) (|ground?| (((|Boolean|) $) 84)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|fullOutput| (((|OutputForm|) $) 75)) (|factor| (((|Factored| $) $) 74)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) 116)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 53) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 52)) (|extDegree| (((|PositiveInteger|) $) 82)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 49)) (|euclideanSize| (((|NonNegativeInteger|) $) 57)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 56)) (|distinguishedRootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) $) 85)) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) 102 (OR (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|))))) (|dimension| (((|CardinalNumber|)) 108)) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) 115)) (|definingPolynomial| (((|SparseUnivariatePolynomial| $)) 90) (((|SparseUnivariatePolynomial| $) $) 89)) (|conjugate| (($ $) 79)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42) (($ (|Fraction| (|Integer|))) 65) (($ (|Integer|)) 125) (($ (|Fraction| (|Integer|))) 122) (($ (|Fraction| (|Integer|))) 105)) (|charthRoot| (((|Union| $ "failed") $) 100 (OR (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|))))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (|algebraic?| (((|Boolean|) $) 112)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 69)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (|Frobenius| (($ $ (|NonNegativeInteger|)) 119 (|has| (|Fraction| (|Integer|)) (|Finite|))) (($ $) 118 (|has| (|Fraction| (|Integer|)) (|Finite|)))) (= (((|Boolean|) $ $) 6)) (/ (($ $ $) 64) (($ $ (|Fraction| (|Integer|))) 109)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 68)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ (|Fraction| (|Integer|))) 67) (($ (|Fraction| (|Integer|)) $) 66) (($ (|Fraction| (|Integer|)) $) 111) (($ $ (|Fraction| (|Integer|))) 110))) 
(((|PseudoAlgebraicClosureOfRationalNumberCategory|) (|Category|)) (T |PseudoAlgebraicClosureOfRationalNumberCategory|)) 
NIL 
(|Join| (|PseudoAlgebraicClosureOfPerfectFieldCategory|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))) (|ExtensionField| (|Fraction| (|Integer|)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| (|Fraction| (|Integer|)) (|Finite|)) (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|))) ((|CharacteristicZero|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|ExtensionField| (|Fraction| (|Integer|))) . T) ((|Field|) . T) ((|FieldOfPrimeCharacteristic|) OR (|has| (|Fraction| (|Integer|)) (|Finite|)) (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|))) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| (|Fraction| (|Integer|))) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| (|Fraction| (|Integer|))) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|PseudoAlgebraicClosureOfPerfectFieldCategory|) . T) ((|RetractableTo| (|Fraction| (|Integer|))) . T) ((|RetractableTo| (|Integer|)) . T) ((|RightModule| (|Fraction| (|Integer|))) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|UniqueFactorizationDomain|) . T) ((|VectorSpace| (|Fraction| (|Integer|))) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 16)) (|vectorise| (((|Vector| $) $ $) 47)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|transcendent?| (((|Boolean|) $) NIL)) (|transcendenceDegree| (((|NonNegativeInteger|)) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|setTower!| (((|Void|) $) 51)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 104) (((|Union| (|Fraction| (|Integer|)) "failed") $) 106) (((|Union| (|Fraction| (|Integer|)) "failed") $) 106)) (|retract| (((|Integer|) $) NIL) (((|Fraction| (|Integer|)) $) 94) (((|Fraction| (|Integer|)) $) 94)) (|rem| (($ $ $) NIL)) (|reduce| (($ (|SparseUnivariatePolynomial| $)) 34)) (|recip| (((|Union| $ "failed") $) NIL)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) NIL (OR (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|)))) (($ $) NIL (OR (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|))))) (|prime?| (((|Boolean|) $) NIL)) (|previousTower| (($ $) 40)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL (OR (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|))))) (|one?| (((|Boolean|) $) 100)) (|newElement| (($ (|SparseUnivariatePolynomial| $) $ (|Symbol|)) 79) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 70) (($ (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|PositiveInteger|) $ (|Symbol|)) 80)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|maxTower| (($ (|List| $)) 38)) (|lift| (((|SparseUnivariatePolynomial| $) $) 29) (((|SparseUnivariatePolynomial| $) $ $) 31)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 86)) (|inGroundField?| (((|Boolean|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|ground?| (((|Boolean|) $) 39)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|fullOutput| (((|OutputForm|) $) 112)) (|factor| (((|Factored| $) $) NIL)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|extDegree| (((|PositiveInteger|) $) 30)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|distinguishedRootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) $) 72)) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) NIL (OR (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|))))) (|dimension| (((|CardinalNumber|)) NIL)) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL)) (|definingPolynomial| (((|SparseUnivariatePolynomial| $)) 52) (((|SparseUnivariatePolynomial| $) $) 41)) (|conjugate| (($ $) NIL)) (|coerce| (((|OutputForm|) $) 111) (($ (|Integer|)) 14) (($ $) NIL) (($ (|Fraction| (|Integer|))) 101) (($ (|Integer|)) 14) (($ (|Fraction| (|Integer|))) 101) (($ (|Fraction| (|Integer|))) 101)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (|has| (|Fraction| (|Integer|)) (|CharacteristicNonZero|)) (|has| (|Fraction| (|Integer|)) (|Finite|))))) (|characteristic| (((|NonNegativeInteger|)) 114)) (|associates?| (((|Boolean|) $ $) NIL)) (|algebraic?| (((|Boolean|) $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) 17 T CONST)) (|One| (($) 73 T CONST)) (|Frobenius| (($ $ (|NonNegativeInteger|)) NIL (|has| (|Fraction| (|Integer|)) (|Finite|))) (($ $) NIL (|has| (|Fraction| (|Integer|)) (|Finite|)))) (= (((|Boolean|) $ $) 97)) (/ (($ $ $) 78) (($ $ (|Fraction| (|Integer|))) NIL)) (- (($ $) 19) (($ $ $) 89)) (+ (($ $ $) 54)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 18) (($ $ $) 57) (($ $ (|Fraction| (|Integer|))) 88) (($ (|Fraction| (|Integer|)) $) 87) (($ (|Fraction| (|Integer|)) $) 87) (($ $ (|Fraction| (|Integer|))) 88))) 
(((|PseudoAlgebraicClosureOfRationalNumber|) (|Join| (|PseudoAlgebraicClosureOfRationalNumberCategory|) (CATEGORY |domain| (SIGNATURE |fullOutput| ((|OutputForm|) $)) (SIGNATURE |newElement| ($ (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|PositiveInteger|) $ (|Symbol|)))))) (T |PseudoAlgebraicClosureOfRationalNumber|)) 
((|fullOutput| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|PseudoAlgebraicClosureOfRationalNumber|)))) (|newElement| (*1 *1 *2 *2 *3 *1 *4) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|PseudoAlgebraicClosureOfRationalNumber|))) (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|Symbol|)) (|isDomain| *1 (|PseudoAlgebraicClosureOfRationalNumber|))))) 
(|Join| (|PseudoAlgebraicClosureOfRationalNumberCategory|) (CATEGORY |domain| (SIGNATURE |fullOutput| ((|OutputForm|) $)) (SIGNATURE |newElement| ($ (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|PositiveInteger|) $ (|Symbol|))))) 
((|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) 31)) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) 24))) 
(((|PadeApproximants| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |pade| ((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|)) (SIGNATURE |padecf| ((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|))) (|Field|) (|UnivariateTaylorSeriesCategory| |#1|) (|UnivariatePolynomialCategory| |#1|)) (T |PadeApproximants|)) 
((|padecf| (*1 *2 *3 *3 *4 *4) (|partial| AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|ContinuedFraction| *6)) (|isDomain| *1 (|PadeApproximants| *5 *4 *6)) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *5)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)))) (|pade| (*1 *2 *3 *3 *4 *4) (|partial| AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Fraction| *6)) (|isDomain| *1 (|PadeApproximants| *5 *4 *6)) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *5)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |pade| ((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|)) (SIGNATURE |padecf| ((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|))) 
((|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) 28) (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) 26))) 
(((|PadeApproximantPackage| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |pade| ((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|))) (SIGNATURE |pade| ((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)))) (|Field|) (|Symbol|) |#1|) (T |PadeApproximantPackage|)) 
((|pade| (*1 *2 *3 *3 *4) (|partial| AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|UnivariateTaylorSeries| *5 *6 *7)) (|ofCategory| *5 (|Field|)) (|ofType| *6 (|Symbol|)) (|ofType| *7 *5) (|isDomain| *2 (|Fraction| (|UnivariatePolynomial| *6 *5))) (|isDomain| *1 (|PadeApproximantPackage| *5 *6 *7)))) (|pade| (*1 *2 *3 *3 *4 *4) (|partial| AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|UnivariateTaylorSeries| *5 *6 *7)) (|ofCategory| *5 (|Field|)) (|ofType| *6 (|Symbol|)) (|ofType| *7 *5) (|isDomain| *2 (|Fraction| (|UnivariatePolynomial| *6 *5))) (|isDomain| *1 (|PadeApproximantPackage| *5 *6 *7))))) 
(CATEGORY |package| (SIGNATURE |pade| ((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|))) (SIGNATURE |pade| ((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sqrt| (($ $ (|Integer|)) 61)) (|sizeLess?| (((|Boolean|) $ $) 58)) (|sample| (($) 16 T CONST)) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) 60)) (|rem| (($ $ $) 54)) (|recip| (((|Union| $ "failed") $) 33)) (|quotientByP| (($ $) 63)) (|quo| (($ $ $) 55)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 50)) (|order| (((|NonNegativeInteger|) $) 68)) (|one?| (((|Boolean|) $) 30)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 51)) (|modulus| (((|Integer|)) 65)) (|moduloP| (((|Integer|) $) 64)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 53) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 52)) (|extend| (($ $ (|Integer|)) 67)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 49)) (|euclideanSize| (((|NonNegativeInteger|) $) 57)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 56)) (|digits| (((|Stream| (|Integer|)) $) 69)) (|complete| (($ $) 66)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (|approximate| (((|Integer|) $ (|Integer|)) 62)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|PAdicIntegerCategory| |#1|) (|Category|) (|Integer|)) (T |PAdicIntegerCategory|)) 
((|digits| (*1 *2 *1) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Stream| (|Integer|))))) (|order| (*1 *2 *1) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|NonNegativeInteger|)))) (|extend| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Integer|)))) (|complete| (*1 *1 *1) (|ofCategory| *1 (|PAdicIntegerCategory| *2))) (|modulus| (*1 *2) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Integer|)))) (|moduloP| (*1 *2 *1) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Integer|)))) (|quotientByP| (*1 *1 *1) (|ofCategory| *1 (|PAdicIntegerCategory| *2))) (|approximate| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Integer|)))) (|sqrt| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Integer|)))) (|root| (*1 *1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|PAdicIntegerCategory| *4))))) 
(|Join| (|EuclideanDomain|) (|CharacteristicZero|) (CATEGORY |domain| (SIGNATURE |digits| ((|Stream| (|Integer|)) $)) (SIGNATURE |order| ((|NonNegativeInteger|) $)) (SIGNATURE |extend| ($ $ (|Integer|))) (SIGNATURE |complete| ($ $)) (SIGNATURE |modulus| ((|Integer|))) (SIGNATURE |moduloP| ((|Integer|) $)) (SIGNATURE |quotientByP| ($ $)) (SIGNATURE |approximate| ((|Integer|) $ (|Integer|))) (SIGNATURE |sqrt| ($ $ (|Integer|))) (SIGNATURE |root| ($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sqrt| (($ $ (|Integer|)) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sample| (($) NIL T CONST)) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) NIL)) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|quotientByP| (($ $) NIL)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|order| (((|NonNegativeInteger|) $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|modulus| (((|Integer|)) NIL)) (|moduloP| (((|Integer|) $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|extend| (($ $ (|Integer|)) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|digits| (((|Stream| (|Integer|)) $) NIL)) (|complete| (($ $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|associates?| (((|Boolean|) $ $) NIL)) (|approximate| (((|Integer|) $ (|Integer|)) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL))) 
(((|PAdicInteger| |#1|) (|PAdicIntegerCategory| |#1|) (|Integer|)) (T |PAdicInteger|)) 
NIL 
(|PAdicIntegerCategory| |#1|) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|wholePart| (((|PAdicInteger| |#1|) $) NIL (|has| (|PAdicInteger| |#1|) (|EuclideanDomain|)))) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|PAdicInteger| |#1|) (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|PAdicInteger| |#1|) (|PolynomialFactorizationExplicit|)))) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sign| (((|Integer|) $) NIL (|has| (|PAdicInteger| |#1|) (|OrderedIntegralDomain|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|PAdicInteger| |#1|) "failed") $) NIL) (((|Union| (|Symbol|) "failed") $) NIL (|has| (|PAdicInteger| |#1|) (|RetractableTo| (|Symbol|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| (|PAdicInteger| |#1|) (|RetractableTo| (|Integer|)))) (((|Union| (|Integer|) "failed") $) NIL (|has| (|PAdicInteger| |#1|) (|RetractableTo| (|Integer|))))) (|retract| (((|PAdicInteger| |#1|) $) NIL) (((|Symbol|) $) NIL (|has| (|PAdicInteger| |#1|) (|RetractableTo| (|Symbol|)))) (((|Fraction| (|Integer|)) $) NIL (|has| (|PAdicInteger| |#1|) (|RetractableTo| (|Integer|)))) (((|Integer|) $) NIL (|has| (|PAdicInteger| |#1|) (|RetractableTo| (|Integer|))))) (|removeZeroes| (($ $) NIL) (($ (|Integer|) $) NIL)) (|rem| (($ $ $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| (|PAdicInteger| |#1|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| (|PAdicInteger| |#1|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|PAdicInteger| |#1|))) (|:| |vec| (|Vector| (|PAdicInteger| |#1|)))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| (|PAdicInteger| |#1|)) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) NIL (|has| (|PAdicInteger| |#1|) (|IntegerNumberSystem|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|positive?| (((|Boolean|) $) NIL (|has| (|PAdicInteger| |#1|) (|OrderedIntegralDomain|)))) (|patternMatch| (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (|has| (|PAdicInteger| |#1|) (|PatternMatchable| (|Integer|)))) (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (|has| (|PAdicInteger| |#1|) (|PatternMatchable| (|Float|))))) (|one?| (((|Boolean|) $) NIL)) (|numerator| (($ $) NIL)) (|numer| (((|PAdicInteger| |#1|) $) NIL)) (|nextItem| (((|Union| $ "failed") $) NIL (|has| (|PAdicInteger| |#1|) (|StepThrough|)))) (|negative?| (((|Boolean|) $) NIL (|has| (|PAdicInteger| |#1|) (|OrderedIntegralDomain|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|min| (($ $ $) NIL (|has| (|PAdicInteger| |#1|) (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| (|PAdicInteger| |#1|) (|OrderedSet|)))) (|map| (($ (|Mapping| (|PAdicInteger| |#1|) (|PAdicInteger| |#1|)) $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|init| (($) NIL (|has| (|PAdicInteger| |#1|) (|StepThrough|)) CONST)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|fractionPart| (($ $) NIL (|has| (|PAdicInteger| |#1|) (|EuclideanDomain|)))) (|floor| (((|PAdicInteger| |#1|) $) NIL (|has| (|PAdicInteger| |#1|) (|IntegerNumberSystem|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|PAdicInteger| |#1|) (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|PAdicInteger| |#1|) (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|eval| (($ $ (|List| (|PAdicInteger| |#1|)) (|List| (|PAdicInteger| |#1|))) NIL (|has| (|PAdicInteger| |#1|) (|Evalable| (|PAdicInteger| |#1|)))) (($ $ (|PAdicInteger| |#1|) (|PAdicInteger| |#1|)) NIL (|has| (|PAdicInteger| |#1|) (|Evalable| (|PAdicInteger| |#1|)))) (($ $ (|Equation| (|PAdicInteger| |#1|))) NIL (|has| (|PAdicInteger| |#1|) (|Evalable| (|PAdicInteger| |#1|)))) (($ $ (|List| (|Equation| (|PAdicInteger| |#1|)))) NIL (|has| (|PAdicInteger| |#1|) (|Evalable| (|PAdicInteger| |#1|)))) (($ $ (|List| (|Symbol|)) (|List| (|PAdicInteger| |#1|))) NIL (|has| (|PAdicInteger| |#1|) (|InnerEvalable| (|Symbol|) (|PAdicInteger| |#1|)))) (($ $ (|Symbol|) (|PAdicInteger| |#1|)) NIL (|has| (|PAdicInteger| |#1|) (|InnerEvalable| (|Symbol|) (|PAdicInteger| |#1|))))) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|elt| (($ $ (|PAdicInteger| |#1|)) NIL (|has| (|PAdicInteger| |#1|) (|Eltable| (|PAdicInteger| |#1|) (|PAdicInteger| |#1|))))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|differentiate| (($ $) NIL (|has| (|PAdicInteger| |#1|) (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|PAdicInteger| |#1|) (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| (|PAdicInteger| |#1|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| (|PAdicInteger| |#1|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| (|PAdicInteger| |#1|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| (|PAdicInteger| |#1|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| (|PAdicInteger| |#1|) (|PAdicInteger| |#1|)) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| (|PAdicInteger| |#1|) (|PAdicInteger| |#1|))) NIL)) (|denominator| (($ $) NIL)) (|denom| (((|PAdicInteger| |#1|) $) NIL)) (|convert| (((|Pattern| (|Integer|)) $) NIL (|has| (|PAdicInteger| |#1|) (|ConvertibleTo| (|Pattern| (|Integer|))))) (((|Pattern| (|Float|)) $) NIL (|has| (|PAdicInteger| |#1|) (|ConvertibleTo| (|Pattern| (|Float|))))) (((|InputForm|) $) NIL (|has| (|PAdicInteger| |#1|) (|ConvertibleTo| (|InputForm|)))) (((|Float|) $) NIL (|has| (|PAdicInteger| |#1|) (|RealConstant|))) (((|DoubleFloat|) $) NIL (|has| (|PAdicInteger| |#1|) (|RealConstant|)))) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) NIL)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| (|PAdicInteger| |#1|) (|PolynomialFactorizationExplicit|))))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ (|PAdicInteger| |#1|)) NIL) (($ (|Symbol|)) NIL (|has| (|PAdicInteger| |#1|) (|RetractableTo| (|Symbol|))))) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| (|PAdicInteger| |#1|) (|PolynomialFactorizationExplicit|))) (|has| (|PAdicInteger| |#1|) (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|ceiling| (((|PAdicInteger| |#1|) $) NIL (|has| (|PAdicInteger| |#1|) (|IntegerNumberSystem|)))) (|associates?| (((|Boolean|) $ $) NIL)) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) NIL)) (|abs| (($ $) NIL (|has| (|PAdicInteger| |#1|) (|OrderedIntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($ $) NIL (|has| (|PAdicInteger| |#1|) (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|PAdicInteger| |#1|) (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| (|PAdicInteger| |#1|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| (|PAdicInteger| |#1|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| (|PAdicInteger| |#1|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| (|PAdicInteger| |#1|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| (|PAdicInteger| |#1|) (|PAdicInteger| |#1|)) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| (|PAdicInteger| |#1|) (|PAdicInteger| |#1|))) NIL)) (>= (((|Boolean|) $ $) NIL (|has| (|PAdicInteger| |#1|) (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| (|PAdicInteger| |#1|) (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| (|PAdicInteger| |#1|) (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| (|PAdicInteger| |#1|) (|OrderedSet|)))) (/ (($ $ $) NIL) (($ (|PAdicInteger| |#1|) (|PAdicInteger| |#1|)) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ (|PAdicInteger| |#1|) $) NIL) (($ $ (|PAdicInteger| |#1|)) NIL))) 
(((|PAdicRational| |#1|) (|Join| (|QuotientFieldCategory| (|PAdicInteger| |#1|)) (CATEGORY |domain| (SIGNATURE |approximate| ((|Fraction| (|Integer|)) $ (|Integer|))) (SIGNATURE |continuedFraction| ((|ContinuedFraction| (|Fraction| (|Integer|))) $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |removeZeroes| ($ (|Integer|) $)))) (|Integer|)) (T |PAdicRational|)) 
((|approximate| (*1 *2 *1 *3) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|PAdicRational| *4)) (|ofType| *4 *3) (|isDomain| *3 (|Integer|)))) (|continuedFraction| (*1 *2 *1) (AND (|isDomain| *2 (|ContinuedFraction| (|Fraction| (|Integer|)))) (|isDomain| *1 (|PAdicRational| *3)) (|ofType| *3 (|Integer|)))) (|removeZeroes| (*1 *1 *1) (AND (|isDomain| *1 (|PAdicRational| *2)) (|ofType| *2 (|Integer|)))) (|removeZeroes| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PAdicRational| *3)) (|ofType| *3 *2)))) 
(|Join| (|QuotientFieldCategory| (|PAdicInteger| |#1|)) (CATEGORY |domain| (SIGNATURE |approximate| ((|Fraction| (|Integer|)) $ (|Integer|))) (SIGNATURE |continuedFraction| ((|ContinuedFraction| (|Fraction| (|Integer|))) $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |removeZeroes| ($ (|Integer|) $)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|wholePart| ((|#2| $) NIL (|has| |#2| (|EuclideanDomain|)))) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sign| (((|Integer|) $) NIL (|has| |#2| (|OrderedIntegralDomain|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) NIL) (((|Union| (|Symbol|) "failed") $) NIL (|has| |#2| (|RetractableTo| (|Symbol|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#2| (|RetractableTo| (|Integer|)))) (((|Union| (|Integer|) "failed") $) NIL (|has| |#2| (|RetractableTo| (|Integer|))))) (|retract| ((|#2| $) NIL) (((|Symbol|) $) NIL (|has| |#2| (|RetractableTo| (|Symbol|)))) (((|Fraction| (|Integer|)) $) NIL (|has| |#2| (|RetractableTo| (|Integer|)))) (((|Integer|) $) NIL (|has| |#2| (|RetractableTo| (|Integer|))))) (|removeZeroes| (($ $) 31) (($ (|Integer|) $) 32)) (|rem| (($ $ $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| |#2|) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) 53)) (|random| (($) NIL (|has| |#2| (|IntegerNumberSystem|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|positive?| (((|Boolean|) $) NIL (|has| |#2| (|OrderedIntegralDomain|)))) (|patternMatch| (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (|has| |#2| (|PatternMatchable| (|Integer|)))) (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (|has| |#2| (|PatternMatchable| (|Float|))))) (|one?| (((|Boolean|) $) NIL)) (|numerator| (($ $) NIL)) (|numer| ((|#2| $) NIL)) (|nextItem| (((|Union| $ "failed") $) NIL (|has| |#2| (|StepThrough|)))) (|negative?| (((|Boolean|) $) NIL (|has| |#2| (|OrderedIntegralDomain|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|min| (($ $ $) NIL (|has| |#2| (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#2| (|OrderedSet|)))) (|map| (($ (|Mapping| |#2| |#2|) $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 49)) (|init| (($) NIL (|has| |#2| (|StepThrough|)) CONST)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|fractionPart| (($ $) NIL (|has| |#2| (|EuclideanDomain|)))) (|floor| ((|#2| $) NIL (|has| |#2| (|IntegerNumberSystem|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|eval| (($ $ (|List| |#2|) (|List| |#2|)) NIL (|has| |#2| (|Evalable| |#2|))) (($ $ |#2| |#2|) NIL (|has| |#2| (|Evalable| |#2|))) (($ $ (|Equation| |#2|)) NIL (|has| |#2| (|Evalable| |#2|))) (($ $ (|List| (|Equation| |#2|))) NIL (|has| |#2| (|Evalable| |#2|))) (($ $ (|List| (|Symbol|)) (|List| |#2|)) NIL (|has| |#2| (|InnerEvalable| (|Symbol|) |#2|))) (($ $ (|Symbol|) |#2|) NIL (|has| |#2| (|InnerEvalable| (|Symbol|) |#2|)))) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|elt| (($ $ |#2|) NIL (|has| |#2| (|Eltable| |#2| |#2|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|differentiate| (($ $) NIL (|has| |#2| (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#2| |#2|)) NIL)) (|denominator| (($ $) NIL)) (|denom| ((|#2| $) NIL)) (|convert| (((|Pattern| (|Integer|)) $) NIL (|has| |#2| (|ConvertibleTo| (|Pattern| (|Integer|))))) (((|Pattern| (|Float|)) $) NIL (|has| |#2| (|ConvertibleTo| (|Pattern| (|Float|))))) (((|InputForm|) $) NIL (|has| |#2| (|ConvertibleTo| (|InputForm|)))) (((|Float|) $) NIL (|has| |#2| (|RealConstant|))) (((|DoubleFloat|) $) NIL (|has| |#2| (|RealConstant|)))) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) 68)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#2| (|PolynomialFactorizationExplicit|))))) (|coerce| (((|OutputForm|) $) 85) (($ (|Integer|)) 19) (($ $) NIL) (($ (|Fraction| (|Integer|))) 24) (($ |#2|) 18) (($ (|Symbol|)) NIL (|has| |#2| (|RetractableTo| (|Symbol|))))) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#2| (|PolynomialFactorizationExplicit|))) (|has| |#2| (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|ceiling| ((|#2| $) NIL (|has| |#2| (|IntegerNumberSystem|)))) (|associates?| (((|Boolean|) $ $) NIL)) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) 60)) (|abs| (($ $) NIL (|has| |#2| (|OrderedIntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) 14 T CONST)) (|One| (($) 16 T CONST)) (D (($ $) NIL (|has| |#2| (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#2| |#2|)) NIL)) (>= (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (= (((|Boolean|) $ $) 35)) (<= (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (/ (($ $ $) 23) (($ |#2| |#2|) 54)) (- (($ $) 39) (($ $ $) 41)) (+ (($ $ $) 37)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) 50)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 42) (($ $ $) 44) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ |#2| $) 55) (($ $ |#2|) NIL))) 
(((|PAdicRationalConstructor| |#1| |#2|) (|Join| (|QuotientFieldCategory| |#2|) (CATEGORY |domain| (SIGNATURE |approximate| ((|Fraction| (|Integer|)) $ (|Integer|))) (SIGNATURE |continuedFraction| ((|ContinuedFraction| (|Fraction| (|Integer|))) $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |removeZeroes| ($ (|Integer|) $)))) (|Integer|) (|PAdicIntegerCategory| |#1|)) (T |PAdicRationalConstructor|)) 
((|approximate| (*1 *2 *1 *3) (AND (|ofType| *4 *3) (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|PAdicRationalConstructor| *4 *5)) (|isDomain| *3 (|Integer|)) (|ofCategory| *5 (|PAdicIntegerCategory| *4)))) (|continuedFraction| (*1 *2 *1) (AND (|ofType| *3 (|Integer|)) (|isDomain| *2 (|ContinuedFraction| (|Fraction| (|Integer|)))) (|isDomain| *1 (|PAdicRationalConstructor| *3 *4)) (|ofCategory| *4 (|PAdicIntegerCategory| *3)))) (|removeZeroes| (*1 *1 *1) (AND (|ofType| *2 (|Integer|)) (|isDomain| *1 (|PAdicRationalConstructor| *2 *3)) (|ofCategory| *3 (|PAdicIntegerCategory| *2)))) (|removeZeroes| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|ofType| *3 *2) (|isDomain| *1 (|PAdicRationalConstructor| *3 *4)) (|ofCategory| *4 (|PAdicIntegerCategory| *3))))) 
(|Join| (|QuotientFieldCategory| |#2|) (CATEGORY |domain| (SIGNATURE |approximate| ((|Fraction| (|Integer|)) $ (|Integer|))) (SIGNATURE |continuedFraction| ((|ContinuedFraction| (|Fraction| (|Integer|))) $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |removeZeroes| ($ (|Integer|) $)))) 
((|translateToOrigin| (((|DistributedMultivariatePolynomial| |#2| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|) (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|)) NIL)) (|theCurve| (((|DistributedMultivariatePolynomial| |#2| |#1|)) 107)) (|singularPoints| (((|List| (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|))) 116)) (|setSingularPoints| (((|List| (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|List| (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|))) 27)) (|setCurve| (((|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|)) 35)) (|rationalPoints| (((|List| (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|))) 60)) (|rationalPlaces| (((|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) 58)) (|projectivePoint| (((|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|) (|List| (|PseudoAlgebraicClosureOfFiniteField| |#1|))) 17)) (|pointDominateBy| (((|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) 21)) (|placesOfDegree| (((|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|PositiveInteger|)) 45 (|has| (|PseudoAlgebraicClosureOfFiniteField| |#1|) (|Finite|)))) (|placesAbove| (((|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|)) 24)) (|parametrize| (((|NeitherSparseOrDensePowerSeries| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) 119)) (|numberRatPlacesExtDeg| (((|Integer|) (|PositiveInteger|)) 47 (|has| (|PseudoAlgebraicClosureOfFiniteField| |#1|) (|Finite|)))) (|numberPlacesDegExtDeg| (((|Integer|) (|PositiveInteger|) (|PositiveInteger|)) 49 (|has| (|PseudoAlgebraicClosureOfFiniteField| |#1|) (|Finite|)))) (|numberOfPlacesOfDegree| (((|Integer|) (|PositiveInteger|)) 43 (|has| (|PseudoAlgebraicClosureOfFiniteField| |#1|) (|Finite|)))) (|lBasis| (((|Record| (|:| |num| (|List| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|:| |den| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) 62) (((|List| (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|NonNegativeInteger|)) NIL)) (|intersectionDivisor| (((|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|)) 135)) (|interpolateFormsForFact| (((|List| (|DistributedMultivariatePolynomial| |#2| (|PseudoAlgebraicClosureOfFiniteField| |#1|))) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|List| (|DistributedMultivariatePolynomial| |#2| |#1|))) 125)) (|interpolateForms| (((|List| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|NonNegativeInteger|)) 123)) (|homogenize| (((|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Integer|)) 13)) (|goppaCode| (((|Matrix| |#1|) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) 67) (((|Matrix| |#1|) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) 69)) (|genusNeg| (((|Integer|)) 105)) (|genus| (((|NonNegativeInteger|)) 103)) (|fullInfClsPt| (((|Void|)) 144)) (|fullDesTree| (((|Void|)) 140)) (|findOrderOfDivisor| (((|Record| (|:| |ord| (|Integer|)) (|:| |num| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|:| |den| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|:| |upTo| (|Integer|))) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|Integer|) (|Integer|)) 32)) (|evalIfCan| (((|Union| |#1| "failed") (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) 132) (((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) 127) (((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) 96)) (|eval| ((|#1| (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) 133) ((|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) 63) ((|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) 98)) (|desingTreeWoFullParam| (((|List| (|DesingTree| (|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |#1| |#2| |#3|)))) 112)) (|desingTree| (((|List| (|DesingTree| (|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |#1| |#2| |#3|)))) 110)) (|classNumber| (((|Integer|)) 56 (|has| (|PseudoAlgebraicClosureOfFiniteField| |#1|) (|Finite|)))) (|adjunctionDivisor| (((|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) 114)) (|ZetaFunction| (((|UnivariateTaylorSeriesCZero| (|Integer|) |t|) (|PositiveInteger|)) 41 (|has| (|PseudoAlgebraicClosureOfFiniteField| |#1|) (|Finite|))) (((|UnivariateTaylorSeriesCZero| (|Integer|) |t|)) 38 (|has| (|PseudoAlgebraicClosureOfFiniteField| |#1|) (|Finite|)))) (|LPolynomial| (((|SparseUnivariatePolynomial| (|Integer|)) (|PositiveInteger|)) 54 (|has| (|PseudoAlgebraicClosureOfFiniteField| |#1|) (|Finite|))) (((|SparseUnivariatePolynomial| (|Integer|))) 52 (|has| (|PseudoAlgebraicClosureOfFiniteField| |#1|) (|Finite|))))) 
(((|PackageForAlgebraicFunctionFieldOverFiniteField| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |homogenize| ((|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Integer|))) (SIGNATURE |fullDesTree| ((|Void|))) (SIGNATURE |fullInfClsPt| ((|Void|))) (SIGNATURE |setCurve| ((|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|))) (SIGNATURE |translateToOrigin| ((|DistributedMultivariatePolynomial| |#2| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|) (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |goppaCode| ((|Matrix| |#1|) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)))) (SIGNATURE |goppaCode| ((|Matrix| |#1|) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)))) (SIGNATURE |pointDominateBy| ((|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |placesAbove| ((|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |projectivePoint| ((|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|) (|List| (|PseudoAlgebraicClosureOfFiniteField| |#1|)))) (SIGNATURE |setSingularPoints| ((|List| (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|List| (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|)))) (SIGNATURE |rationalPlaces| ((|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)))) (SIGNATURE |theCurve| ((|DistributedMultivariatePolynomial| |#2| |#1|))) (SIGNATURE |genus| ((|NonNegativeInteger|))) (SIGNATURE |genusNeg| ((|Integer|))) (SIGNATURE |desingTreeWoFullParam| ((|List| (|DesingTree| (|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |#1| |#2| |#3|))))) (SIGNATURE |desingTree| ((|List| (|DesingTree| (|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |#1| |#2| |#3|))))) (SIGNATURE |rationalPoints| ((|List| (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|)))) (SIGNATURE |singularPoints| ((|List| (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|)))) (SIGNATURE |parametrize| ((|NeitherSparseOrDensePowerSeries| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |lBasis| ((|List| (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|NonNegativeInteger|))) (SIGNATURE |lBasis| ((|Record| (|:| |num| (|List| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|:| |den| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)))) (SIGNATURE |findOrderOfDivisor| ((|Record| (|:| |ord| (|Integer|)) (|:| |num| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|:| |den| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|:| |upTo| (|Integer|))) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|Integer|) (|Integer|))) (SIGNATURE |interpolateFormsForFact| ((|List| (|DistributedMultivariatePolynomial| |#2| (|PseudoAlgebraicClosureOfFiniteField| |#1|))) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|List| (|DistributedMultivariatePolynomial| |#2| |#1|)))) (SIGNATURE |interpolateForms| ((|List| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|NonNegativeInteger|))) (SIGNATURE |eval| (|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |eval| (|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |eval| (|#1| (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |intersectionDivisor| ((|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|))) (SIGNATURE |adjunctionDivisor| ((|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)))) (IF (|has| (|PseudoAlgebraicClosureOfFiniteField| |#1|) (|Finite|)) (PROGN (SIGNATURE |LPolynomial| ((|SparseUnivariatePolynomial| (|Integer|)))) (SIGNATURE |LPolynomial| ((|SparseUnivariatePolynomial| (|Integer|)) (|PositiveInteger|))) (SIGNATURE |classNumber| ((|Integer|))) (SIGNATURE |placesOfDegree| ((|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|PositiveInteger|))) (SIGNATURE |numberOfPlacesOfDegree| ((|Integer|) (|PositiveInteger|))) (SIGNATURE |numberRatPlacesExtDeg| ((|Integer|) (|PositiveInteger|))) (SIGNATURE |numberPlacesDegExtDeg| ((|Integer|) (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |ZetaFunction| ((|UnivariateTaylorSeriesCZero| (|Integer|) |t|))) (SIGNATURE |ZetaFunction| ((|UnivariateTaylorSeriesCZero| (|Integer|) |t|) (|PositiveInteger|)))) |noBranch|)) (|FiniteFieldCategory|) (|List| (|Symbol|)) (|BlowUpMethodCategory|)) (T |PackageForAlgebraicFunctionFieldOverFiniteField|)) 
((|ZetaFunction| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|UnivariateTaylorSeriesCZero| (|Integer|) |t|)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *4 *5 *6)) (|ofCategory| (|PseudoAlgebraicClosureOfFiniteField| *4) (|Finite|)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|ZetaFunction| (*1 *2) (AND (|isDomain| *2 (|UnivariateTaylorSeriesCZero| (|Integer|) |t|)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *3 *4 *5)) (|ofCategory| (|PseudoAlgebraicClosureOfFiniteField| *3) (|Finite|)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|numberPlacesDegExtDeg| (*1 *2 *3 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *4 *5 *6)) (|ofCategory| (|PseudoAlgebraicClosureOfFiniteField| *4) (|Finite|)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|numberRatPlacesExtDeg| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *4 *5 *6)) (|ofCategory| (|PseudoAlgebraicClosureOfFiniteField| *4) (|Finite|)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|numberOfPlacesOfDegree| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *4 *5 *6)) (|ofCategory| (|PseudoAlgebraicClosureOfFiniteField| *4) (|Finite|)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|placesOfDegree| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|List| 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(|ofCategory| *6 (|BlowUpMethodCategory|)))) (|LPolynomial| (*1 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *3 *4 *5)) (|ofCategory| (|PseudoAlgebraicClosureOfFiniteField| *3) (|Finite|)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|adjunctionDivisor| (*1 *2) (AND (|isDomain| *2 (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *3))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *3 *4 *5)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|intersectionDivisor| (*1 *2 *3) (AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *5 *4)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|ofType| *5 (|List| (|Symbol|))) (|isDomain| *2 (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *4))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *4 *5 *6)) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|evalIfCan| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Fraction| (|DistributedMultivariatePolynomial| *5 *2))) (|isDomain| *4 (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *2)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *2 (|FiniteFieldCategory|)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *2 *5 *6)) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|evalIfCan| (*1 *2 *3 *3 *4) (|partial| AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *5 *2)) (|isDomain| *4 (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *2)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *2 (|FiniteFieldCategory|)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *2 *5 *6)) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|evalIfCan| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *5 *2)) (|isDomain| *4 (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *2)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *2 (|FiniteFieldCategory|)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *2 *5 *6)) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|eval| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|DistributedMultivariatePolynomial| *5 *2))) (|isDomain| *4 (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *2)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *2 (|FiniteFieldCategory|)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *2 *5 *6)) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|eval| (*1 *2 *3 *3 *4) (AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *5 *2)) (|isDomain| *4 (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *2)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *2 (|FiniteFieldCategory|)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *2 *5 *6)) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|eval| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *5 *2)) (|isDomain| *4 (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *2)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *2 (|FiniteFieldCategory|)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *2 *5 *6)) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|interpolateForms| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *5))) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|FiniteFieldCategory|)) (|isDomain| *2 (|List| (|DistributedMultivariatePolynomial| *6 *5))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *5 *6 *7)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|BlowUpMethodCategory|)))) (|interpolateFormsForFact| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *5))) (|isDomain| *4 (|List| (|DistributedMultivariatePolynomial| *6 *5))) (|ofCategory| *5 (|FiniteFieldCategory|)) (|ofType| *6 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|DistributedMultivariatePolynomial| *6 (|PseudoAlgebraicClosureOfFiniteField| *5)))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *5 *6 *7)) (|ofCategory| *7 (|BlowUpMethodCategory|)))) (|findOrderOfDivisor| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *5))) (|ofCategory| *5 (|FiniteFieldCategory|)) (|isDomain| *2 (|Record| (|:| |ord| (|Integer|)) (|:| |num| (|DistributedMultivariatePolynomial| *6 *5)) (|:| |den| (|DistributedMultivariatePolynomial| *6 *5)) (|:| |upTo| (|Integer|)))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *5 *6 *7)) (|isDomain| *4 (|Integer|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|BlowUpMethodCategory|)))) (|lBasis| (*1 *2 *3) (AND (|isDomain| *3 (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *4))) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Record| (|:| |num| (|List| (|DistributedMultivariatePolynomial| *5 *4))) (|:| |den| (|DistributedMultivariatePolynomial| *5 *4)))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *4 *5 *6)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|lBasis| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *5))) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|FiniteFieldCategory|)) (|isDomain| *2 (|List| (|Fraction| (|DistributedMultivariatePolynomial| *6 *5)))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *5 *6 *7)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|BlowUpMethodCategory|)))) (|parametrize| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *6 *5)) (|isDomain| *4 (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *5)) (|ofCategory| *5 (|FiniteFieldCategory|)) (|ofType| *6 (|List| (|Symbol|))) (|isDomain| *2 (|NeitherSparseOrDensePowerSeries| (|PseudoAlgebraicClosureOfFiniteField| *5))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *5 *6 *7)) (|ofCategory| *7 (|BlowUpMethodCategory|)))) (|singularPoints| (*1 *2) (AND (|isDomain| *2 (|List| (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| *3))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *3 *4 *5)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|rationalPoints| (*1 *2) (AND (|isDomain| *2 (|List| (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| *3))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *3 *4 *5)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|desingTree| (*1 *2) (AND (|isDomain| *2 (|List| (|DesingTree| (|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| *3 *4 *5)))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *3 *4 *5)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|desingTreeWoFullParam| (*1 *2) (AND (|isDomain| *2 (|List| (|DesingTree| (|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| *3 *4 *5)))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *3 *4 *5)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|genusNeg| (*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *3 *4 *5)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|genus| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *3 *4 *5)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|theCurve| (*1 *2) (AND (|isDomain| *2 (|DistributedMultivariatePolynomial| *4 *3)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *3 *4 *5)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|rationalPlaces| (*1 *2) (AND (|isDomain| *2 (|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *3))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *3 *4 *5)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|setSingularPoints| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| *3))) (|ofCategory| *3 (|FiniteFieldCategory|)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *3 *4 *5)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|projectivePoint| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|PseudoAlgebraicClosureOfFiniteField| *4))) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| *4)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *4 *5 *6)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|placesAbove| (*1 *2 *3) (AND (|isDomain| *3 (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *4))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *4 *5 *6)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|pointDominateBy| (*1 *2 *3) (AND (|isDomain| *3 (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| *4)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *4 *5 *6)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|goppaCode| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *5))) (|isDomain| *4 (|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *5))) (|ofCategory| *5 (|FiniteFieldCategory|)) (|isDomain| *2 (|Matrix| *5)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *5 *6 *7)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|BlowUpMethodCategory|)))) (|goppaCode| (*1 *2 *3 *3) (AND (|isDomain| *3 (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| *4))) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *4 *5 *6)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|translateToOrigin| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *6 *5)) (|isDomain| *4 (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| *5)) (|ofCategory| *5 (|FiniteFieldCategory|)) (|ofType| *6 (|List| (|Symbol|))) (|isDomain| *2 (|DistributedMultivariatePolynomial| *6 (|PseudoAlgebraicClosureOfFiniteField| *5))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *5 *6 *7)) (|ofCategory| *7 (|BlowUpMethodCategory|)))) (|setCurve| (*1 *2 *2) (AND (|isDomain| *2 (|DistributedMultivariatePolynomial| *4 *3)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|List| (|Symbol|))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *3 *4 *5)) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|fullInfClsPt| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *3 *4 *5)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|fullDesTree| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *3 *4 *5)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|homogenize| (*1 *2 *2 *3) (AND (|isDomain| *2 (|DistributedMultivariatePolynomial| *5 *4)) (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|ofType| *5 (|List| (|Symbol|))) (|isDomain| *1 (|PackageForAlgebraicFunctionFieldOverFiniteField| *4 *5 *6)) (|ofCategory| *6 (|BlowUpMethodCategory|))))) 
(CATEGORY |package| (SIGNATURE |homogenize| ((|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Integer|))) (SIGNATURE |fullDesTree| ((|Void|))) (SIGNATURE |fullInfClsPt| ((|Void|))) (SIGNATURE |setCurve| ((|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|))) (SIGNATURE |translateToOrigin| ((|DistributedMultivariatePolynomial| |#2| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|) (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |goppaCode| ((|Matrix| |#1|) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)))) (SIGNATURE |goppaCode| ((|Matrix| |#1|) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)))) (SIGNATURE |pointDominateBy| ((|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |placesAbove| ((|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |projectivePoint| ((|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|) (|List| (|PseudoAlgebraicClosureOfFiniteField| |#1|)))) (SIGNATURE |setSingularPoints| ((|List| (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|List| (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|)))) (SIGNATURE |rationalPlaces| ((|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)))) (SIGNATURE |theCurve| ((|DistributedMultivariatePolynomial| |#2| |#1|))) (SIGNATURE |genus| ((|NonNegativeInteger|))) (SIGNATURE |genusNeg| ((|Integer|))) (SIGNATURE |desingTreeWoFullParam| ((|List| (|DesingTree| (|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |#1| |#2| |#3|))))) (SIGNATURE |desingTree| ((|List| (|DesingTree| (|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |#1| |#2| |#3|))))) (SIGNATURE |rationalPoints| ((|List| (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|)))) (SIGNATURE |singularPoints| ((|List| (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|)))) (SIGNATURE |parametrize| ((|NeitherSparseOrDensePowerSeries| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |lBasis| ((|List| (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|NonNegativeInteger|))) (SIGNATURE |lBasis| ((|Record| (|:| |num| (|List| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|:| |den| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)))) (SIGNATURE |findOrderOfDivisor| ((|Record| (|:| |ord| (|Integer|)) (|:| |num| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|:| |den| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|:| |upTo| (|Integer|))) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|Integer|) (|Integer|))) (SIGNATURE |interpolateFormsForFact| ((|List| (|DistributedMultivariatePolynomial| |#2| (|PseudoAlgebraicClosureOfFiniteField| |#1|))) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|List| (|DistributedMultivariatePolynomial| |#2| |#1|)))) (SIGNATURE |interpolateForms| ((|List| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|NonNegativeInteger|))) (SIGNATURE |eval| (|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |eval| (|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |eval| (|#1| (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) (SIGNATURE |intersectionDivisor| ((|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|))) (SIGNATURE |adjunctionDivisor| ((|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)))) (IF (|has| (|PseudoAlgebraicClosureOfFiniteField| |#1|) (|Finite|)) (PROGN (SIGNATURE |LPolynomial| ((|SparseUnivariatePolynomial| (|Integer|)))) (SIGNATURE |LPolynomial| ((|SparseUnivariatePolynomial| (|Integer|)) (|PositiveInteger|))) (SIGNATURE |classNumber| ((|Integer|))) (SIGNATURE |placesOfDegree| ((|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|PositiveInteger|))) (SIGNATURE |numberOfPlacesOfDegree| ((|Integer|) (|PositiveInteger|))) (SIGNATURE |numberRatPlacesExtDeg| ((|Integer|) (|PositiveInteger|))) (SIGNATURE |numberPlacesDegExtDeg| ((|Integer|) (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |ZetaFunction| ((|UnivariateTaylorSeriesCZero| (|Integer|) |t|))) (SIGNATURE |ZetaFunction| ((|UnivariateTaylorSeriesCZero| (|Integer|) |t|) (|PositiveInteger|)))) |noBranch|)) 
((|theCurve| (((|DistributedMultivariatePolynomial| |#2| |#1|)) 83)) (|singularPoints| (((|List| (|ProjectivePlane| |#1|))) 92)) (|setSingularPoints| (((|List| (|ProjectivePlane| |#1|)) (|List| (|ProjectivePlane| |#1|))) 24)) (|setCurve| (((|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|)) 75)) (|rationalPoints| (((|List| (|ProjectivePlane| |#1|))) 65)) (|rationalPlaces| (((|List| (|Places| |#1|))) 63)) (|projectivePoint| (((|ProjectivePlane| |#1|) (|List| |#1|)) 27)) (|pointDominateBy| (((|ProjectivePlane| |#1|) (|Places| |#1|)) 18)) (|placesOfDegree| (((|List| (|Places| |#1|)) (|PositiveInteger|)) 50 (|has| |#1| (|Finite|)))) (|placesAbove| (((|List| (|Places| |#1|)) (|ProjectivePlane| |#1|)) 21)) (|parametrize| (((|NeitherSparseOrDensePowerSeries| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|)) 95)) (|numberRatPlacesExtDeg| (((|Integer|) (|PositiveInteger|)) 52 (|has| |#1| (|Finite|)))) (|numberPlacesDegExtDeg| (((|Integer|) (|PositiveInteger|) (|PositiveInteger|)) 54 (|has| |#1| (|Finite|)))) (|numberOfPlacesOfDegree| (((|Integer|) (|PositiveInteger|)) 48 (|has| |#1| (|Finite|)))) (|lBasis| (((|Record| (|:| |num| (|List| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|:| |den| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|Divisor| (|Places| |#1|))) 33) (((|List| (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|Divisor| (|Places| |#1|)) (|NonNegativeInteger|)) NIL)) (|intersectionDivisor| (((|Divisor| (|Places| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|)) 107)) (|interpolateFormsForFact| (((|List| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Divisor| (|Places| |#1|)) (|List| (|DistributedMultivariatePolynomial| |#2| |#1|))) 31)) (|interpolateForms| (((|List| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Divisor| (|Places| |#1|)) (|NonNegativeInteger|)) 97)) (|homogenize| (((|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Integer|)) 13)) (|goppaCode| (((|Matrix| |#1|) (|Divisor| (|Places| |#1|)) (|List| (|Places| |#1|))) 38) (((|Matrix| |#1|) (|Divisor| (|Places| |#1|)) (|Divisor| (|Places| |#1|))) 40)) (|genusNeg| (((|Integer|)) 81)) (|genus| (((|NonNegativeInteger|)) 79)) (|fullInfClsPt| (((|Void|)) 116)) (|fullDesTree| (((|Void|)) 112)) (|findOrderOfDivisor| (((|Record| (|:| |ord| (|Integer|)) (|:| |num| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|:| |den| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|:| |upTo| (|Integer|))) (|Divisor| (|Places| |#1|)) (|Integer|) (|Integer|)) NIL)) (|evalIfCan| (((|Union| |#1| "failed") (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Places| |#1|)) 105) (((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|)) 104) (((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|)) 73)) (|eval| ((|#1| (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Places| |#1|)) 102) ((|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|)) 34) ((|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|)) 70)) (|desingTreeWoFullParam| (((|List| (|DesingTree| (|InfClsPt| |#1| |#2| |#3|)))) 88)) (|desingTree| (((|List| (|DesingTree| (|InfClsPt| |#1| |#2| |#3|)))) 86)) (|classNumber| (((|Integer|)) 61 (|has| |#1| (|Finite|)))) (|adjunctionDivisor| (((|Divisor| (|Places| |#1|))) 90)) (|ZetaFunction| (((|UnivariateTaylorSeriesCZero| (|Integer|) |t|) (|PositiveInteger|)) 46 (|has| |#1| (|Finite|))) (((|UnivariateTaylorSeriesCZero| (|Integer|) |t|)) 43 (|has| |#1| (|Finite|)))) (|LPolynomial| (((|SparseUnivariatePolynomial| (|Integer|)) (|PositiveInteger|)) 59 (|has| |#1| (|Finite|))) (((|SparseUnivariatePolynomial| (|Integer|))) 57 (|has| |#1| (|Finite|))))) 
(((|PackageForAlgebraicFunctionField| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |homogenize| ((|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Integer|))) (SIGNATURE |interpolateFormsForFact| ((|List| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Divisor| (|Places| |#1|)) (|List| (|DistributedMultivariatePolynomial| |#2| |#1|)))) (SIGNATURE |fullDesTree| ((|Void|))) (SIGNATURE |fullInfClsPt| ((|Void|))) (SIGNATURE |setCurve| ((|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|))) (SIGNATURE |projectivePoint| ((|ProjectivePlane| |#1|) (|List| |#1|))) (SIGNATURE |pointDominateBy| ((|ProjectivePlane| |#1|) (|Places| |#1|))) (SIGNATURE |placesAbove| ((|List| (|Places| |#1|)) (|ProjectivePlane| |#1|))) (SIGNATURE |setSingularPoints| ((|List| (|ProjectivePlane| |#1|)) (|List| (|ProjectivePlane| |#1|)))) (SIGNATURE |goppaCode| ((|Matrix| |#1|) (|Divisor| (|Places| |#1|)) (|Divisor| (|Places| |#1|)))) (SIGNATURE |goppaCode| ((|Matrix| |#1|) (|Divisor| (|Places| |#1|)) (|List| (|Places| |#1|)))) (SIGNATURE |rationalPlaces| ((|List| (|Places| |#1|)))) (SIGNATURE |theCurve| ((|DistributedMultivariatePolynomial| |#2| |#1|))) (SIGNATURE |genus| ((|NonNegativeInteger|))) (SIGNATURE |genusNeg| ((|Integer|))) (SIGNATURE |desingTreeWoFullParam| ((|List| (|DesingTree| (|InfClsPt| |#1| |#2| |#3|))))) (SIGNATURE |desingTree| ((|List| (|DesingTree| (|InfClsPt| |#1| |#2| |#3|))))) (SIGNATURE |rationalPoints| ((|List| (|ProjectivePlane| |#1|)))) (SIGNATURE |singularPoints| ((|List| (|ProjectivePlane| |#1|)))) (SIGNATURE |parametrize| ((|NeitherSparseOrDensePowerSeries| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|))) (SIGNATURE |lBasis| ((|List| (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|Divisor| (|Places| |#1|)) (|NonNegativeInteger|))) (SIGNATURE |lBasis| ((|Record| (|:| |num| (|List| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|:| |den| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|Divisor| (|Places| |#1|)))) (SIGNATURE |findOrderOfDivisor| ((|Record| (|:| |ord| (|Integer|)) (|:| |num| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|:| |den| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|:| |upTo| (|Integer|))) (|Divisor| (|Places| |#1|)) (|Integer|) (|Integer|))) (SIGNATURE |interpolateForms| ((|List| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Divisor| (|Places| |#1|)) (|NonNegativeInteger|))) (SIGNATURE |eval| (|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|))) (SIGNATURE |eval| (|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|))) (SIGNATURE |eval| (|#1| (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Places| |#1|))) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|))) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|))) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Places| |#1|))) (SIGNATURE |intersectionDivisor| ((|Divisor| (|Places| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|))) (SIGNATURE |adjunctionDivisor| ((|Divisor| (|Places| |#1|)))) (IF (|has| |#1| (|Finite|)) (PROGN (SIGNATURE |LPolynomial| ((|SparseUnivariatePolynomial| (|Integer|)))) (SIGNATURE |LPolynomial| ((|SparseUnivariatePolynomial| (|Integer|)) (|PositiveInteger|))) (SIGNATURE |classNumber| ((|Integer|))) (SIGNATURE |placesOfDegree| ((|List| (|Places| |#1|)) (|PositiveInteger|))) (SIGNATURE |numberOfPlacesOfDegree| ((|Integer|) (|PositiveInteger|))) (SIGNATURE |numberRatPlacesExtDeg| ((|Integer|) (|PositiveInteger|))) (SIGNATURE |numberPlacesDegExtDeg| ((|Integer|) (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |ZetaFunction| ((|UnivariateTaylorSeriesCZero| (|Integer|) |t|))) (SIGNATURE |ZetaFunction| ((|UnivariateTaylorSeriesCZero| (|Integer|) |t|) (|PositiveInteger|)))) |noBranch|)) (|Field|) (|List| (|Symbol|)) (|BlowUpMethodCategory|)) (T |PackageForAlgebraicFunctionField|)) 
((|ZetaFunction| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|UnivariateTaylorSeriesCZero| (|Integer|) |t|)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *4 *5 *6)) (|ofCategory| *4 (|Finite|)) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|ZetaFunction| (*1 *2) (AND (|isDomain| *2 (|UnivariateTaylorSeriesCZero| (|Integer|) |t|)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *3 *4 *5)) (|ofCategory| *3 (|Finite|)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|numberPlacesDegExtDeg| (*1 *2 *3 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *4 *5 *6)) (|ofCategory| *4 (|Finite|)) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|numberRatPlacesExtDeg| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *4 *5 *6)) (|ofCategory| *4 (|Finite|)) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|numberOfPlacesOfDegree| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *4 *5 *6)) (|ofCategory| *4 (|Finite|)) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|placesOfDegree| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|List| (|Places| *4))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *4 *5 *6)) (|ofCategory| *4 (|Finite|)) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|classNumber| (*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *3 *4 *5)) (|ofCategory| *3 (|Finite|)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|LPolynomial| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *4 *5 *6)) (|ofCategory| *4 (|Finite|)) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|LPolynomial| (*1 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *3 *4 *5)) (|ofCategory| *3 (|Finite|)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|adjunctionDivisor| (*1 *2) (AND (|isDomain| *2 (|Divisor| (|Places| *3))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|intersectionDivisor| (*1 *2 *3) (AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *5 *4)) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|isDomain| *2 (|Divisor| (|Places| *4))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *4 *5 *6)) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|evalIfCan| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Fraction| (|DistributedMultivariatePolynomial| *5 *2))) (|isDomain| *4 (|Places| *2)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *2 *5 *6)) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|evalIfCan| (*1 *2 *3 *3 *4) (|partial| AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *5 *2)) (|isDomain| *4 (|Places| *2)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *2 *5 *6)) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|evalIfCan| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *5 *2)) (|isDomain| *4 (|Places| *2)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *2 *5 *6)) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|eval| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|DistributedMultivariatePolynomial| *5 *2))) (|isDomain| *4 (|Places| *2)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *2 *5 *6)) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|eval| (*1 *2 *3 *3 *4) (AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *5 *2)) (|isDomain| *4 (|Places| *2)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *2 *5 *6)) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|eval| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *5 *2)) (|isDomain| *4 (|Places| *2)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *2 *5 *6)) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|interpolateForms| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Divisor| (|Places| *5))) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|List| (|DistributedMultivariatePolynomial| *6 *5))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *5 *6 *7)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|BlowUpMethodCategory|)))) (|findOrderOfDivisor| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|Divisor| (|Places| *5))) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Record| (|:| |ord| (|Integer|)) (|:| |num| (|DistributedMultivariatePolynomial| *6 *5)) (|:| |den| (|DistributedMultivariatePolynomial| *6 *5)) (|:| |upTo| (|Integer|)))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *5 *6 *7)) (|isDomain| *4 (|Integer|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|BlowUpMethodCategory|)))) (|lBasis| (*1 *2 *3) (AND (|isDomain| *3 (|Divisor| (|Places| *4))) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|Record| (|:| |num| (|List| (|DistributedMultivariatePolynomial| *5 *4))) (|:| |den| (|DistributedMultivariatePolynomial| *5 *4)))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *4 *5 *6)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|lBasis| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Divisor| (|Places| *5))) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|List| (|Fraction| (|DistributedMultivariatePolynomial| *6 *5)))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *5 *6 *7)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|BlowUpMethodCategory|)))) (|parametrize| (*1 *2 *3 *4) (AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *6 *5)) (|isDomain| *4 (|Places| *5)) (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|isDomain| *2 (|NeitherSparseOrDensePowerSeries| *5)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *5 *6 *7)) (|ofCategory| *7 (|BlowUpMethodCategory|)))) (|singularPoints| (*1 *2) (AND (|isDomain| *2 (|List| (|ProjectivePlane| *3))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|rationalPoints| (*1 *2) (AND (|isDomain| *2 (|List| (|ProjectivePlane| *3))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|desingTree| (*1 *2) (AND (|isDomain| *2 (|List| (|DesingTree| (|InfClsPt| *3 *4 *5)))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|desingTreeWoFullParam| (*1 *2) (AND (|isDomain| *2 (|List| (|DesingTree| (|InfClsPt| *3 *4 *5)))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|genusNeg| (*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|genus| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|theCurve| (*1 *2) (AND (|isDomain| *2 (|DistributedMultivariatePolynomial| *4 *3)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|rationalPlaces| (*1 *2) (AND (|isDomain| *2 (|List| (|Places| *3))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|goppaCode| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Divisor| (|Places| *5))) (|isDomain| *4 (|List| (|Places| *5))) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Matrix| *5)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *5 *6 *7)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|BlowUpMethodCategory|)))) (|goppaCode| (*1 *2 *3 *3) (AND (|isDomain| *3 (|Divisor| (|Places| *4))) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *4 *5 *6)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|setSingularPoints| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|ProjectivePlane| *3))) (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *3 *4 *5)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|placesAbove| (*1 *2 *3) (AND (|isDomain| *3 (|ProjectivePlane| *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|List| (|Places| *4))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *4 *5 *6)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|pointDominateBy| (*1 *2 *3) (AND (|isDomain| *3 (|Places| *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|ProjectivePlane| *4)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *4 *5 *6)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|projectivePoint| (*1 *2 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|ProjectivePlane| *4)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *4 *5 *6)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|setCurve| (*1 *2 *2) (AND (|isDomain| *2 (|DistributedMultivariatePolynomial| *4 *3)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *3 *4 *5)) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|fullInfClsPt| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|fullDesTree| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|BlowUpMethodCategory|)))) (|interpolateFormsForFact| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| (|DistributedMultivariatePolynomial| *5 *4))) (|isDomain| *3 (|Divisor| (|Places| *4))) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *4 *5 *6)) (|ofCategory| *6 (|BlowUpMethodCategory|)))) (|homogenize| (*1 *2 *2 *3) (AND (|isDomain| *2 (|DistributedMultivariatePolynomial| *5 *4)) (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|isDomain| *1 (|PackageForAlgebraicFunctionField| *4 *5 *6)) (|ofCategory| *6 (|BlowUpMethodCategory|))))) 
(CATEGORY |package| (SIGNATURE |homogenize| ((|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Integer|))) (SIGNATURE |interpolateFormsForFact| ((|List| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Divisor| (|Places| |#1|)) (|List| (|DistributedMultivariatePolynomial| |#2| |#1|)))) (SIGNATURE |fullDesTree| ((|Void|))) (SIGNATURE |fullInfClsPt| ((|Void|))) (SIGNATURE |setCurve| ((|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|))) (SIGNATURE |projectivePoint| ((|ProjectivePlane| |#1|) (|List| |#1|))) (SIGNATURE |pointDominateBy| ((|ProjectivePlane| |#1|) (|Places| |#1|))) (SIGNATURE |placesAbove| ((|List| (|Places| |#1|)) (|ProjectivePlane| |#1|))) (SIGNATURE |setSingularPoints| ((|List| (|ProjectivePlane| |#1|)) (|List| (|ProjectivePlane| |#1|)))) (SIGNATURE |goppaCode| ((|Matrix| |#1|) (|Divisor| (|Places| |#1|)) (|Divisor| (|Places| |#1|)))) (SIGNATURE |goppaCode| ((|Matrix| |#1|) (|Divisor| (|Places| |#1|)) (|List| (|Places| |#1|)))) (SIGNATURE |rationalPlaces| ((|List| (|Places| |#1|)))) (SIGNATURE |theCurve| ((|DistributedMultivariatePolynomial| |#2| |#1|))) (SIGNATURE |genus| ((|NonNegativeInteger|))) (SIGNATURE |genusNeg| ((|Integer|))) (SIGNATURE |desingTreeWoFullParam| ((|List| (|DesingTree| (|InfClsPt| |#1| |#2| |#3|))))) (SIGNATURE |desingTree| ((|List| (|DesingTree| (|InfClsPt| |#1| |#2| |#3|))))) (SIGNATURE |rationalPoints| ((|List| (|ProjectivePlane| |#1|)))) (SIGNATURE |singularPoints| ((|List| (|ProjectivePlane| |#1|)))) (SIGNATURE |parametrize| ((|NeitherSparseOrDensePowerSeries| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|))) (SIGNATURE |lBasis| ((|List| (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|Divisor| (|Places| |#1|)) (|NonNegativeInteger|))) (SIGNATURE |lBasis| ((|Record| (|:| |num| (|List| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|:| |den| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|Divisor| (|Places| |#1|)))) (SIGNATURE |findOrderOfDivisor| ((|Record| (|:| |ord| (|Integer|)) (|:| |num| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|:| |den| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|:| |upTo| (|Integer|))) (|Divisor| (|Places| |#1|)) (|Integer|) (|Integer|))) (SIGNATURE |interpolateForms| ((|List| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Divisor| (|Places| |#1|)) (|NonNegativeInteger|))) (SIGNATURE |eval| (|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|))) (SIGNATURE |eval| (|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|))) (SIGNATURE |eval| (|#1| (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Places| |#1|))) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|))) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|))) (SIGNATURE |evalIfCan| ((|Union| |#1| "failed") (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Places| |#1|))) (SIGNATURE |intersectionDivisor| ((|Divisor| (|Places| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|))) (SIGNATURE |adjunctionDivisor| ((|Divisor| (|Places| |#1|)))) (IF (|has| |#1| (|Finite|)) (PROGN (SIGNATURE |LPolynomial| ((|SparseUnivariatePolynomial| (|Integer|)))) (SIGNATURE |LPolynomial| ((|SparseUnivariatePolynomial| (|Integer|)) (|PositiveInteger|))) (SIGNATURE |classNumber| ((|Integer|))) (SIGNATURE |placesOfDegree| ((|List| (|Places| |#1|)) (|PositiveInteger|))) (SIGNATURE |numberOfPlacesOfDegree| ((|Integer|) (|PositiveInteger|))) (SIGNATURE |numberRatPlacesExtDeg| ((|Integer|) (|PositiveInteger|))) (SIGNATURE |numberPlacesDegExtDeg| ((|Integer|) (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |ZetaFunction| ((|UnivariateTaylorSeriesCZero| (|Integer|) |t|))) (SIGNATURE |ZetaFunction| ((|UnivariateTaylorSeriesCZero| (|Integer|) |t|) (|PositiveInteger|)))) |noBranch|)) 
((~= (((|Boolean|) $ $) NIL)) (|shade| (((|Integer|) $) 15)) (|pastel| (($ (|Color|)) 11)) (|light| (($ (|Color|)) 12)) (|latex| (((|String|) $) NIL)) (|hue| (((|Color|) $) 13)) (|hash| (((|SingleInteger|) $) NIL)) (|dim| (($ (|Color|)) 9)) (|dark| (($ (|Color|)) 8)) (|coerce| (((|OutputForm|) $) 23) (($ (|Color|)) 16)) (|bright| (($ (|Color|)) 10)) (= (((|Boolean|) $ $) NIL))) 
(((|Palette|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |dark| ($ (|Color|))) (SIGNATURE |dim| ($ (|Color|))) (SIGNATURE |bright| ($ (|Color|))) (SIGNATURE |pastel| ($ (|Color|))) (SIGNATURE |light| ($ (|Color|))) (SIGNATURE |hue| ((|Color|) $)) (SIGNATURE |shade| ((|Integer|) $)) (SIGNATURE |coerce| ($ (|Color|)))))) (T |Palette|)) 
((|dark| (*1 *1 *2) (AND (|isDomain| *2 (|Color|)) (|isDomain| *1 (|Palette|)))) (|dim| (*1 *1 *2) (AND (|isDomain| *2 (|Color|)) (|isDomain| *1 (|Palette|)))) (|bright| (*1 *1 *2) (AND (|isDomain| *2 (|Color|)) (|isDomain| *1 (|Palette|)))) (|pastel| (*1 *1 *2) (AND (|isDomain| *2 (|Color|)) (|isDomain| *1 (|Palette|)))) (|light| (*1 *1 *2) (AND (|isDomain| *2 (|Color|)) (|isDomain| *1 (|Palette|)))) (|hue| (*1 *2 *1) (AND (|isDomain| *2 (|Color|)) (|isDomain| *1 (|Palette|)))) (|shade| (*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Palette|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Color|)) (|isDomain| *1 (|Palette|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |dark| ($ (|Color|))) (SIGNATURE |dim| ($ (|Color|))) (SIGNATURE |bright| ($ (|Color|))) (SIGNATURE |pastel| ($ (|Color|))) (SIGNATURE |light| ($ (|Color|))) (SIGNATURE |hue| ((|Color|) $)) (SIGNATURE |shade| ((|Integer|) $)) (SIGNATURE |coerce| ($ (|Color|))))) 
((|coerce| (((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|)))) 21) (((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|))) 16))) 
(((|PolynomialAN2Expression|) (CATEGORY |package| (SIGNATURE |coerce| ((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|)))) (SIGNATURE |coerce| ((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|))))))) (T |PolynomialAN2Expression|)) 
((|coerce| (*1 *2 *3) (AND (|isDomain| *3 (|Fraction| (|Polynomial| (|AlgebraicNumber|)))) (|isDomain| *2 (|Expression| (|Integer|))) (|isDomain| *1 (|PolynomialAN2Expression|)))) (|coerce| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| (|AlgebraicNumber|))) (|isDomain| *2 (|Expression| (|Integer|))) (|isDomain| *1 (|PolynomialAN2Expression|))))) 
(CATEGORY |package| (SIGNATURE |coerce| ((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|)))) (SIGNATURE |coerce| ((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|)))))) 
((|parametrize| ((|#6| |#3| |#7| (|Integer|)) 36) ((|#6| |#3| |#3| |#7|) 33) ((|#6| |#3| |#7|) 31) ((|#6| |#3| (|List| |#6|)) 28))) 
(((|ParametrizationPackage| |#1| |#2| |#3| |#4| |#5| |#6| |#7|) (CATEGORY |package| (SIGNATURE |parametrize| (|#6| |#3| (|List| |#6|))) (SIGNATURE |parametrize| (|#6| |#3| |#7|)) (SIGNATURE |parametrize| (|#6| |#3| |#3| |#7|)) (SIGNATURE |parametrize| (|#6| |#3| |#7| (|Integer|)))) (|Field|) (|List| (|Symbol|)) (|PolynomialCategory| |#1| |#4| (|OrderedVariableList| |#2|)) (|DirectProductCategory| (|#| |#2|) (|NonNegativeInteger|)) (|ProjectiveSpaceCategory| |#1|) (|LocalPowerSeriesCategory| |#1|) (|PlacesCategory| |#1| |#6|)) (T |ParametrizationPackage|)) 
((|parametrize| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|Integer|)) (|ofCategory| *6 (|Field|)) (|ofType| *7 (|List| (|Symbol|))) (|ofCategory| *8 (|DirectProductCategory| (|#| *7) (|NonNegativeInteger|))) (|ofCategory| *2 (|LocalPowerSeriesCategory| *6)) (|isDomain| *1 (|ParametrizationPackage| *6 *7 *3 *8 *9 *2 *4)) (|ofCategory| *3 (|PolynomialCategory| *6 *8 (|OrderedVariableList| *7))) (|ofCategory| *9 (|ProjectiveSpaceCategory| *6)) (|ofCategory| *4 (|PlacesCategory| *6 *2)))) (|parametrize| (*1 *2 *3 *3 *4) (AND (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|DirectProductCategory| (|#| *6) (|NonNegativeInteger|))) (|ofCategory| *2 (|LocalPowerSeriesCategory| *5)) (|isDomain| *1 (|ParametrizationPackage| *5 *6 *3 *7 *8 *2 *4)) (|ofCategory| *3 (|PolynomialCategory| *5 *7 (|OrderedVariableList| *6))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *5)) (|ofCategory| *4 (|PlacesCategory| *5 *2)))) (|parametrize| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|DirectProductCategory| (|#| *6) (|NonNegativeInteger|))) (|ofCategory| *2 (|LocalPowerSeriesCategory| *5)) (|isDomain| *1 (|ParametrizationPackage| *5 *6 *3 *7 *8 *2 *4)) (|ofCategory| *3 (|PolynomialCategory| *5 *7 (|OrderedVariableList| *6))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *5)) (|ofCategory| *4 (|PlacesCategory| *5 *2)))) (|parametrize| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *2)) (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|DirectProductCategory| (|#| *6) (|NonNegativeInteger|))) (|ofCategory| *2 (|LocalPowerSeriesCategory| *5)) (|isDomain| *1 (|ParametrizationPackage| *5 *6 *3 *7 *8 *2 *9)) (|ofCategory| *3 (|PolynomialCategory| *5 *7 (|OrderedVariableList| *6))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *5)) (|ofCategory| *9 (|PlacesCategory| *5 *2))))) 
(CATEGORY |package| (SIGNATURE |parametrize| (|#6| |#3| (|List| |#6|))) (SIGNATURE |parametrize| (|#6| |#3| |#7|)) (SIGNATURE |parametrize| (|#6| |#3| |#3| |#7|)) (SIGNATURE |parametrize| (|#6| |#3| |#7| (|Integer|)))) 
((|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) 14))) 
(((|ParametricPlaneCurveFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)))) (|Type|) (|Type|)) (T |ParametricPlaneCurveFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|ParametricPlaneCurve| *5)) (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|ParametricPlaneCurve| *6)) (|isDomain| *1 (|ParametricPlaneCurveFunctions2| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |map| ((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)))) 
((|curve| (($ |#1| |#1|) 8)) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) 10))) 
(((|ParametricPlaneCurve| |#1|) (CATEGORY |domain| (SIGNATURE |curve| ($ |#1| |#1|)) (SIGNATURE |coordinate| (|#1| $ (|NonNegativeInteger|)))) (|Type|)) (T |ParametricPlaneCurve|)) 
((|coordinate| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|ParametricPlaneCurve| *2)) (|ofCategory| *2 (|Type|)))) (|curve| (*1 *1 *2 *2) (AND (|isDomain| *1 (|ParametricPlaneCurve| *2)) (|ofCategory| *2 (|Type|))))) 
(CATEGORY |domain| (SIGNATURE |curve| ($ |#1| |#1|)) (SIGNATURE |coordinate| (|#1| $ (|NonNegativeInteger|)))) 
((|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) 14))) 
(((|ParametricSpaceCurveFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)))) (|Type|) (|Type|)) (T |ParametricSpaceCurveFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|ParametricSpaceCurve| *5)) (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|ParametricSpaceCurve| *6)) (|isDomain| *1 (|ParametricSpaceCurveFunctions2| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |map| ((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)))) 
((|curve| (($ |#1| |#1| |#1|) 8)) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) 10))) 
(((|ParametricSpaceCurve| |#1|) (CATEGORY |domain| (SIGNATURE |curve| ($ |#1| |#1| |#1|)) (SIGNATURE |coordinate| (|#1| $ (|NonNegativeInteger|)))) (|Type|)) (T |ParametricSpaceCurve|)) 
((|coordinate| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|ParametricSpaceCurve| *2)) (|ofCategory| *2 (|Type|)))) (|curve| (*1 *1 *2 *2 *2) (AND (|isDomain| *1 (|ParametricSpaceCurve| *2)) (|ofCategory| *2 (|Type|))))) 
(CATEGORY |domain| (SIGNATURE |curve| ($ |#1| |#1| |#1|)) (SIGNATURE |coordinate| (|#1| $ (|NonNegativeInteger|)))) 
((|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) 14))) 
(((|ParametricSurfaceFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)))) (|Type|) (|Type|)) (T |ParametricSurfaceFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|ParametricSurface| *5)) (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|ParametricSurface| *6)) (|isDomain| *1 (|ParametricSurfaceFunctions2| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |map| ((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)))) 
((|surface| (($ |#1| |#1| |#1|) 8)) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) 10))) 
(((|ParametricSurface| |#1|) (CATEGORY |domain| (SIGNATURE |surface| ($ |#1| |#1| |#1|)) (SIGNATURE |coordinate| (|#1| $ (|NonNegativeInteger|)))) (|Type|)) (T |ParametricSurface|)) 
((|coordinate| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|ParametricSurface| *2)) (|ofCategory| *2 (|Type|)))) (|surface| (*1 *1 *2 *2 *2) (AND (|isDomain| *1 (|ParametricSurface| *2)) (|ofCategory| *2 (|Type|))))) 
(CATEGORY |domain| (SIGNATURE |surface| ($ |#1| |#1| |#1|)) (SIGNATURE |coordinate| (|#1| $ (|NonNegativeInteger|)))) 
((|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) 30)) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) 26)) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) 39) (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) 38)) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) 40)) (|partitions| (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|)) 22) (((|Stream| (|List| (|Integer|))) (|Integer|)) 16) (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|) (|Integer|)) 12)) (|conjugates| (((|Stream| (|List| (|Integer|))) (|Stream| (|List| (|Integer|)))) 24)) (|conjugate| (((|List| (|Integer|)) (|List| (|Integer|))) 23))) 
(((|PartitionsAndPermutations|) (CATEGORY |package| (SIGNATURE |partitions| ((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |partitions| ((|Stream| (|List| (|Integer|))) (|Integer|))) (SIGNATURE |partitions| ((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|))) (SIGNATURE |conjugate| ((|List| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |conjugates| ((|Stream| (|List| (|Integer|))) (|Stream| (|List| (|Integer|))))) (SIGNATURE |shuffle| ((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |shufflein| ((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|))))) (SIGNATURE |sequences| ((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |sequences| ((|Stream| (|List| (|Integer|))) (|List| (|Integer|)))) (SIGNATURE |permutations| ((|Stream| (|List| (|Integer|))) (|Integer|))))) (T |PartitionsAndPermutations|)) 
((|permutations| (*1 *2 *3) (AND (|isDomain| *2 (|Stream| (|List| (|Integer|)))) (|isDomain| *1 (|PartitionsAndPermutations|)) (|isDomain| *3 (|Integer|)))) (|sequences| (*1 *2 *3) (AND (|isDomain| *2 (|Stream| (|List| (|Integer|)))) (|isDomain| *1 (|PartitionsAndPermutations|)) (|isDomain| *3 (|List| (|Integer|))))) (|sequences| (*1 *2 *3 *3) (AND (|isDomain| *2 (|Stream| (|List| (|Integer|)))) (|isDomain| *1 (|PartitionsAndPermutations|)) (|isDomain| *3 (|List| (|Integer|))))) (|shufflein| (*1 *2 *3 *2) (AND (|isDomain| *2 (|Stream| (|List| (|Integer|)))) (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *1 (|PartitionsAndPermutations|)))) (|shuffle| (*1 *2 *3 *3) (AND (|isDomain| *2 (|Stream| (|List| (|Integer|)))) (|isDomain| *1 (|PartitionsAndPermutations|)) (|isDomain| *3 (|List| (|Integer|))))) (|conjugates| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| (|List| (|Integer|)))) (|isDomain| *1 (|PartitionsAndPermutations|)))) (|conjugate| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|PartitionsAndPermutations|)))) (|partitions| (*1 *2 *3 *3) (AND (|isDomain| *2 (|Stream| (|List| (|Integer|)))) (|isDomain| *1 (|PartitionsAndPermutations|)) (|isDomain| *3 (|Integer|)))) (|partitions| (*1 *2 *3) (AND (|isDomain| *2 (|Stream| (|List| (|Integer|)))) (|isDomain| *1 (|PartitionsAndPermutations|)) (|isDomain| *3 (|Integer|)))) (|partitions| (*1 *2 *3 *3 *3) (AND (|isDomain| *2 (|Stream| (|List| (|Integer|)))) (|isDomain| *1 (|PartitionsAndPermutations|)) (|isDomain| *3 (|Integer|))))) 
(CATEGORY |package| (SIGNATURE |partitions| ((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |partitions| ((|Stream| (|List| (|Integer|))) (|Integer|))) (SIGNATURE |partitions| ((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|))) (SIGNATURE |conjugate| ((|List| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |conjugates| ((|Stream| (|List| (|Integer|))) (|Stream| (|List| (|Integer|))))) (SIGNATURE |shuffle| ((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |shufflein| ((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|))))) (SIGNATURE |sequences| ((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |sequences| ((|Stream| (|List| (|Integer|))) (|List| (|Integer|)))) (SIGNATURE |permutations| ((|Stream| (|List| (|Integer|))) (|Integer|)))) 
((|convert| (((|Pattern| (|Float|)) $) 9 (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|))))) (((|Pattern| (|Integer|)) $) 8 (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|))))))) 
(((|Patternable| |#1|) (|Category|) (|Type|)) (T |Patternable|)) 
NIL 
(|Join| (CATEGORY |package| (IF (|has| |t#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (ATTRIBUTE (|ConvertibleTo| (|Pattern| (|Integer|)))) |noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|Pattern| (|Float|)))) (ATTRIBUTE (|ConvertibleTo| (|Pattern| (|Float|)))) |noBranch|))) 
(((|ConvertibleTo| (|Pattern| (|Float|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) ((|ConvertibleTo| (|Pattern| (|Integer|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|))))) 
((~= (((|Boolean|) $ $) NIL)) (|new| (($) 14)) (|makeResult| (($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|)) 27)) (|lists| (((|PatternMatchResult| |#1| |#3|) $) 16)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|failed?| (((|Boolean|) $) 22)) (|failed| (($) 19)) (|coerce| (((|OutputForm|) $) 30)) (|atoms| (((|PatternMatchResult| |#1| |#2|) $) 15)) (= (((|Boolean|) $ $) 25))) 
(((|PatternMatchListResult| |#1| |#2| |#3|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |failed?| ((|Boolean|) $)) (SIGNATURE |failed| ($)) (SIGNATURE |new| ($)) (SIGNATURE |makeResult| ($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|))) (SIGNATURE |atoms| ((|PatternMatchResult| |#1| |#2|) $)) (SIGNATURE |lists| ((|PatternMatchResult| |#1| |#3|) $)))) (|SetCategory|) (|SetCategory|) (|ListAggregate| |#2|)) (T |PatternMatchListResult|)) 
((|failed?| (*1 *2 *1) (AND (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PatternMatchListResult| *3 *4 *5)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *5 (|ListAggregate| *4)))) (|failed| (*1 *1) (AND (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|PatternMatchListResult| *2 *3 *4)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *4 (|ListAggregate| *3)))) (|new| (*1 *1) (AND (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|PatternMatchListResult| *2 *3 *4)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *4 (|ListAggregate| *3)))) (|makeResult| (*1 *1 *2 *3) (AND (|isDomain| *2 (|PatternMatchResult| *4 *5)) (|isDomain| *3 (|PatternMatchResult| *4 *6)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|ListAggregate| *5)) (|isDomain| *1 (|PatternMatchListResult| *4 *5 *6)))) (|atoms| (*1 *2 *1) (AND (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|PatternMatchResult| *3 *4)) (|isDomain| *1 (|PatternMatchListResult| *3 *4 *5)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *5 (|ListAggregate| *4)))) (|lists| (*1 *2 *1) (AND (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|PatternMatchResult| *3 *5)) (|isDomain| *1 (|PatternMatchListResult| *3 *4 *5)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *5 (|ListAggregate| *4))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |failed?| ((|Boolean|) $)) (SIGNATURE |failed| ($)) (SIGNATURE |new| ($)) (SIGNATURE |makeResult| ($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|))) (SIGNATURE |atoms| ((|PatternMatchResult| |#1| |#2|) $)) (SIGNATURE |lists| ((|PatternMatchResult| |#1| |#3|) $)))) 
((~= (((|Boolean|) $ $) 7)) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) 12)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (= (((|Boolean|) $ $) 6))) 
(((|PatternMatchable| |#1|) (|Category|) (|SetCategory|)) (T |PatternMatchable|)) 
((|patternMatch| (*1 *2 *1 *3 *2) (AND (|isDomain| *2 (|PatternMatchResult| *4 *1)) (|isDomain| *3 (|Pattern| *4)) (|ofCategory| *1 (|PatternMatchable| *4)) (|ofCategory| *4 (|SetCategory|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |patternMatch| ((|PatternMatchResult| |t#1| $) $ (|Pattern| |t#1|) (|PatternMatchResult| |t#1| $))))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((|is?| (((|Boolean|) (|List| |#2|) |#3|) 22) (((|Boolean|) |#2| |#3|) 17)) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) 42 (AND (|not| (|has| |#2| (|RetractableTo| (|Symbol|)))) (|not| (|has| |#2| (|Ring|))))) (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) 41 (AND (|has| |#2| (|Ring|)) (|not| (|has| |#2| (|RetractableTo| (|Symbol|)))))) (((|List| (|Equation| |#2|)) |#2| |#3|) 34 (|has| |#2| (|RetractableTo| (|Symbol|)))) (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) 20))) 
(((|PatternMatch| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |is?| ((|Boolean|) |#2| |#3|)) (SIGNATURE |is?| ((|Boolean|) (|List| |#2|) |#3|)) (SIGNATURE |Is| ((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|)) (IF (|has| |#2| (|RetractableTo| (|Symbol|))) (SIGNATURE |Is| ((|List| (|Equation| |#2|)) |#2| |#3|)) (IF (|has| |#2| (|Ring|)) (SIGNATURE |Is| ((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|)) (SIGNATURE |Is| ((|PatternMatchResult| |#1| |#2|) |#2| |#3|))))) (|SetCategory|) (|PatternMatchable| |#1|) (|ConvertibleTo| (|Pattern| |#1|))) (T |PatternMatch|)) 
((|Is| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|SetCategory|)) (|isDomain| *2 (|PatternMatchResult| *5 *3)) (|isDomain| *1 (|PatternMatch| *5 *3 *4)) (|not| (|ofCategory| *3 (|RetractableTo| (|Symbol|)))) (|not| (|ofCategory| *3 (|Ring|))) (|ofCategory| *3 (|PatternMatchable| *5)) (|ofCategory| *4 (|ConvertibleTo| (|Pattern| *5))))) (|Is| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|SetCategory|)) (|isDomain| *2 (|List| (|Equation| (|Polynomial| *3)))) (|isDomain| *1 (|PatternMatch| *5 *3 *4)) (|ofCategory| *3 (|Ring|)) (|not| (|ofCategory| *3 (|RetractableTo| (|Symbol|)))) (|ofCategory| *3 (|PatternMatchable| *5)) (|ofCategory| *4 (|ConvertibleTo| (|Pattern| *5))))) (|Is| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|SetCategory|)) (|isDomain| *2 (|List| (|Equation| *3))) (|isDomain| *1 (|PatternMatch| *5 *3 *4)) (|ofCategory| *3 (|RetractableTo| (|Symbol|))) (|ofCategory| *3 (|PatternMatchable| *5)) (|ofCategory| *4 (|ConvertibleTo| (|Pattern| *5))))) (|Is| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|PatternMatchable| *5)) (|isDomain| *2 (|PatternMatchListResult| *5 *6 (|List| *6))) (|isDomain| *1 (|PatternMatch| *5 *6 *4)) (|isDomain| *3 (|List| *6)) (|ofCategory| *4 (|ConvertibleTo| (|Pattern| *5))))) (|is?| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *6 (|PatternMatchable| *5)) (|ofCategory| *5 (|SetCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PatternMatch| *5 *6 *4)) (|ofCategory| *4 (|ConvertibleTo| (|Pattern| *5))))) (|is?| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|SetCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PatternMatch| *5 *3 *4)) (|ofCategory| *3 (|PatternMatchable| *5)) (|ofCategory| *4 (|ConvertibleTo| (|Pattern| *5)))))) 
(CATEGORY |package| (SIGNATURE |is?| ((|Boolean|) |#2| |#3|)) (SIGNATURE |is?| ((|Boolean|) (|List| |#2|) |#3|)) (SIGNATURE |Is| ((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|)) (IF (|has| |#2| (|RetractableTo| (|Symbol|))) (SIGNATURE |Is| ((|List| (|Equation| |#2|)) |#2| |#3|)) (IF (|has| |#2| (|Ring|)) (SIGNATURE |Is| ((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|)) (SIGNATURE |Is| ((|PatternMatchResult| |#1| |#2|) |#2| |#3|))))) 
((|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) 21))) 
(((|PatternMatchResultFunctions2| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |map| ((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)))) (|SetCategory|) (|SetCategory|) (|SetCategory|)) (T |PatternMatchResultFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *7 *6)) (|isDomain| *4 (|PatternMatchResult| *5 *6)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|PatternMatchResult| *5 *7)) (|isDomain| *1 (|PatternMatchResultFunctions2| *5 *6 *7))))) 
(CATEGORY |package| (SIGNATURE |map| ((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)))) 
((~= (((|Boolean|) $ $) NIL)) (|union| (($ $ $) 37)) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) 34)) (|new| (($) 11)) (|latex| (((|String|) $) NIL)) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) 20)) (|hash| (((|SingleInteger|) $) NIL)) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) 48)) (|failed?| (((|Boolean|) $) 14)) (|failed| (($) 12)) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) 25)) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) 23)) (|coerce| (((|OutputForm|) $) 42)) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) 46)) (|addMatch| (($ (|Pattern| |#1|) |#2| $) 45)) (= (((|Boolean|) $ $) 39))) 
(((|PatternMatchResult| |#1| |#2|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |failed?| ((|Boolean|) $)) (SIGNATURE |failed| ($)) (SIGNATURE |new| ($)) (SIGNATURE |union| ($ $ $)) (SIGNATURE |getMatch| ((|Union| |#2| "failed") (|Pattern| |#1|) $)) (SIGNATURE |addMatch| ($ (|Pattern| |#1|) |#2| $)) (SIGNATURE |insertMatch| ($ (|Pattern| |#1|) |#2| $)) (SIGNATURE |addMatchRestricted| ($ (|Pattern| |#1|) |#2| $ |#2|)) (SIGNATURE |destruct| ((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $)) (SIGNATURE |construct| ($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))))) (SIGNATURE |satisfy?| ((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|))))) (|SetCategory|) (|SetCategory|)) (T |PatternMatchResult|)) 
((|failed?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PatternMatchResult| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)))) (|failed| (*1 *1) (AND (|isDomain| *1 (|PatternMatchResult| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|new| (*1 *1) (AND (|isDomain| *1 (|PatternMatchResult| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|union| (*1 *1 *1 *1) (AND (|isDomain| *1 (|PatternMatchResult| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|getMatch| (*1 *2 *3 *1) (|partial| AND (|isDomain| *3 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)) (|isDomain| *1 (|PatternMatchResult| *4 *2)))) (|addMatch| (*1 *1 *2 *3 *1) (AND (|isDomain| *2 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *1 (|PatternMatchResult| *4 *3)) (|ofCategory| *3 (|SetCategory|)))) (|insertMatch| (*1 *1 *2 *3 *1) (AND (|isDomain| *2 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *1 (|PatternMatchResult| *4 *3)) (|ofCategory| *3 (|SetCategory|)))) (|addMatchRestricted| (*1 *1 *2 *3 *1 *3) (AND (|isDomain| *2 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *1 (|PatternMatchResult| *4 *3)) (|ofCategory| *3 (|SetCategory|)))) (|destruct| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| *4)))) (|isDomain| *1 (|PatternMatchResult| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)))) (|construct| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| *4)))) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *1 (|PatternMatchResult| *3 *4)) (|ofCategory| *3 (|SetCategory|)))) (|satisfy?| (*1 *2 *1 *3) (|partial| AND (|isDomain| *3 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PatternMatchResult| *4 *5)) (|ofCategory| *5 (|SetCategory|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |failed?| ((|Boolean|) $)) (SIGNATURE |failed| ($)) (SIGNATURE |new| ($)) (SIGNATURE |union| ($ $ $)) (SIGNATURE |getMatch| ((|Union| |#2| "failed") (|Pattern| |#1|) $)) (SIGNATURE |addMatch| ($ (|Pattern| |#1|) |#2| $)) (SIGNATURE |insertMatch| ($ (|Pattern| |#1|) |#2| $)) (SIGNATURE |addMatchRestricted| ($ (|Pattern| |#1|) |#2| $ |#2|)) (SIGNATURE |destruct| ((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $)) (SIGNATURE |construct| ($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))))) (SIGNATURE |satisfy?| ((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|))))) 
((|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) 30) (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) 42) (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) 33)) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) 39) (((|Boolean|) |#2| (|Pattern| |#1|)) 35)) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) 14)) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) 23)) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) 19))) 
(((|PatternFunctions1| |#1| |#2|) (CATEGORY |package| (SIGNATURE |suchThat| ((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|))) (SIGNATURE |suchThat| ((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|)))) (SIGNATURE |suchThat| ((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|)))) (SIGNATURE |predicate| ((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|))) (SIGNATURE |satisfy?| ((|Boolean|) |#2| (|Pattern| |#1|))) (SIGNATURE |satisfy?| ((|Boolean|) (|List| |#2|) (|Pattern| |#1|))) (SIGNATURE |addBadValue| ((|Pattern| |#1|) (|Pattern| |#1|) |#2|)) (SIGNATURE |badValues| ((|List| |#2|) (|Pattern| |#1|)))) (|SetCategory|) (|Type|)) (T |PatternFunctions1|)) 
((|badValues| (*1 *2 *3) (AND (|isDomain| *3 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|PatternFunctions1| *4 *5)) (|ofCategory| *5 (|Type|)))) (|addBadValue| (*1 *2 *2 *3) (AND (|isDomain| *2 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *1 (|PatternFunctions1| *4 *3)) (|ofCategory| *3 (|Type|)))) (|satisfy?| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PatternFunctions1| *5 *6)))) (|satisfy?| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *5 (|SetCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PatternFunctions1| *5 *3)) (|ofCategory| *3 (|Type|)))) (|predicate| (*1 *2 *3) (AND (|isDomain| *3 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Mapping| (|Boolean|) *5)) (|isDomain| *1 (|PatternFunctions1| *4 *5)) (|ofCategory| *5 (|Type|)))) (|suchThat| (*1 *2 *2 *3 *4) (AND (|isDomain| *2 (|Pattern| *5)) (|isDomain| *3 (|List| (|Symbol|))) (|isDomain| *4 (|Mapping| (|Boolean|) (|List| *6))) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|Type|)) (|isDomain| *1 (|PatternFunctions1| *5 *6)))) (|suchThat| (*1 *2 *2 *3) (AND (|isDomain| *2 (|Pattern| *4)) (|isDomain| *3 (|List| (|Mapping| (|Boolean|) *5))) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|Type|)) (|isDomain| *1 (|PatternFunctions1| *4 *5)))) (|suchThat| (*1 *2 *2 *3) (AND (|isDomain| *2 (|Pattern| *4)) (|isDomain| *3 (|Mapping| (|Boolean|) *5)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|Type|)) (|isDomain| *1 (|PatternFunctions1| *4 *5))))) 
(CATEGORY |package| (SIGNATURE |suchThat| ((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|))) (SIGNATURE |suchThat| ((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|)))) (SIGNATURE |suchThat| ((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|)))) (SIGNATURE |predicate| ((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|))) (SIGNATURE |satisfy?| ((|Boolean|) |#2| (|Pattern| |#1|))) (SIGNATURE |satisfy?| ((|Boolean|) (|List| |#2|) (|Pattern| |#1|))) (SIGNATURE |addBadValue| ((|Pattern| |#1|) (|Pattern| |#1|) |#2|)) (SIGNATURE |badValues| ((|List| |#2|) (|Pattern| |#1|)))) 
((|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) 17))) 
(((|PatternFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)))) (|SetCategory|) (|SetCategory|)) (T |PatternFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|isDomain| *2 (|Pattern| *6)) (|isDomain| *1 (|PatternFunctions2| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |map| ((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)))) 
((~= (((|Boolean|) $ $) NIL)) (|withPredicates| (($ $ (|List| (|Any|))) 62)) (|variables| (((|List| $) $) 116)) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) 22)) (|symbol?| (((|Boolean|) $) 29)) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) 24)) (|setPredicates| (($ $ (|List| (|Any|))) 61)) (|retractIfCan| (((|Union| |#1| "failed") $) 59) (((|Union| (|Symbol|) "failed") $) 138)) (|retract| ((|#1| $) 55) (((|Symbol|) $) NIL)) (|resetBadValues| (($ $) 106)) (|quoted?| (((|Boolean|) $) 45)) (|predicates| (((|List| (|Any|)) $) 43)) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) 63)) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) 70)) (|optional?| (((|Boolean|) $) 48)) (|multiple?| (((|Boolean|) $) 47)) (|latex| (((|String|) $) NIL)) (|isTimes| (((|Union| (|List| $) "failed") $) 34)) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) 41)) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) 81)) (|isPlus| (((|Union| (|List| $) "failed") $) 31)) (|isOp| (((|Union| (|List| $) "failed") $ (|BasicOperator|)) 105) (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) 93)) (|isList| (((|Union| (|List| $) "failed") $) 35)) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) 38)) (|inR?| (((|Boolean|) $) 28)) (|hash| (((|SingleInteger|) $) NIL)) (|hasTopPredicate?| (((|Boolean|) $) 20)) (|hasPredicate?| (((|Boolean|) $) 44)) (|getBadValues| (((|List| (|Any|)) $) 109)) (|generic?| (((|Boolean|) $) 46)) (|elt| (($ (|BasicOperator|) (|List| $)) 90)) (|depth| (((|NonNegativeInteger|) $) 27)) (|copy| (($ $) 60)) (|convert| (($ (|List| $)) 57)) (|constant?| (((|Boolean|) $) 25)) (|coerce| (((|OutputForm|) $) 50) (($ |#1|) 18) (($ (|Symbol|)) 64)) (|addBadValue| (($ $ (|Any|)) 108)) (|Zero| (($) 89 T CONST)) (|One| (($) 71 T CONST)) (= (((|Boolean|) $ $) 77)) (/ (($ $ $) 98)) (+ (($ $ $) 102)) (** (($ $ (|NonNegativeInteger|)) 97) (($ $ $) 51)) (* (($ $ $) 103))) 
(((|Pattern| |#1|) (|Join| (|SetCategory|) (|RetractableTo| |#1|) (|RetractableTo| (|Symbol|)) (CATEGORY |domain| (SIGNATURE 0 ($) |constant|) (SIGNATURE 1 ($) |constant|) (SIGNATURE |isPlus| ((|Union| (|List| $) "failed") $)) (SIGNATURE |isTimes| ((|Union| (|List| $) "failed") $)) (SIGNATURE |isOp| ((|Union| (|List| $) "failed") $ (|BasicOperator|))) (SIGNATURE |isOp| ((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $)) (SIGNATURE |isExpt| ((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $)) (SIGNATURE |isQuotient| ((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $)) (SIGNATURE |isList| ((|Union| (|List| $) "failed") $)) (SIGNATURE |isPower| ((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $)) (SIGNATURE |elt| ($ (|BasicOperator|) (|List| $))) (SIGNATURE + ($ $ $)) (SIGNATURE * ($ $ $)) (SIGNATURE ** ($ $ (|NonNegativeInteger|))) (SIGNATURE ** ($ $ $)) (SIGNATURE / ($ $ $)) (SIGNATURE |depth| ((|NonNegativeInteger|) $)) (SIGNATURE |convert| ($ (|List| $))) (SIGNATURE |copy| ($ $)) (SIGNATURE |inR?| ((|Boolean|) $)) (SIGNATURE |quoted?| ((|Boolean|) $)) (SIGNATURE |symbol?| ((|Boolean|) $)) (SIGNATURE |constant?| ((|Boolean|) $)) (SIGNATURE |generic?| ((|Boolean|) $)) (SIGNATURE |multiple?| ((|Boolean|) $)) (SIGNATURE |optional?| ((|Boolean|) $)) (SIGNATURE |hasPredicate?| ((|Boolean|) $)) (SIGNATURE |predicates| ((|List| (|Any|)) $)) (SIGNATURE |setPredicates| ($ $ (|List| (|Any|)))) (SIGNATURE |withPredicates| ($ $ (|List| (|Any|)))) (SIGNATURE |patternVariable| ($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |setTopPredicate| ($ $ (|List| (|Symbol|)) (|Any|))) (SIGNATURE |topPredicate| ((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $)) (SIGNATURE |hasTopPredicate?| ((|Boolean|) $)) (SIGNATURE |resetBadValues| ($ $)) (SIGNATURE |addBadValue| ($ $ (|Any|))) (SIGNATURE |getBadValues| ((|List| (|Any|)) $)) (SIGNATURE |variables| ((|List| $) $)) (SIGNATURE |optpair| ((|Union| (|List| $) "failed") (|List| $))))) (|SetCategory|)) (T |Pattern|)) 
((|Zero| (*1 *1) (AND (|isDomain| *1 (|Pattern| *2)) (|ofCategory| *2 (|SetCategory|)))) (|One| (*1 *1) (AND (|isDomain| *1 (|Pattern| *2)) (|ofCategory| *2 (|SetCategory|)))) (|isPlus| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|List| (|Pattern| *3))) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|isTimes| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|List| (|Pattern| *3))) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|isOp| (*1 *2 *1 *3) (|partial| AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *2 (|List| (|Pattern| *4))) (|isDomain| *1 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|)))) (|isOp| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| (|Pattern| *3))))) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|isExpt| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|Record| (|:| |val| (|Pattern| *3)) (|:| |exponent| (|NonNegativeInteger|)))) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|isQuotient| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|Record| (|:| |num| (|Pattern| *3)) (|:| |den| (|Pattern| *3)))) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|isList| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|List| (|Pattern| *3))) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|isPower| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|Record| (|:| |val| (|Pattern| *3)) (|:| |exponent| (|Pattern| *3)))) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|elt| (*1 *1 *2 *3) (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|List| (|Pattern| *4))) (|isDomain| *1 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|)))) (+ (*1 *1 *1 *1) (AND (|isDomain| *1 (|Pattern| *2)) (|ofCategory| *2 (|SetCategory|)))) (* (*1 *1 *1 *1) (AND (|isDomain| *1 (|Pattern| *2)) (|ofCategory| *2 (|SetCategory|)))) (** (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (** (*1 *1 *1 *1) (AND (|isDomain| *1 (|Pattern| *2)) (|ofCategory| *2 (|SetCategory|)))) (/ (*1 *1 *1 *1) (AND (|isDomain| *1 (|Pattern| *2)) (|ofCategory| *2 (|SetCategory|)))) (|depth| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Pattern| *3))) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|copy| (*1 *1 *1) (AND (|isDomain| *1 (|Pattern| *2)) (|ofCategory| *2 (|SetCategory|)))) (|inR?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|quoted?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|symbol?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|constant?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|generic?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|multiple?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|optional?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|hasPredicate?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|predicates| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Any|))) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|setPredicates| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Any|))) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|withPredicates| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Any|))) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|patternVariable| (*1 *1 *2 *3 *3 *3) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|Boolean|)) (|isDomain| *1 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|)))) (|setTopPredicate| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *3 (|Any|)) (|isDomain| *1 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|)))) (|topPredicate| (*1 *2 *1) (AND (|isDomain| *2 (|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|)))) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|hasTopPredicate?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|resetBadValues| (*1 *1 *1) (AND (|isDomain| *1 (|Pattern| *2)) (|ofCategory| *2 (|SetCategory|)))) (|addBadValue| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Any|)) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|getBadValues| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Any|))) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|variables| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Pattern| *3))) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|)))) (|optpair| (*1 *2 *2) (|partial| AND (|isDomain| *2 (|List| (|Pattern| *3))) (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(|Join| (|SetCategory|) (|RetractableTo| |#1|) (|RetractableTo| (|Symbol|)) (CATEGORY |domain| (SIGNATURE (|Zero|) ($) |constant|) (SIGNATURE (|One|) ($) |constant|) (SIGNATURE |isPlus| ((|Union| (|List| $) "failed") $)) (SIGNATURE |isTimes| ((|Union| (|List| $) "failed") $)) (SIGNATURE |isOp| ((|Union| (|List| $) "failed") $ (|BasicOperator|))) (SIGNATURE |isOp| ((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $)) (SIGNATURE |isExpt| ((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $)) (SIGNATURE |isQuotient| ((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $)) (SIGNATURE |isList| ((|Union| (|List| $) "failed") $)) (SIGNATURE |isPower| ((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $)) (SIGNATURE |elt| ($ (|BasicOperator|) (|List| $))) (SIGNATURE + ($ $ $)) (SIGNATURE * ($ $ $)) (SIGNATURE ** ($ $ (|NonNegativeInteger|))) (SIGNATURE ** ($ $ $)) (SIGNATURE / ($ $ $)) (SIGNATURE |depth| ((|NonNegativeInteger|) $)) (SIGNATURE |convert| ($ (|List| $))) (SIGNATURE |copy| ($ $)) (SIGNATURE |inR?| ((|Boolean|) $)) (SIGNATURE |quoted?| ((|Boolean|) $)) (SIGNATURE |symbol?| ((|Boolean|) $)) (SIGNATURE |constant?| ((|Boolean|) $)) (SIGNATURE |generic?| ((|Boolean|) $)) (SIGNATURE |multiple?| ((|Boolean|) $)) (SIGNATURE |optional?| ((|Boolean|) $)) (SIGNATURE |hasPredicate?| ((|Boolean|) $)) (SIGNATURE |predicates| ((|List| (|Any|)) $)) (SIGNATURE |setPredicates| ($ $ (|List| (|Any|)))) (SIGNATURE |withPredicates| ($ $ (|List| (|Any|)))) (SIGNATURE |patternVariable| ($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |setTopPredicate| ($ $ (|List| (|Symbol|)) (|Any|))) (SIGNATURE |topPredicate| ((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $)) (SIGNATURE |hasTopPredicate?| ((|Boolean|) $)) (SIGNATURE |resetBadValues| ($ $)) (SIGNATURE |addBadValue| ($ $ (|Any|))) (SIGNATURE |getBadValues| ((|List| (|Any|)) $)) (SIGNATURE |variables| ((|List| $) $)) (SIGNATURE |optpair| ((|Union| (|List| $) "failed") (|List| $))))) 
((~= (((|Boolean|) $ $) NIL)) (|varList| (((|List| |#1|) $) 16)) (|retractable?| (((|Boolean|) $) 38)) (|retractIfCan| (((|Union| (|LyndonWord| |#1|) "failed") $) 41)) (|retract| (((|LyndonWord| |#1|) $) 39)) (|rest| (($ $) 18)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|listOfTerms| (((|List| (|LyndonWord| |#1|)) $) 23)) (|length| (((|NonNegativeInteger|) $) 45)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|first| (((|LyndonWord| |#1|) $) 17)) (|coerce| (((|OutputForm|) $) 37) (($ (|LyndonWord| |#1|)) 21) (((|OrderedFreeMonoid| |#1|) $) 27) (($ |#1|) 20)) (|One| (($) 8 T CONST)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 11)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 48))) 
(((|PoincareBirkhoffWittLyndonBasis| |#1|) (|Join| (|OrderedSet|) (|RetractableTo| (|LyndonWord| |#1|)) (CATEGORY |domain| (SIGNATURE 1 ($) |constant|) (SIGNATURE |coerce| ((|OrderedFreeMonoid| |#1|) $)) (SIGNATURE |coerce| ($ |#1|)) (SIGNATURE |first| ((|LyndonWord| |#1|) $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |listOfTerms| ((|List| (|LyndonWord| |#1|)) $)) (SIGNATURE |rest| ($ $)) (SIGNATURE |retractable?| ((|Boolean|) $)) (SIGNATURE |varList| ((|List| |#1|) $)))) (|OrderedSet|)) (T |PoincareBirkhoffWittLyndonBasis|)) 
((|One| (*1 *1) (AND (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|OrderedFreeMonoid| *3)) (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|first| (*1 *2 *1) (AND (|isDomain| *2 (|LyndonWord| *3)) (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|length| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|listOfTerms| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|LyndonWord| *3))) (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|rest| (*1 *1 *1) (AND (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|retractable?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *3)) (|ofCategory| *3 (|OrderedSet|)))) (|varList| (*1 *2 *1) (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *3)) (|ofCategory| *3 (|OrderedSet|))))) 
(|Join| (|OrderedSet|) (|RetractableTo| (|LyndonWord| |#1|)) (CATEGORY |domain| (SIGNATURE (|One|) ($) |constant|) (SIGNATURE |coerce| ((|OrderedFreeMonoid| |#1|) $)) (SIGNATURE |coerce| ($ |#1|)) (SIGNATURE |first| ((|LyndonWord| |#1|) $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |listOfTerms| ((|List| (|LyndonWord| |#1|)) $)) (SIGNATURE |rest| ($ $)) (SIGNATURE |retractable?| ((|Boolean|) $)) (SIGNATURE |varList| ((|List| |#1|) $)))) 
((|compose| ((|#1| |#1| |#1|) 19))) 
(((|PolynomialComposition| |#1| |#2|) (CATEGORY |package| (SIGNATURE |compose| (|#1| |#1| |#1|))) (|UnivariatePolynomialCategory| |#2|) (|Ring|)) (T |PolynomialComposition|)) 
((|compose| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|PolynomialComposition| *2 *3)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(CATEGORY |package| (SIGNATURE |compose| (|#1| |#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) 13)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) 12)) (= (((|Boolean|) $ $) 6))) 
(((|PartialDifferentialEquationsSolverCategory|) (|Category|)) (T |PartialDifferentialEquationsSolverCategory|)) 
((|measure| (*1 *2 *3 *4) (AND (|ofCategory| *1 (|PartialDifferentialEquationsSolverCategory|)) (|isDomain| *3 (|RoutinesTable|)) (|isDomain| *4 (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) (|isDomain| *2 (|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)))))) (|PDESolve| (*1 *2 *3) (AND (|ofCategory| *1 (|PartialDifferentialEquationsSolverCategory|)) (|isDomain| *3 (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) (|isDomain| *2 (|Result|))))) 
(|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE |measure| ((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))))) (SIGNATURE |PDESolve| ((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))))))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) 23)) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) 22)) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) 26) (((|List| |#1|) |#1|) 28))) 
(((|PolynomialDecomposition| |#1| |#2|) (CATEGORY |package| (SIGNATURE |decompose| ((|List| |#1|) |#1|)) (SIGNATURE |decompose| ((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |leftFactor| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE |rightFactorCandidate| (|#1| |#1| (|NonNegativeInteger|)))) (|UnivariatePolynomialCategory| |#2|) (|Field|)) (T |PolynomialDecomposition|)) 
((|rightFactorCandidate| (*1 *2 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Field|)) (|isDomain| *1 (|PolynomialDecomposition| *2 *4)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)))) (|leftFactor| (*1 *2 *2 *2) (|partial| AND (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|PolynomialDecomposition| *2 *3)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|decompose| (*1 *2 *3 *4 *4) (|partial| AND (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Record| (|:| |left| *3) (|:| |right| *3))) (|isDomain| *1 (|PolynomialDecomposition| *3 *5)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|decompose| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PolynomialDecomposition| *3 *4)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |decompose| ((|List| |#1|) |#1|)) (SIGNATURE |decompose| ((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |leftFactor| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE |rightFactorCandidate| (|#1| |#1| (|NonNegativeInteger|)))) 
((|solve| (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|)) 92) (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|)) 87) (((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|)) 76) (((|Result|) (|NumericalPDEProblem|)) 77)) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|RoutinesTable|)) 50) (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|)) 52))) 
(((|AnnaPartialDifferentialEquationPackage|) (CATEGORY |package| (SIGNATURE |solve| ((|Result|) (|NumericalPDEProblem|))) (SIGNATURE |solve| ((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|))) (SIGNATURE |solve| ((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|))) (SIGNATURE |solve| ((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|))) (SIGNATURE |measure| ((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|))) (SIGNATURE |measure| ((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|RoutinesTable|))))) (T |AnnaPartialDifferentialEquationPackage|)) 
((|measure| (*1 *2 *3 *4) (AND (|isDomain| *3 (|NumericalPDEProblem|)) (|isDomain| *4 (|RoutinesTable|)) (|isDomain| *2 (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) (|isDomain| *1 (|AnnaPartialDifferentialEquationPackage|)))) (|measure| (*1 *2 *3) (AND (|isDomain| *3 (|NumericalPDEProblem|)) (|isDomain| *2 (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) (|isDomain| *1 (|AnnaPartialDifferentialEquationPackage|)))) (|solve| (*1 *2 *3 *3 *3 *3 *4 *4 *5 *6 *7) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *6 (|List| (|List| (|Expression| *3)))) (|isDomain| *7 (|String|)) (|isDomain| *5 (|List| (|Expression| (|Float|)))) (|isDomain| *3 (|Float|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaPartialDifferentialEquationPackage|)))) (|solve| (*1 *2 *3 *3 *3 *3 *4 *4 *5 *6 *7 *8) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *6 (|List| (|List| (|Expression| *3)))) (|isDomain| *7 (|String|)) (|isDomain| *8 (|DoubleFloat|)) (|isDomain| *5 (|List| (|Expression| (|Float|)))) (|isDomain| *3 (|Float|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaPartialDifferentialEquationPackage|)))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|NumericalPDEProblem|)) (|isDomain| *4 (|RoutinesTable|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaPartialDifferentialEquationPackage|)))) (|solve| (*1 *2 *3) (AND (|isDomain| *3 (|NumericalPDEProblem|)) (|isDomain| *2 (|Result|)) (|isDomain| *1 (|AnnaPartialDifferentialEquationPackage|))))) 
(CATEGORY |package| (SIGNATURE |solve| ((|Result|) (|NumericalPDEProblem|))) (SIGNATURE |solve| ((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|))) (SIGNATURE |solve| ((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|))) (SIGNATURE |solve| ((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|))) (SIGNATURE |measure| ((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|))) (SIGNATURE |measure| ((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|RoutinesTable|)))) 
((~= (((|Boolean|) $ $) NIL)) (|retract| (((|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))) $) 10)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 12) (($ (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) 9)) (= (((|Boolean|) $ $) NIL))) 
(((|NumericalPDEProblem|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))))) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE |retract| ((|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))) $))))) (T |NumericalPDEProblem|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|NumericalPDEProblem|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) (|isDomain| *1 (|NumericalPDEProblem|)))) (|retract| (*1 *2 *1) (AND (|isDomain| *2 (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) (|isDomain| *1 (|NumericalPDEProblem|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))))) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE |retract| ((|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))) $)))) 
((|differentiate| (($ $ |#2|) NIL) (($ $ (|List| |#2|)) 10) (($ $ |#2| (|NonNegativeInteger|)) 12) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) 15)) (D (($ $ |#2|) 16) (($ $ (|List| |#2|)) 18) (($ $ |#2| (|NonNegativeInteger|)) 19) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) 21))) 
(((|PartialDifferentialRing&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE D (|#1| |#1| (|List| |#2|) (|List| (|NonNegativeInteger|)))) (SIGNATURE D (|#1| |#1| |#2| (|NonNegativeInteger|))) (SIGNATURE D (|#1| |#1| (|List| |#2|))) (SIGNATURE D (|#1| |#1| |#2|)) (SIGNATURE |differentiate| (|#1| |#1| (|List| |#2|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |differentiate| (|#1| |#1| |#2| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| |#2|))) (SIGNATURE |differentiate| (|#1| |#1| |#2|))) (|PartialDifferentialRing| |#2|) (|SetCategory|)) (T |PartialDifferentialRing&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE D (|#1| |#1| (|List| |#2|) (|List| (|NonNegativeInteger|)))) (SIGNATURE D (|#1| |#1| |#2| (|NonNegativeInteger|))) (SIGNATURE D (|#1| |#1| (|List| |#2|))) (SIGNATURE D (|#1| |#1| |#2|)) (SIGNATURE |differentiate| (|#1| |#1| (|List| |#2|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |differentiate| (|#1| |#1| |#2| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| |#2|))) (SIGNATURE |differentiate| (|#1| |#1| |#2|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|differentiate| (($ $ |#1|) 41) (($ $ (|List| |#1|)) 40) (($ $ |#1| (|NonNegativeInteger|)) 39) (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) 38)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $ |#1|) 37) (($ $ (|List| |#1|)) 36) (($ $ |#1| (|NonNegativeInteger|)) 35) (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) 34)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|PartialDifferentialRing| |#1|) (|Category|) (|SetCategory|)) (T |PartialDifferentialRing|)) 
((|differentiate| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PartialDifferentialRing| *2)) (|ofCategory| *2 (|SetCategory|)))) (|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *1 (|PartialDifferentialRing| *3)) (|ofCategory| *3 (|SetCategory|)))) (|differentiate| (*1 *1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|PartialDifferentialRing| *2)) (|ofCategory| *2 (|SetCategory|)))) (|differentiate| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *4)) (|isDomain| *3 (|List| (|NonNegativeInteger|))) (|ofCategory| *1 (|PartialDifferentialRing| *4)) (|ofCategory| *4 (|SetCategory|)))) (D (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PartialDifferentialRing| *2)) (|ofCategory| *2 (|SetCategory|)))) (D (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *1 (|PartialDifferentialRing| *3)) (|ofCategory| *3 (|SetCategory|)))) (D (*1 *1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|PartialDifferentialRing| *2)) (|ofCategory| *2 (|SetCategory|)))) (D (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *4)) (|isDomain| *3 (|List| (|NonNegativeInteger|))) (|ofCategory| *1 (|PartialDifferentialRing| *4)) (|ofCategory| *4 (|SetCategory|))))) 
(|Join| (|Ring|) (CATEGORY |domain| (SIGNATURE |differentiate| ($ $ |t#1|)) (SIGNATURE |differentiate| ($ $ (|List| |t#1|))) (SIGNATURE |differentiate| ($ $ |t#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| ($ $ (|List| |t#1|) (|List| (|NonNegativeInteger|)))) (SIGNATURE D ($ $ |t#1|)) (SIGNATURE D ($ $ (|List| |t#1|))) (SIGNATURE D ($ $ |t#1| (|NonNegativeInteger|))) (SIGNATURE D ($ $ (|List| |t#1|) (|List| (|NonNegativeInteger|)))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) 26)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setvalue!| ((|#1| $ |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setright!| (($ $ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setleft!| (($ $ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "left" $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "right" $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) NIL T CONST)) (|right| (($ $) 25)) (|ptree| (($ |#1|) 12) (($ $ $) 17)) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) NIL)) (|node?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|left| (($ $) 23)) (|leaves| (((|List| |#1|) $) NIL)) (|leaf?| (((|Boolean|) $) 20)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#1| $ "value") NIL) (($ $ "left") NIL) (($ $ "right") NIL)) (|distance| (((|Integer|) $ $) NIL)) (|cyclic?| (((|Boolean|) $) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) NIL)) (|coerce| (((|OutputForm|) $) 29 (|has| |#1| (|SetCategory|))) (((|Tree| |#1|) $) 9)) (|children| (((|List| $) $) NIL)) (|child?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 21 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|PendantTree| |#1|) (|Join| (|BinaryRecursiveAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |ptree| ($ |#1|)) (SIGNATURE |ptree| ($ $ $)) (SIGNATURE |coerce| ((|Tree| |#1|) $)))) (|SetCategory|)) (T |PendantTree|)) 
((|ptree| (*1 *1 *2) (AND (|isDomain| *1 (|PendantTree| *2)) (|ofCategory| *2 (|SetCategory|)))) (|ptree| (*1 *1 *1 *1) (AND (|isDomain| *1 (|PendantTree| *2)) (|ofCategory| *2 (|SetCategory|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Tree| *3)) (|isDomain| *1 (|PendantTree| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(|Join| (|BinaryRecursiveAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |ptree| ($ |#1|)) (SIGNATURE |ptree| ($ $ $)) (SIGNATURE |coerce| ((|Tree| |#1|) $)))) 
((|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) 39))) 
(((|Permanent| |#1| |#2|) (CATEGORY |package| (SIGNATURE |permanent| (|#2| (|SquareMatrix| |#1| |#2|)))) (|PositiveInteger|) (|Join| (|Ring|) (CATEGORY |package| (ATTRIBUTE (|commutative| "*"))))) (T |Permanent|)) 
((|permanent| (*1 *2 *3) (AND (|isDomain| *3 (|SquareMatrix| *4 *2)) (|ofType| *4 (|PositiveInteger|)) (|ofCategory| *2 (|Join| (|Ring|) (CATEGORY |package| (ATTRIBUTE (|commutative| "*"))))) (|isDomain| *1 (|Permanent| *4 *2))))) 
(CATEGORY |package| (SIGNATURE |permanent| (|#2| (|SquareMatrix| |#1| |#2|)))) 
((~= (((|Boolean|) $ $) 7)) (|sample| (($) 19 T CONST)) (|recip| (((|Union| $ "failed") $) 15)) (|orbit| (((|Set| |#1|) $ |#1|) 34)) (|one?| (((|Boolean|) $) 18)) (|min| (($ $ $) 32 (OR (|has| |#1| (|OrderedSet|)) (|has| |#1| (|Finite|))))) (|max| (($ $ $) 31 (OR (|has| |#1| (|OrderedSet|)) (|has| |#1| (|Finite|))))) (|latex| (((|String|) $) 9)) (|inv| (($ $) 26)) (|hash| (((|SingleInteger|) $) 10)) (|eval| ((|#1| $ |#1|) 36)) (|elt| ((|#1| $ |#1|) 35)) (|cycles| (($ (|List| (|List| |#1|))) 37)) (|cycle| (($ (|List| |#1|)) 38)) (|conjugate| (($ $ $) 22)) (|commutator| (($ $ $) 21)) (|coerce| (((|OutputForm|) $) 11)) (^ (($ $ (|PositiveInteger|)) 12) (($ $ (|NonNegativeInteger|)) 16) (($ $ (|Integer|)) 23)) (|One| (($) 20 T CONST)) (>= (((|Boolean|) $ $) 29 (OR (|has| |#1| (|OrderedSet|)) (|has| |#1| (|Finite|))))) (> (((|Boolean|) $ $) 28 (OR (|has| |#1| (|OrderedSet|)) (|has| |#1| (|Finite|))))) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 30 (OR (|has| |#1| (|OrderedSet|)) (|has| |#1| (|Finite|))))) (< (((|Boolean|) $ $) 33)) (/ (($ $ $) 25)) (** (($ $ (|PositiveInteger|)) 13) (($ $ (|NonNegativeInteger|)) 17) (($ $ (|Integer|)) 24)) (* (($ $ $) 14))) 
(((|PermutationCategory| |#1|) (|Category|) (|SetCategory|)) (T |PermutationCategory|)) 
((|cycle| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *1 (|PermutationCategory| *3)))) (|cycles| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *1 (|PermutationCategory| *3)))) (|eval| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|PermutationCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (|elt| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|PermutationCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (|orbit| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|PermutationCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Set| *3)))) (< (*1 *2 *1 *1) (AND (|ofCategory| *1 (|PermutationCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) 
(|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |cycle| ($ (|List| |t#1|))) (SIGNATURE |cycles| ($ (|List| (|List| |t#1|)))) (SIGNATURE |eval| (|t#1| $ |t#1|)) (SIGNATURE |elt| (|t#1| $ |t#1|)) (SIGNATURE |orbit| ((|Set| |t#1|) $ |t#1|)) (SIGNATURE < ((|Boolean|) $ $)) (IF (|has| |t#1| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |noBranch|) (IF (|has| |t#1| (|Finite|)) (ATTRIBUTE (|OrderedSet|)) |noBranch|))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Group|) . T) ((|Monoid|) . T) ((|OrderedSet|) OR (|has| |#1| (|OrderedSet|)) (|has| |#1| (|Finite|))) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) 106)) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) 128)) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) 129)) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) 96)) (|random| (((|Permutation| |#1|) $ (|Integer|)) 101) (((|Permutation| |#1|) $) 102)) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) 108)) (|order| (((|NonNegativeInteger|) $) 103)) (|orbits| (((|Set| (|Set| |#1|)) $) 126)) (|orbit| (((|Set| |#1|) $ |#1|) 119) (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) 137) (((|Set| (|List| |#1|)) $ (|List| |#1|)) 140)) (|movedPoints| (((|Set| |#1|) $) 99)) (|member?| (((|Boolean|) (|Permutation| |#1|) $) 90)) (|latex| (((|String|) $) NIL)) (|initializeGroupForWordProblem| (((|Void|) $) 93) (((|Void|) $ (|Integer|) (|Integer|)) 141)) (|hash| (((|SingleInteger|) $) NIL)) (|generators| (((|List| (|Permutation| |#1|)) $) 94)) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) 97)) (|degree| (((|NonNegativeInteger|) $) 104)) (|coerce| (((|OutputForm|) $) 117) (((|List| (|Permutation| |#1|)) $) 22) (($ (|List| (|Permutation| |#1|))) 107)) (|base| (((|List| |#1|) $) 105)) (= (((|Boolean|) $ $) 134)) (<= (((|Boolean|) $ $) 132)) (< (((|Boolean|) $ $) 131))) 
(((|PermutationGroup| |#1|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ((|List| (|Permutation| |#1|)) $)) (SIGNATURE |coerce| ($ (|List| (|Permutation| |#1|)))) (SIGNATURE |generators| ((|List| (|Permutation| |#1|)) $)) (SIGNATURE |elt| ((|Permutation| |#1|) $ (|NonNegativeInteger|))) (SIGNATURE |random| ((|Permutation| |#1|) $ (|Integer|))) (SIGNATURE |random| ((|Permutation| |#1|) $)) (SIGNATURE |order| ((|NonNegativeInteger|) $)) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |base| ((|List| |#1|) $)) (SIGNATURE |strongGenerators| ((|List| (|Permutation| |#1|)) $)) (SIGNATURE |wordsForStrongGenerators| ((|List| (|List| (|NonNegativeInteger|))) $)) (SIGNATURE |permutationGroup| ($ (|List| (|Permutation| |#1|)))) (SIGNATURE |orbit| ((|Set| |#1|) $ |#1|)) (SIGNATURE |orbit| ((|Set| (|Set| |#1|)) $ (|Set| |#1|))) (SIGNATURE |orbit| ((|Set| (|List| |#1|)) $ (|List| |#1|))) (SIGNATURE |orbits| ((|Set| (|Set| |#1|)) $)) (SIGNATURE |member?| ((|Boolean|) (|Permutation| |#1|) $)) (SIGNATURE |wordInStrongGenerators| ((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $)) (SIGNATURE |wordInGenerators| ((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $)) (SIGNATURE |movedPoints| ((|Set| |#1|) $)) (SIGNATURE < ((|Boolean|) $ $)) (SIGNATURE <= ((|Boolean|) $ $)) (SIGNATURE |initializeGroupForWordProblem| ((|Void|) $)) (SIGNATURE |initializeGroupForWordProblem| ((|Void|) $ (|Integer|) (|Integer|))))) (|SetCategory|)) (T |PermutationGroup|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Permutation| *3))) (|isDomain| *1 (|PermutationGroup| *3)) (|ofCategory| *3 (|SetCategory|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Permutation| *3))) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|PermutationGroup| *3)))) (|generators| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Permutation| *3))) (|isDomain| *1 (|PermutationGroup| *3)) (|ofCategory| *3 (|SetCategory|)))) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Permutation| *4)) (|isDomain| *1 (|PermutationGroup| *4)) (|ofCategory| *4 (|SetCategory|)))) (|random| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Permutation| *4)) (|isDomain| *1 (|PermutationGroup| *4)) (|ofCategory| *4 (|SetCategory|)))) (|random| (*1 *2 *1) (AND (|isDomain| *2 (|Permutation| *3)) (|isDomain| *1 (|PermutationGroup| *3)) (|ofCategory| *3 (|SetCategory|)))) (|order| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|PermutationGroup| *3)) (|ofCategory| *3 (|SetCategory|)))) (|degree| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|PermutationGroup| *3)) (|ofCategory| *3 (|SetCategory|)))) (|base| (*1 *2 *1) (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PermutationGroup| *3)) (|ofCategory| *3 (|SetCategory|)))) (|strongGenerators| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Permutation| *3))) (|isDomain| *1 (|PermutationGroup| *3)) (|ofCategory| *3 (|SetCategory|)))) (|wordsForStrongGenerators| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|List| (|NonNegativeInteger|)))) (|isDomain| *1 (|PermutationGroup| *3)) (|ofCategory| *3 (|SetCategory|)))) (|permutationGroup| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Permutation| *3))) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|PermutationGroup| *3)))) (|orbit| (*1 *2 *1 *3) (AND (|isDomain| *2 (|Set| *3)) (|isDomain| *1 (|PermutationGroup| *3)) (|ofCategory| *3 (|SetCategory|)))) (|orbit| (*1 *2 *1 *3) (AND (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Set| (|Set| *4))) (|isDomain| *1 (|PermutationGroup| *4)) (|isDomain| *3 (|Set| *4)))) (|orbit| (*1 *2 *1 *3) (AND (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Set| (|List| *4))) (|isDomain| *1 (|PermutationGroup| *4)) (|isDomain| *3 (|List| *4)))) (|orbits| (*1 *2 *1) (AND (|isDomain| *2 (|Set| (|Set| *3))) (|isDomain| *1 (|PermutationGroup| *3)) (|ofCategory| *3 (|SetCategory|)))) (|member?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Permutation| *4)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PermutationGroup| *4)))) (|wordInStrongGenerators| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Permutation| *4)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|List| (|NonNegativeInteger|))) (|isDomain| *1 (|PermutationGroup| *4)))) (|wordInGenerators| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Permutation| *4)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|List| (|NonNegativeInteger|))) (|isDomain| *1 (|PermutationGroup| *4)))) (|movedPoints| (*1 *2 *1) (AND (|isDomain| *2 (|Set| *3)) (|isDomain| *1 (|PermutationGroup| *3)) (|ofCategory| *3 (|SetCategory|)))) (< (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PermutationGroup| *3)) (|ofCategory| *3 (|SetCategory|)))) (<= (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PermutationGroup| *3)) (|ofCategory| *3 (|SetCategory|)))) (|initializeGroupForWordProblem| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|PermutationGroup| *3)) (|ofCategory| *3 (|SetCategory|)))) (|initializeGroupForWordProblem| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|PermutationGroup| *4)) (|ofCategory| *4 (|SetCategory|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ((|List| (|Permutation| |#1|)) $)) (SIGNATURE |coerce| ($ (|List| (|Permutation| |#1|)))) (SIGNATURE |generators| ((|List| (|Permutation| |#1|)) $)) (SIGNATURE |elt| ((|Permutation| |#1|) $ (|NonNegativeInteger|))) (SIGNATURE |random| ((|Permutation| |#1|) $ (|Integer|))) (SIGNATURE |random| ((|Permutation| |#1|) $)) (SIGNATURE |order| ((|NonNegativeInteger|) $)) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |base| ((|List| |#1|) $)) (SIGNATURE |strongGenerators| ((|List| (|Permutation| |#1|)) $)) (SIGNATURE |wordsForStrongGenerators| ((|List| (|List| (|NonNegativeInteger|))) $)) (SIGNATURE |permutationGroup| ($ (|List| (|Permutation| |#1|)))) (SIGNATURE |orbit| ((|Set| |#1|) $ |#1|)) (SIGNATURE |orbit| ((|Set| (|Set| |#1|)) $ (|Set| |#1|))) (SIGNATURE |orbit| ((|Set| (|List| |#1|)) $ (|List| |#1|))) (SIGNATURE |orbits| ((|Set| (|Set| |#1|)) $)) (SIGNATURE |member?| ((|Boolean|) (|Permutation| |#1|) $)) (SIGNATURE |wordInStrongGenerators| ((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $)) (SIGNATURE |wordInGenerators| ((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $)) (SIGNATURE |movedPoints| ((|Set| |#1|) $)) (SIGNATURE < ((|Boolean|) $ $)) (SIGNATURE <= ((|Boolean|) $ $)) (SIGNATURE |initializeGroupForWordProblem| ((|Void|) $)) (SIGNATURE |initializeGroupForWordProblem| ((|Void|) $ (|Integer|) (|Integer|))))) 
((~= (((|Boolean|) $ $) NIL)) (|sort| (((|List| $) (|List| $)) 76)) (|sign| (((|Integer|) $) 59)) (|sample| (($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL)) (|order| (((|NonNegativeInteger|) $) 57)) (|orbit| (((|Set| |#1|) $ |#1|) 48)) (|one?| (((|Boolean|) $) NIL)) (|odd?| (((|Boolean|) $) 62)) (|numberOfCycles| (((|NonNegativeInteger|) $) 60)) (|movedPoints| (((|Set| |#1|) $) 41)) (|min| (($ $ $) NIL (OR (|has| |#1| (|Finite|)) (|has| |#1| (|OrderedSet|))))) (|max| (($ $ $) NIL (OR (|has| |#1| (|Finite|)) (|has| |#1| (|OrderedSet|))))) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) 35)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 92)) (|hash| (((|SingleInteger|) $) NIL)) (|fixedPoints| (((|Set| |#1|) $) 98 (|has| |#1| (|Finite|)))) (|even?| (((|Boolean|) $) 58)) (|eval| ((|#1| $ |#1|) 46)) (|elt| ((|#1| $ |#1|) 93)) (|degree| (((|NonNegativeInteger|) $) 43)) (|cycles| (($ (|List| (|List| |#1|))) 84)) (|cyclePartition| (((|Partition|) $) 52)) (|cycle| (($ (|List| |#1|)) 21)) (|conjugate| (($ $ $) NIL)) (|commutator| (($ $ $) NIL)) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) 38)) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) 87)) (|coerceImages| (($ (|List| |#1|)) 95)) (|coerce| (((|OutputForm|) $) 83) (($ (|List| (|List| |#1|))) 65) (($ (|List| |#1|)) 66)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|One| (($) 16 T CONST)) (>= (((|Boolean|) $ $) NIL (OR (|has| |#1| (|Finite|)) (|has| |#1| (|OrderedSet|))))) (> (((|Boolean|) $ $) NIL (OR (|has| |#1| (|Finite|)) (|has| |#1| (|OrderedSet|))))) (= (((|Boolean|) $ $) 44)) (<= (((|Boolean|) $ $) NIL (OR (|has| |#1| (|Finite|)) (|has| |#1| (|OrderedSet|))))) (< (((|Boolean|) $ $) 64)) (/ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ $ $) 22))) 
(((|Permutation| |#1|) (|Join| (|PermutationCategory| |#1|) (CATEGORY |domain| (SIGNATURE |listRepresentation| ((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $)) (SIGNATURE |coercePreimagesImages| ($ (|List| (|List| |#1|)))) (SIGNATURE |coerce| ($ (|List| (|List| |#1|)))) (SIGNATURE |coerce| ($ (|List| |#1|))) (SIGNATURE |coerceListOfPairs| ($ (|List| (|List| |#1|)))) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |movedPoints| ((|Set| |#1|) $)) (SIGNATURE |cyclePartition| ((|Partition|) $)) (SIGNATURE |order| ((|NonNegativeInteger|) $)) (SIGNATURE |numberOfCycles| ((|NonNegativeInteger|) $)) (SIGNATURE |sign| ((|Integer|) $)) (SIGNATURE |even?| ((|Boolean|) $)) (SIGNATURE |odd?| ((|Boolean|) $)) (SIGNATURE |sort| ((|List| $) (|List| $))) (IF (|has| |#1| (|Finite|)) (SIGNATURE |fixedPoints| ((|Set| |#1|) $)) |noBranch|) (IF (|has| |#1| (|IntegerNumberSystem|)) (SIGNATURE |coerceImages| ($ (|List| |#1|))) (IF (|has| |#1| (|Finite|)) (SIGNATURE |coerceImages| ($ (|List| |#1|))) |noBranch|)))) (|SetCategory|)) (T |Permutation|)) 
((|listRepresentation| (*1 *2 *1) (AND (|isDomain| *2 (|Record| (|:| |preimage| (|List| *3)) (|:| |image| (|List| *3)))) (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|)))) (|coercePreimagesImages| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Permutation| *3)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Permutation| *3)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Permutation| *3)))) (|coerceListOfPairs| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Permutation| *3)))) (|degree| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|)))) (|movedPoints| (*1 *2 *1) (AND (|isDomain| *2 (|Set| *3)) (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|)))) (|cyclePartition| (*1 *2 *1) (AND (|isDomain| *2 (|Partition|)) (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|)))) (|order| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|)))) (|numberOfCycles| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|)))) (|sign| (*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|)))) (|even?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|)))) (|odd?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|)))) (|sort| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|Permutation| *3))) (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|)))) (|fixedPoints| (*1 *2 *1) (AND (|isDomain| *2 (|Set| *3)) (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|Finite|)) (|ofCategory| *3 (|SetCategory|)))) (|coerceImages| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Permutation| *3))))) 
(|Join| (|PermutationCategory| |#1|) (CATEGORY |domain| (SIGNATURE |listRepresentation| ((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $)) (SIGNATURE |coercePreimagesImages| ($ (|List| (|List| |#1|)))) (SIGNATURE |coerce| ($ (|List| (|List| |#1|)))) (SIGNATURE |coerce| ($ (|List| |#1|))) (SIGNATURE |coerceListOfPairs| ($ (|List| (|List| |#1|)))) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |movedPoints| ((|Set| |#1|) $)) (SIGNATURE |cyclePartition| ((|Partition|) $)) (SIGNATURE |order| ((|NonNegativeInteger|) $)) (SIGNATURE |numberOfCycles| ((|NonNegativeInteger|) $)) (SIGNATURE |sign| ((|Integer|) $)) (SIGNATURE |even?| ((|Boolean|) $)) (SIGNATURE |odd?| ((|Boolean|) $)) (SIGNATURE |sort| ((|List| $) (|List| $))) (IF (|has| |#1| (|Finite|)) (SIGNATURE |fixedPoints| ((|Set| |#1|) $)) |noBranch|) (IF (|has| |#1| (|IntegerNumberSystem|)) (SIGNATURE |coerceImages| ($ (|List| |#1|))) (IF (|has| |#1| (|Finite|)) (SIGNATURE |coerceImages| ($ (|List| |#1|))) |noBranch|)))) 
((|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) 127)) (|randomR| ((|#1|) 75)) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) 136)) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) 67)) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) 146)) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) 91))) 
(((|PolynomialFactorizationByRecursion| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquationByRecursion| ((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |factorByRecursion| ((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |factorSquareFreeByRecursion| ((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |randomR| (|#1|)) (SIGNATURE |bivariateSLPEBR| ((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|)) (SIGNATURE |factorSFBRlcUnit| ((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)))) (|PolynomialFactorizationExplicit|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |PolynomialFactorizationByRecursion|)) 
((|factorSFBRlcUnit| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *5 (|PolynomialFactorizationExplicit|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|PolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *8))) (|isDomain| *1 (|PolynomialFactorizationByRecursion| *5 *6 *7 *8)) (|isDomain| *4 (|SparseUnivariatePolynomial| *8)))) (|bivariateSLPEBR| (*1 *2 *2 *3 *4) (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *7))) (|isDomain| *3 (|SparseUnivariatePolynomial| *7)) (|ofCategory| *7 (|PolynomialCategory| *5 *6 *4)) (|ofCategory| *5 (|PolynomialFactorizationExplicit|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|PolynomialFactorizationByRecursion| *5 *6 *4 *7)))) (|randomR| (*1 *2) (AND (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|PolynomialFactorizationExplicit|)) (|isDomain| *1 (|PolynomialFactorizationByRecursion| *2 *3 *4 *5)) (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4)))) (|factorSquareFreeByRecursion| (*1 *2 *3) (AND (|ofCategory| *4 (|PolynomialFactorizationExplicit|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *7))) (|isDomain| *1 (|PolynomialFactorizationByRecursion| *4 *5 *6 *7)) (|isDomain| *3 (|SparseUnivariatePolynomial| *7)))) (|factorByRecursion| (*1 *2 *3) (AND (|ofCategory| *4 (|PolynomialFactorizationExplicit|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *7))) (|isDomain| *1 (|PolynomialFactorizationByRecursion| *4 *5 *6 *7)) (|isDomain| *3 (|SparseUnivariatePolynomial| *7)))) (|solveLinearPolynomialEquationByRecursion| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *7))) (|isDomain| *3 (|SparseUnivariatePolynomial| *7)) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|PolynomialFactorizationExplicit|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *1 (|PolynomialFactorizationByRecursion| *4 *5 *6 *7))))) 
(CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquationByRecursion| ((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |factorByRecursion| ((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |factorSquareFreeByRecursion| ((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |randomR| (|#1|)) (SIGNATURE |bivariateSLPEBR| ((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|)) (SIGNATURE |factorSFBRlcUnit| ((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)))) 
((|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) 36)) (|randomR| ((|#1|) 53)) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) 101)) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) 88)) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) 112))) 
(((|PolynomialFactorizationByRecursionUnivariate| |#1| |#2|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquationByRecursion| ((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |factorByRecursion| ((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |factorSquareFreeByRecursion| ((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |randomR| (|#1|)) (SIGNATURE |factorSFBRlcUnit| ((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)))) (|PolynomialFactorizationExplicit|) (|UnivariatePolynomialCategory| |#1|)) (T |PolynomialFactorizationByRecursionUnivariate|)) 
((|factorSFBRlcUnit| (*1 *2 *3) (AND (|ofCategory| *4 (|PolynomialFactorizationExplicit|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *5))) (|isDomain| *1 (|PolynomialFactorizationByRecursionUnivariate| *4 *5)) (|isDomain| *3 (|SparseUnivariatePolynomial| *5)))) (|randomR| (*1 *2) (AND (|ofCategory| *2 (|PolynomialFactorizationExplicit|)) (|isDomain| *1 (|PolynomialFactorizationByRecursionUnivariate| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|factorSquareFreeByRecursion| (*1 *2 *3) (AND (|ofCategory| *4 (|PolynomialFactorizationExplicit|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *5))) (|isDomain| *1 (|PolynomialFactorizationByRecursionUnivariate| *4 *5)) (|isDomain| *3 (|SparseUnivariatePolynomial| *5)))) (|factorByRecursion| (*1 *2 *3) (AND (|ofCategory| *4 (|PolynomialFactorizationExplicit|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *5))) (|isDomain| *1 (|PolynomialFactorizationByRecursionUnivariate| *4 *5)) (|isDomain| *3 (|SparseUnivariatePolynomial| *5)))) (|solveLinearPolynomialEquationByRecursion| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *5))) (|isDomain| *3 (|SparseUnivariatePolynomial| *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|PolynomialFactorizationExplicit|)) (|isDomain| *1 (|PolynomialFactorizationByRecursionUnivariate| *4 *5))))) 
(CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquationByRecursion| ((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |factorByRecursion| ((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |factorSquareFreeByRecursion| ((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |randomR| (|#1|)) (SIGNATURE |factorSFBRlcUnit| ((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)))) 
((|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 39)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 18)) (|charthRoot| (((|Union| $ "failed") $) 33))) 
(((|PolynomialFactorizationExplicit&| |#1|) (CATEGORY |domain| (SIGNATURE |charthRoot| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)))) (|PolynomialFactorizationExplicit|)) (T |PolynomialFactorizationExplicit&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |charthRoot| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 58)) (|squareFreePart| (($ $) 50)) (|squareFree| (((|Factored| $) $) 51)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 55)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|prime?| (((|Boolean|) $) 52)) (|one?| (((|Boolean|) $) 30)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 56)) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 57)) (|factor| (((|Factored| $) $) 49)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 54 (|has| $ (|CharacteristicNonZero|)))) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42)) (|charthRoot| (((|Union| $ "failed") $) 53 (|has| $ (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|PolynomialFactorizationExplicit|) (|Category|)) (T |PolynomialFactorizationExplicit|)) 
((|gcdPolynomial| (*1 *2 *2 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|PolynomialFactorizationExplicit|)))) (|squareFreePolynomial| (*1 *2 *3) (AND (|ofCategory| *1 (|PolynomialFactorizationExplicit|)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *1))) (|isDomain| *3 (|SparseUnivariatePolynomial| *1)))) (|factorPolynomial| (*1 *2 *3) (AND (|ofCategory| *1 (|PolynomialFactorizationExplicit|)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *1))) (|isDomain| *3 (|SparseUnivariatePolynomial| *1)))) (|factorSquareFreePolynomial| (*1 *2 *3) (AND (|ofCategory| *1 (|PolynomialFactorizationExplicit|)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *1))) (|isDomain| *3 (|SparseUnivariatePolynomial| *1)))) (|solveLinearPolynomialEquation| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *1))) (|isDomain| *3 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|PolynomialFactorizationExplicit|)))) (|conditionP| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|Matrix| *1)) (|ofCategory| *1 (|CharacteristicNonZero|)) (|ofCategory| *1 (|PolynomialFactorizationExplicit|)) (|isDomain| *2 (|Vector| *1)))) (|charthRoot| (*1 *1 *1) (|partial| AND (|ofCategory| *1 (|CharacteristicNonZero|)) (|ofCategory| *1 (|PolynomialFactorizationExplicit|))))) 
(|Join| (|UniqueFactorizationDomain|) (CATEGORY |domain| (SIGNATURE |squareFreePolynomial| ((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $))) (SIGNATURE |factorPolynomial| ((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $))) (SIGNATURE |factorSquareFreePolynomial| ((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $))) (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $))) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $))) (IF (|has| $ (|CharacteristicNonZero|)) (PROGN (SIGNATURE |conditionP| ((|Union| (|Vector| $) "failed") (|Matrix| $))) (SIGNATURE |charthRoot| ((|Union| $ "failed") $))) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|UniqueFactorizationDomain|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|transcendent?| (((|Boolean|) $) NIL)) (|transcendenceDegree| (((|NonNegativeInteger|)) NIL)) (|trace| (($ $ (|PositiveInteger|)) NIL (|has| $ (|Finite|))) (($ $) NIL)) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|size| (((|NonNegativeInteger|)) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| $ "failed") $) NIL)) (|retract| (($ $) NIL)) (|represents| (($ (|Vector| $)) NIL)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL)) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) NIL)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|primitiveElement| (($) NIL)) (|primitive?| (((|Boolean|) $) NIL)) (|primeFrobenius| (($ $) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) NIL) (((|PositiveInteger|) $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|normalElement| (($) NIL (|has| $ (|Finite|)))) (|normal?| (((|Boolean|) $) NIL (|has| $ (|Finite|)))) (|norm| (($ $ (|PositiveInteger|)) NIL (|has| $ (|Finite|))) (($ $) NIL)) (|nextItem| (((|Union| $ "failed") $) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) NIL (|has| $ (|Finite|))) (((|SparseUnivariatePolynomial| $) $) NIL)) (|lookup| (((|PositiveInteger|) $) NIL)) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| $) $) NIL (|has| $ (|Finite|)))) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $ $) NIL (|has| $ (|Finite|))) (((|SparseUnivariatePolynomial| $) $) NIL (|has| $ (|Finite|)))) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| $)) NIL (|has| $ (|Finite|)))) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|init| (($) NIL T CONST)) (|index| (($ (|PositiveInteger|)) NIL)) (|inGroundField?| (((|Boolean|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|generator| (($) NIL (|has| $ (|Finite|)))) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) NIL)) (|factor| (((|Factored| $) $) NIL)) (|extensionDegree| (((|PositiveInteger|)) NIL) (((|OnePointCompletion| (|PositiveInteger|))) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|enumerate| (((|List| $)) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) NIL) (((|NonNegativeInteger|) $) NIL)) (|dimension| (((|CardinalNumber|)) NIL)) (|differentiate| (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (|degree| (((|PositiveInteger|) $) NIL) (((|OnePointCompletion| (|PositiveInteger|)) $) NIL)) (|definingPolynomial| (((|SparseUnivariatePolynomial| $)) NIL)) (|createPrimitiveElement| (($) NIL)) (|createNormalElement| (($) NIL (|has| $ (|Finite|)))) (|coordinates| (((|Matrix| $) (|Vector| $)) NIL) (((|Vector| $) $) NIL)) (|convert| (((|Integer|) $) NIL)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL)) (|charthRoot| (((|Union| $ "failed") $) NIL) (($ $) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|basis| (((|Vector| $) (|PositiveInteger|)) NIL) (((|Vector| $)) NIL)) (|associates?| (((|Boolean|) $ $) NIL)) (|algebraic?| (((|Boolean|) $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (|Frobenius| (($ $ (|NonNegativeInteger|)) NIL (|has| $ (|Finite|))) (($ $) NIL (|has| $ (|Finite|)))) (D (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (= (((|Boolean|) $ $) NIL)) (/ (($ $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL))) 
(((|PrimeField| |#1|) (|Join| (|FiniteFieldCategory|) (|FiniteAlgebraicExtensionField| $) (|ConvertibleTo| (|Integer|))) (|PositiveInteger|)) (T |PrimeField|)) 
NIL 
(|Join| (|FiniteFieldCategory|) (|FiniteAlgebraicExtensionField| $) (|ConvertibleTo| (|Integer|))) 
((|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) 76)) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) 16)) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) 14))) 
(((|PointsOfFiniteOrder| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |order| ((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|))) (SIGNATURE |torsion?| ((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|))) (SIGNATURE |torsionIfCan| ((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)))) (|Join| (|OrderedSet|) (|IntegralDomain|) (|RetractableTo| (|Integer|))) (|FunctionSpace| |#1|) (|UnivariatePolynomialCategory| |#2|) (|UnivariatePolynomialCategory| (|Fraction| |#3|)) (|FunctionFieldCategory| |#2| |#3| |#4|)) (T |PointsOfFiniteOrder|)) 
((|torsionIfCan| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|FiniteDivisor| *5 *6 *7 *8)) (|ofCategory| *5 (|FunctionSpace| *4)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|ofCategory| *8 (|FunctionFieldCategory| *5 *6 *7)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| *8))) (|isDomain| *1 (|PointsOfFiniteOrder| *4 *5 *6 *7 *8)))) (|torsion?| (*1 *2 *3) (AND (|isDomain| *3 (|FiniteDivisor| *5 *6 *7 *8)) (|ofCategory| *5 (|FunctionSpace| *4)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|ofCategory| *8 (|FunctionFieldCategory| *5 *6 *7)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PointsOfFiniteOrder| *4 *5 *6 *7 *8)))) (|order| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|FiniteDivisor| *5 *6 *7 *8)) (|ofCategory| *5 (|FunctionSpace| *4)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|ofCategory| *8 (|FunctionFieldCategory| *5 *6 *7)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|PointsOfFiniteOrder| *4 *5 *6 *7 *8))))) 
(CATEGORY |package| (SIGNATURE |order| ((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|))) (SIGNATURE |torsion?| ((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|))) (SIGNATURE |torsionIfCan| ((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)))) 
((|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) 56)) (|torsion?| (((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) 13)) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) 11))) 
(((|PointsOfFiniteOrderRational| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |order| ((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|))) (SIGNATURE |torsion?| ((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|))) (SIGNATURE |torsionIfCan| ((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)))) (|UnivariatePolynomialCategory| (|Fraction| (|Integer|))) (|UnivariatePolynomialCategory| (|Fraction| |#1|)) (|FunctionFieldCategory| (|Fraction| (|Integer|)) |#1| |#2|)) (T |PointsOfFiniteOrderRational|)) 
((|torsionIfCan| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|FiniteDivisor| (|Fraction| (|Integer|)) *4 *5 *6)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *6 (|FunctionFieldCategory| (|Fraction| (|Integer|)) *4 *5)) (|isDomain| *2 (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| *6))) (|isDomain| *1 (|PointsOfFiniteOrderRational| *4 *5 *6)))) (|torsion?| (*1 *2 *3) (AND (|isDomain| *3 (|FiniteDivisor| (|Fraction| (|Integer|)) *4 *5 *6)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *6 (|FunctionFieldCategory| (|Fraction| (|Integer|)) *4 *5)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PointsOfFiniteOrderRational| *4 *5 *6)))) (|order| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|FiniteDivisor| (|Fraction| (|Integer|)) *4 *5 *6)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *6 (|FunctionFieldCategory| (|Fraction| (|Integer|)) *4 *5)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|PointsOfFiniteOrderRational| *4 *5 *6))))) 
(CATEGORY |package| (SIGNATURE |order| ((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|))) (SIGNATURE |torsion?| ((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|))) (SIGNATURE |torsionIfCan| ((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)))) 
((|univariate| (((|SparseUnivariatePolynomial| |#1|) |#2|) 36)) (|translate| ((|#2| |#2| (|List| |#1|)) 59) ((|#2| |#2| (|List| |#1|) (|Integer|)) 61)) (|totalDegree| (((|NonNegativeInteger|) |#2|) 70)) (|subsInVar| ((|#2| |#2| |#2| (|Integer|)) 51)) (|subs2ndVar| ((|#2| |#2| |#2|) 49)) (|subs1stVar| ((|#2| |#2| |#2|) 48)) (|replaceVarByZero| ((|#2| |#2| (|Integer|)) 64)) (|replaceVarByOne| ((|#2| |#2| (|Integer|)) 60)) (|monomials| (((|List| |#2|) |#2|) 15)) (|minimalForm| ((|#2| |#2|) 82)) (|mapExponents| ((|#2| (|Mapping| |#3| |#3|) |#2|) 40)) (|listVariable| (((|List| |#2|)) 26)) (|listAllMonoExp| (((|List| |#3|) (|Integer|)) 92)) (|listAllMono| (((|List| |#2|) (|NonNegativeInteger|)) 93)) (|homogenize| ((|#2| |#2| (|Integer|)) 71)) (|firstExponent| ((|#3| |#2|) NIL)) (|degreeOfMinimalForm| (((|NonNegativeInteger|) |#2|) 83)) (|degree| (((|NonNegativeInteger|) |#2| (|Integer|)) 67)) (|degOneCoef| ((|#1| |#2| (|PositiveInteger|)) 80)) (|constant| ((|#1| |#2|) 81))) 
(((|PackageForPoly| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |mapExponents| (|#2| (|Mapping| |#3| |#3|) |#2|)) (SIGNATURE |degree| ((|NonNegativeInteger|) |#2| (|Integer|))) (SIGNATURE |univariate| ((|SparseUnivariatePolynomial| |#1|) |#2|)) (SIGNATURE |totalDegree| ((|NonNegativeInteger|) |#2|)) (SIGNATURE |subs1stVar| (|#2| |#2| |#2|)) (SIGNATURE |subs2ndVar| (|#2| |#2| |#2|)) (SIGNATURE |subsInVar| (|#2| |#2| |#2| (|Integer|))) (SIGNATURE |minimalForm| (|#2| |#2|)) (SIGNATURE |firstExponent| (|#3| |#2|)) (SIGNATURE |replaceVarByZero| (|#2| |#2| (|Integer|))) (SIGNATURE |replaceVarByOne| (|#2| |#2| (|Integer|))) (SIGNATURE |translate| (|#2| |#2| (|List| |#1|) (|Integer|))) (SIGNATURE |translate| (|#2| |#2| (|List| |#1|))) (SIGNATURE |degOneCoef| (|#1| |#2| (|PositiveInteger|))) (SIGNATURE |constant| (|#1| |#2|)) (SIGNATURE |homogenize| (|#2| |#2| (|Integer|))) (SIGNATURE |listAllMonoExp| ((|List| |#3|) (|Integer|))) (SIGNATURE |listAllMono| ((|List| |#2|) (|NonNegativeInteger|))) (SIGNATURE |degreeOfMinimalForm| ((|NonNegativeInteger|) |#2|)) (SIGNATURE |listVariable| ((|List| |#2|))) (SIGNATURE |monomials| ((|List| |#2|) |#2|))) (|Ring|) (|FiniteAbelianMonoidRing| |#1| |#3|) (|DirectProductCategory| |#4| (|NonNegativeInteger|)) (|NonNegativeInteger|)) (T |PackageForPoly|)) 
((|monomials| (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *6 (|NonNegativeInteger|))) (|ofType| *6 (|NonNegativeInteger|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PackageForPoly| *4 *3 *5 *6)) (|ofCategory| *3 (|FiniteAbelianMonoidRing| *4 *5)))) (|listVariable| (*1 *2) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *6 (|NonNegativeInteger|))) (|ofType| *6 (|NonNegativeInteger|)) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|PackageForPoly| *3 *4 *5 *6)) (|ofCategory| *4 (|FiniteAbelianMonoidRing| *3 *5)))) (|degreeOfMinimalForm| (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *6 *2)) (|ofType| *6 *2) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|PackageForPoly| *4 *3 *5 *6)) (|ofCategory| *3 (|FiniteAbelianMonoidRing| *4 *5)))) (|listAllMono| (*1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *7 *3)) (|ofType| *7 *3) (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|PackageForPoly| *4 *5 *6 *7)) (|ofCategory| *5 (|FiniteAbelianMonoidRing| *4 *6)))) (|listAllMonoExp| (*1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *7 (|NonNegativeInteger|))) (|ofType| *7 (|NonNegativeInteger|)) (|isDomain| *2 (|List| *6)) (|isDomain| *1 (|PackageForPoly| *4 *5 *6 *7)) (|ofCategory| *5 (|FiniteAbelianMonoidRing| *4 *6)))) (|homogenize| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *6 (|NonNegativeInteger|))) (|ofType| *6 (|NonNegativeInteger|)) (|isDomain| *1 (|PackageForPoly| *4 *2 *5 *6)) (|ofCategory| *2 (|FiniteAbelianMonoidRing| *4 *5)))) (|constant| (*1 *2 *3) (AND (|ofCategory| *4 (|DirectProductCategory| *5 (|NonNegativeInteger|))) (|ofType| *5 (|NonNegativeInteger|)) (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|PackageForPoly| *2 *3 *4 *5)) (|ofCategory| *3 (|FiniteAbelianMonoidRing| *2 *4)))) (|degOneCoef| (*1 *2 *3 *4) (AND (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|DirectProductCategory| *6 (|NonNegativeInteger|))) (|ofType| *6 (|NonNegativeInteger|)) (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|PackageForPoly| *2 *3 *5 *6)) (|ofCategory| *3 (|FiniteAbelianMonoidRing| *2 *5)))) (|translate| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *6 (|NonNegativeInteger|))) (|ofType| *6 (|NonNegativeInteger|)) (|isDomain| *1 (|PackageForPoly| *4 *2 *5 *6)) (|ofCategory| *2 (|FiniteAbelianMonoidRing| *4 *5)))) (|translate| (*1 *2 *2 *3 *4) (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|Integer|)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *7 (|NonNegativeInteger|))) (|ofType| *7 (|NonNegativeInteger|)) (|isDomain| *1 (|PackageForPoly| *5 *2 *6 *7)) (|ofCategory| *2 (|FiniteAbelianMonoidRing| *5 *6)))) (|replaceVarByOne| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *6 (|NonNegativeInteger|))) (|ofType| *6 (|NonNegativeInteger|)) (|isDomain| *1 (|PackageForPoly| *4 *2 *5 *6)) (|ofCategory| *2 (|FiniteAbelianMonoidRing| *4 *5)))) (|replaceVarByZero| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *6 (|NonNegativeInteger|))) (|ofType| *6 (|NonNegativeInteger|)) (|isDomain| *1 (|PackageForPoly| *4 *2 *5 *6)) (|ofCategory| *2 (|FiniteAbelianMonoidRing| *4 *5)))) (|firstExponent| (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|DirectProductCategory| *5 (|NonNegativeInteger|))) (|isDomain| *1 (|PackageForPoly| *4 *3 *2 *5)) (|ofCategory| *3 (|FiniteAbelianMonoidRing| *4 *2)) (|ofType| *5 (|NonNegativeInteger|)))) (|minimalForm| (*1 *2 *2) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|DirectProductCategory| *5 (|NonNegativeInteger|))) (|ofType| *5 (|NonNegativeInteger|)) (|isDomain| *1 (|PackageForPoly| *3 *2 *4 *5)) (|ofCategory| *2 (|FiniteAbelianMonoidRing| *3 *4)))) (|subsInVar| (*1 *2 *2 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *6 (|NonNegativeInteger|))) (|ofType| *6 (|NonNegativeInteger|)) (|isDomain| *1 (|PackageForPoly| *4 *2 *5 *6)) (|ofCategory| *2 (|FiniteAbelianMonoidRing| *4 *5)))) (|subs2ndVar| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|DirectProductCategory| *5 (|NonNegativeInteger|))) (|ofType| *5 (|NonNegativeInteger|)) (|isDomain| *1 (|PackageForPoly| *3 *2 *4 *5)) (|ofCategory| *2 (|FiniteAbelianMonoidRing| *3 *4)))) (|subs1stVar| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|DirectProductCategory| *5 (|NonNegativeInteger|))) (|ofType| *5 (|NonNegativeInteger|)) (|isDomain| *1 (|PackageForPoly| *3 *2 *4 *5)) (|ofCategory| *2 (|FiniteAbelianMonoidRing| *3 *4)))) (|totalDegree| (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *6 *2)) (|ofType| *6 *2) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|PackageForPoly| *4 *3 *5 *6)) (|ofCategory| *3 (|FiniteAbelianMonoidRing| *4 *5)))) (|univariate| (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *6 (|NonNegativeInteger|))) (|ofType| *6 (|NonNegativeInteger|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|isDomain| *1 (|PackageForPoly| *4 *3 *5 *6)) (|ofCategory| *3 (|FiniteAbelianMonoidRing| *4 *5)))) (|degree| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Integer|)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *7 *2)) (|ofType| *7 *2) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|PackageForPoly| *5 *3 *6 *7)) (|ofCategory| *3 (|FiniteAbelianMonoidRing| *5 *6)))) (|mapExponents| (*1 *2 *3 *2) (AND (|isDomain| *3 (|Mapping| *5 *5)) (|ofCategory| *5 (|DirectProductCategory| *6 (|NonNegativeInteger|))) (|ofType| *6 (|NonNegativeInteger|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|PackageForPoly| *4 *2 *5 *6)) (|ofCategory| *2 (|FiniteAbelianMonoidRing| *4 *5))))) 
(CATEGORY |package| (SIGNATURE |mapExponents| (|#2| (|Mapping| |#3| |#3|) |#2|)) (SIGNATURE |degree| ((|NonNegativeInteger|) |#2| (|Integer|))) (SIGNATURE |univariate| ((|SparseUnivariatePolynomial| |#1|) |#2|)) (SIGNATURE |totalDegree| ((|NonNegativeInteger|) |#2|)) (SIGNATURE |subs1stVar| (|#2| |#2| |#2|)) (SIGNATURE |subs2ndVar| (|#2| |#2| |#2|)) (SIGNATURE |subsInVar| (|#2| |#2| |#2| (|Integer|))) (SIGNATURE |minimalForm| (|#2| |#2|)) (SIGNATURE |firstExponent| (|#3| |#2|)) (SIGNATURE |replaceVarByZero| (|#2| |#2| (|Integer|))) (SIGNATURE |replaceVarByOne| (|#2| |#2| (|Integer|))) (SIGNATURE |translate| (|#2| |#2| (|List| |#1|) (|Integer|))) (SIGNATURE |translate| (|#2| |#2| (|List| |#1|))) (SIGNATURE |degOneCoef| (|#1| |#2| (|PositiveInteger|))) (SIGNATURE |constant| (|#1| |#2|)) (SIGNATURE |homogenize| (|#2| |#2| (|Integer|))) (SIGNATURE |listAllMonoExp| ((|List| |#3|) (|Integer|))) (SIGNATURE |listAllMono| ((|List| |#2|) (|NonNegativeInteger|))) (SIGNATURE |degreeOfMinimalForm| ((|NonNegativeInteger|) |#2|)) (SIGNATURE |listVariable| ((|List| |#2|))) (SIGNATURE |monomials| ((|List| |#2|) |#2|))) 
((|polyred| ((|#2| |#2|) 25)) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) 15)) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) 35)) (|doubleDisc| (((|Integer|) |#2|) 42)) (|badNum| (((|Integer|) |#2|) 21) (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) 20))) 
(((|PointsOfFiniteOrderTools| |#1| |#2|) (CATEGORY |package| (SIGNATURE |getGoodPrime| ((|PositiveInteger|) (|Integer|))) (SIGNATURE |badNum| ((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|)) (SIGNATURE |badNum| ((|Integer|) |#2|)) (SIGNATURE |mix| ((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|)))))) (SIGNATURE |doubleDisc| ((|Integer|) |#2|)) (SIGNATURE |polyred| (|#2| |#2|))) (|UnivariatePolynomialCategory| (|Fraction| (|Integer|))) (|UnivariatePolynomialCategory| (|Fraction| |#1|))) (T |PointsOfFiniteOrderTools|)) 
((|polyred| (*1 *2 *2) (AND (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|)))) (|isDomain| *1 (|PointsOfFiniteOrderTools| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Fraction| *3))))) (|doubleDisc| (*1 *2 *3) (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *2))) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PointsOfFiniteOrderTools| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|mix| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *2))) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PointsOfFiniteOrderTools| *4 *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|badNum| (*1 *2 *3) (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *2))) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PointsOfFiniteOrderTools| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|badNum| (*1 *2 *3) (AND (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|)))) (|isDomain| *1 (|PointsOfFiniteOrderTools| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3))))) (|getGoodPrime| (*1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|PointsOfFiniteOrderTools| *4 *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))))) 
(CATEGORY |package| (SIGNATURE |getGoodPrime| ((|PositiveInteger|) (|Integer|))) (SIGNATURE |badNum| ((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|)) (SIGNATURE |badNum| ((|Integer|) |#2|)) (SIGNATURE |mix| ((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|)))))) (SIGNATURE |doubleDisc| ((|Integer|) |#2|)) (SIGNATURE |polyred| (|#2| |#2|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|wholePart| ((|#1| $) 80)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sample| (($) NIL T CONST)) (|rem| (($ $ $) NIL)) (|recip| (((|Union| $ "failed") $) 74)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|partialFraction| (($ |#1| (|Factored| |#1|)) 72)) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) 40)) (|padicFraction| (($ $) 48)) (|one?| (((|Boolean|) $) NIL)) (|numberOfFractionalTerms| (((|Integer|) $) 77)) (|nthFractionalTerm| (($ $ (|Integer|)) 79)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|firstNumer| ((|#1| $) 76)) (|firstDenom| (((|Factored| |#1|) $) 75)) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) 73)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|compactFraction| (($ $) 38)) (|coerce| (((|OutputForm|) $) 98) (($ (|Integer|)) 53) (($ $) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ |#1|) 30) (((|Fraction| |#1|) $) 58) (($ (|Fraction| (|Factored| |#1|))) 66)) (|characteristic| (((|NonNegativeInteger|)) 51)) (|associates?| (((|Boolean|) $ $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) 23 T CONST)) (|One| (($) 11 T CONST)) (= (((|Boolean|) $ $) 67)) (/ (($ $ $) NIL)) (- (($ $) 87) (($ $ $) NIL)) (+ (($ $ $) 37)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 89) (($ $ $) 36) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ |#1| $) 88) (($ $ |#1|) NIL))) 
(((|PartialFraction| |#1|) (|Join| (|Field|) (|Algebra| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ((|Fraction| |#1|) $)) (SIGNATURE |coerce| ($ (|Fraction| (|Factored| |#1|)))) (SIGNATURE |compactFraction| ($ $)) (SIGNATURE |firstDenom| ((|Factored| |#1|) $)) (SIGNATURE |firstNumer| (|#1| $)) (SIGNATURE |nthFractionalTerm| ($ $ (|Integer|))) (SIGNATURE |numberOfFractionalTerms| ((|Integer|) $)) (SIGNATURE |padicallyExpand| ((|SparseUnivariatePolynomial| |#1|) |#1| |#1|)) (SIGNATURE |padicFraction| ($ $)) (SIGNATURE |partialFraction| ($ |#1| (|Factored| |#1|))) (SIGNATURE |wholePart| (|#1| $)))) (|EuclideanDomain|)) (T |PartialFraction|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Fraction| *3)) (|isDomain| *1 (|PartialFraction| *3)) (|ofCategory| *3 (|EuclideanDomain|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Factored| *3))) (|ofCategory| *3 (|EuclideanDomain|)) (|isDomain| *1 (|PartialFraction| *3)))) (|compactFraction| (*1 *1 *1) (AND (|isDomain| *1 (|PartialFraction| *2)) (|ofCategory| *2 (|EuclideanDomain|)))) (|firstDenom| (*1 *2 *1) (AND (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|PartialFraction| *3)) (|ofCategory| *3 (|EuclideanDomain|)))) (|firstNumer| (*1 *2 *1) (AND (|isDomain| *1 (|PartialFraction| *2)) (|ofCategory| *2 (|EuclideanDomain|)))) (|nthFractionalTerm| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PartialFraction| *3)) (|ofCategory| *3 (|EuclideanDomain|)))) (|numberOfFractionalTerms| (*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PartialFraction| *3)) (|ofCategory| *3 (|EuclideanDomain|)))) (|padicallyExpand| (*1 *2 *3 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) (|isDomain| *1 (|PartialFraction| *3)) (|ofCategory| *3 (|EuclideanDomain|)))) (|padicFraction| (*1 *1 *1) (AND (|isDomain| *1 (|PartialFraction| *2)) (|ofCategory| *2 (|EuclideanDomain|)))) (|partialFraction| (*1 *1 *2 *3) (AND (|isDomain| *3 (|Factored| *2)) (|ofCategory| *2 (|EuclideanDomain|)) (|isDomain| *1 (|PartialFraction| *2)))) (|wholePart| (*1 *2 *1) (AND (|isDomain| *1 (|PartialFraction| *2)) (|ofCategory| *2 (|EuclideanDomain|))))) 
(|Join| (|Field|) (|Algebra| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ((|Fraction| |#1|) $)) (SIGNATURE |coerce| ($ (|Fraction| (|Factored| |#1|)))) (SIGNATURE |compactFraction| ($ $)) (SIGNATURE |firstDenom| ((|Factored| |#1|) $)) (SIGNATURE |firstNumer| (|#1| $)) (SIGNATURE |nthFractionalTerm| ($ $ (|Integer|))) (SIGNATURE |numberOfFractionalTerms| ((|Integer|) $)) (SIGNATURE |padicallyExpand| ((|SparseUnivariatePolynomial| |#1|) |#1| |#1|)) (SIGNATURE |padicFraction| ($ $)) (SIGNATURE |partialFraction| ($ |#1| (|Factored| |#1|))) (SIGNATURE |wholePart| (|#1| $)))) 
((|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) 16) (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) 17))) 
(((|PartialFractionPackage| |#1|) (CATEGORY |package| (SIGNATURE |partialFraction| ((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |partialFraction| ((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (T |PartialFractionPackage|)) 
((|partialFraction| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|Factored| (|Polynomial| *6))) (|isDomain| *5 (|Symbol|)) (|isDomain| *3 (|Polynomial| *6)) (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|PartialFractionPackage| *6)))) (|partialFraction| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5))) (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|PartialFractionPackage| *5))))) 
(CATEGORY |package| (SIGNATURE |partialFraction| ((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |partialFraction| ((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)))) 
((|gcdPrimitive| ((|#4| (|List| |#4|)) 119) (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) 65) ((|#4| |#4| |#4|) 118)) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) 112) (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) 48) ((|#4| (|List| |#4|)) 53) ((|#4| |#4| |#4|) 82))) 
(((|PolynomialGcdPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |gcd| (|#4| |#4| |#4|)) (SIGNATURE |gcd| (|#4| (|List| |#4|))) (SIGNATURE |gcd| ((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |gcd| ((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|)))) (SIGNATURE |gcdPrimitive| (|#4| |#4| |#4|)) (SIGNATURE |gcdPrimitive| ((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |gcdPrimitive| (|#4| (|List| |#4|)))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|EuclideanDomain|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |PolynomialGcdPackage|)) 
((|gcdPrimitive| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|PolynomialCategory| *6 *4 *5)) (|isDomain| *1 (|PolynomialGcdPackage| *4 *5 *6 *2)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|EuclideanDomain|)))) (|gcdPrimitive| (*1 *2 *2 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *6)) (|ofCategory| *6 (|PolynomialCategory| *5 *3 *4)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|EuclideanDomain|)) (|isDomain| *1 (|PolynomialGcdPackage| *3 *4 *5 *6)))) (|gcdPrimitive| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|EuclideanDomain|)) (|isDomain| *1 (|PolynomialGcdPackage| *3 *4 *5 *2)) (|ofCategory| *2 (|PolynomialCategory| *5 *3 *4)))) (|gcd| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|SparseUnivariatePolynomial| *7))) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|EuclideanDomain|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *7)) (|isDomain| *1 (|PolynomialGcdPackage| *4 *5 *6 *7)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)))) (|gcd| (*1 *2 *2 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *6)) (|ofCategory| *6 (|PolynomialCategory| *5 *3 *4)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|EuclideanDomain|)) (|isDomain| *1 (|PolynomialGcdPackage| *3 *4 *5 *6)))) (|gcd| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|PolynomialCategory| *6 *4 *5)) (|isDomain| *1 (|PolynomialGcdPackage| *4 *5 *6 *2)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|EuclideanDomain|)))) (|gcd| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|EuclideanDomain|)) (|isDomain| *1 (|PolynomialGcdPackage| *3 *4 *5 *2)) (|ofCategory| *2 (|PolynomialCategory| *5 *3 *4))))) 
(CATEGORY |package| (SIGNATURE |gcd| (|#4| |#4| |#4|)) (SIGNATURE |gcd| (|#4| (|List| |#4|))) (SIGNATURE |gcd| ((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |gcd| ((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|)))) (SIGNATURE |gcdPrimitive| (|#4| |#4| |#4|)) (SIGNATURE |gcdPrimitive| ((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |gcdPrimitive| (|#4| (|List| |#4|)))) 
((|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) 22) (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) 19)) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) 46) (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) 47)) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) 23)) (|mathieu24| (((|PermutationGroup| (|Integer|))) 36) (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) 35)) (|mathieu23| (((|PermutationGroup| (|Integer|))) 34) (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) 33)) (|mathieu22| (((|PermutationGroup| (|Integer|))) 32) (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) 31)) (|mathieu12| (((|PermutationGroup| (|Integer|))) 30) (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) 29)) (|mathieu11| (((|PermutationGroup| (|Integer|))) 28) (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) 27)) (|janko2| (((|PermutationGroup| (|Integer|))) 38) (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) 37)) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) 50) (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) 51)) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) 48) (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) 49)) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) 43) (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) 45)) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) 40))) 
(((|PermutationGroupExamples|) (CATEGORY |package| (SIGNATURE |symmetricGroup| ((|PermutationGroup| (|Integer|)) (|PositiveInteger|))) (SIGNATURE |symmetricGroup| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |alternatingGroup| ((|PermutationGroup| (|Integer|)) (|PositiveInteger|))) (SIGNATURE |alternatingGroup| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |abelianGroup| ((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|)))) (SIGNATURE |cyclicGroup| ((|PermutationGroup| (|Integer|)) (|PositiveInteger|))) (SIGNATURE |cyclicGroup| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |dihedralGroup| ((|PermutationGroup| (|Integer|)) (|PositiveInteger|))) (SIGNATURE |dihedralGroup| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |mathieu11| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |mathieu11| ((|PermutationGroup| (|Integer|)))) (SIGNATURE |mathieu12| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |mathieu12| ((|PermutationGroup| (|Integer|)))) (SIGNATURE |mathieu22| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |mathieu22| ((|PermutationGroup| (|Integer|)))) (SIGNATURE |mathieu23| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |mathieu23| ((|PermutationGroup| (|Integer|)))) (SIGNATURE |mathieu24| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |mathieu24| ((|PermutationGroup| (|Integer|)))) (SIGNATURE |janko2| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |janko2| ((|PermutationGroup| (|Integer|)))) (SIGNATURE |rubiksGroup| ((|PermutationGroup| (|Integer|)))) (SIGNATURE |youngGroup| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |youngGroup| ((|PermutationGroup| (|Integer|)) (|Partition|))))) (T |PermutationGroupExamples|)) 
((|youngGroup| (*1 *2 *3) (AND (|isDomain| *3 (|Partition|)) (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|youngGroup| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|rubiksGroup| (*1 *2) (AND (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|janko2| (*1 *2) (AND (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|janko2| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|mathieu24| (*1 *2) (AND (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|mathieu24| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|mathieu23| (*1 *2) (AND (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|mathieu23| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|mathieu22| (*1 *2) (AND (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|mathieu22| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|mathieu12| (*1 *2) (AND (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|mathieu12| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|mathieu11| (*1 *2) (AND (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|mathieu11| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|dihedralGroup| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|dihedralGroup| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|cyclicGroup| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|cyclicGroup| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|abelianGroup| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|PositiveInteger|))) (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|alternatingGroup| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|alternatingGroup| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|symmetricGroup| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|)))) (|symmetricGroup| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|))))) 
(CATEGORY |package| (SIGNATURE |symmetricGroup| ((|PermutationGroup| (|Integer|)) (|PositiveInteger|))) (SIGNATURE |symmetricGroup| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |alternatingGroup| ((|PermutationGroup| (|Integer|)) (|PositiveInteger|))) (SIGNATURE |alternatingGroup| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |abelianGroup| ((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|)))) (SIGNATURE |cyclicGroup| ((|PermutationGroup| (|Integer|)) (|PositiveInteger|))) (SIGNATURE |cyclicGroup| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |dihedralGroup| ((|PermutationGroup| (|Integer|)) (|PositiveInteger|))) (SIGNATURE |dihedralGroup| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |mathieu11| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |mathieu11| ((|PermutationGroup| (|Integer|)))) (SIGNATURE |mathieu12| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |mathieu12| ((|PermutationGroup| (|Integer|)))) (SIGNATURE |mathieu22| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |mathieu22| ((|PermutationGroup| (|Integer|)))) (SIGNATURE |mathieu23| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |mathieu23| ((|PermutationGroup| (|Integer|)))) (SIGNATURE |mathieu24| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |mathieu24| ((|PermutationGroup| (|Integer|)))) (SIGNATURE |janko2| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |janko2| ((|PermutationGroup| (|Integer|)))) (SIGNATURE |rubiksGroup| ((|PermutationGroup| (|Integer|)))) (SIGNATURE |youngGroup| ((|PermutationGroup| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |youngGroup| ((|PermutationGroup| (|Integer|)) (|Partition|)))) 
((|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) 10)) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) 9))) 
(((|PolyGroebner| |#1|) (CATEGORY |package| (SIGNATURE |lexGroebner| ((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)))) (SIGNATURE |totalGroebner| ((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))))) (|GcdDomain|)) (T |PolyGroebner|)) 
((|totalGroebner| (*1 *2 *2 *3) (AND (|isDomain| *2 (|List| (|Polynomial| *4))) (|isDomain| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|GcdDomain|)) (|isDomain| *1 (|PolyGroebner| *4)))) (|lexGroebner| (*1 *2 *2 *3) (AND (|isDomain| *2 (|List| (|Polynomial| *4))) (|isDomain| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|GcdDomain|)) (|isDomain| *1 (|PolyGroebner| *4))))) 
(CATEGORY |package| (SIGNATURE |lexGroebner| ((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)))) (SIGNATURE |totalGroebner| ((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))))) 
((|coerce| (((|Expression| |#1|) (|Pi|)) 15))) 
(((|PiCoercions| |#1|) (CATEGORY |package| (SIGNATURE |coerce| ((|Expression| |#1|) (|Pi|)))) (|Join| (|OrderedSet|) (|IntegralDomain|))) (T |PiCoercions|)) 
((|coerce| (*1 *2 *3) (AND (|isDomain| *3 (|Pi|)) (|isDomain| *2 (|Expression| *4)) (|isDomain| *1 (|PiCoercions| *4)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|)))))) 
(CATEGORY |package| (SIGNATURE |coerce| ((|Expression| |#1|) (|Pi|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 50)) (|one?| (((|Boolean|) $) 30)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 49)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|PrincipalIdealDomain|) (|Category|)) (T |PrincipalIdealDomain|)) 
((|principalIdeal| (*1 *2 *3) (AND (|ofCategory| *1 (|PrincipalIdealDomain|)) (|isDomain| *2 (|Record| (|:| |coef| (|List| *1)) (|:| |generator| *1))) (|isDomain| *3 (|List| *1)))) (|expressIdealMember| (*1 *2 *2 *1) (|partial| AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|PrincipalIdealDomain|))))) 
(|Join| (|GcdDomain|) (CATEGORY |domain| (SIGNATURE |principalIdeal| ((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $))) (SIGNATURE |expressIdealMember| ((|Union| (|List| $) "failed") (|List| $) $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|sample| (($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL)) (|qcoerce| (($ (|Integer|)) 7)) (|one?| (((|Boolean|) $) NIL)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|gcd| (($ $ $) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (^ (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|PositiveInteger|)) NIL)) (|One| (($) NIL T CONST)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|PositiveInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ $ $) NIL))) 
(((|PositiveInteger|) (|Join| (|AbelianSemiGroup|) (|OrderedSet|) (|Monoid|) (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $)) (ATTRIBUTE (|commutative| "*")) (SIGNATURE |qcoerce| ($ (|Integer|)))))) (T |PositiveInteger|)) 
((|gcd| (*1 *1 *1 *1) (|isDomain| *1 (|PositiveInteger|))) (|qcoerce| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PositiveInteger|))))) 
(|Join| (|AbelianSemiGroup|) (|OrderedSet|) (|Monoid|) (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $)) (ATTRIBUTE (|commutative| "*")) (SIGNATURE |qcoerce| ($ (|Integer|))))) 
((|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) 22))) 
(((|PolynomialInterpolationAlgorithms| |#1| |#2|) (CATEGORY |package| (SIGNATURE |LagrangeInterpolation| (|#2| (|List| |#1|) (|List| |#1|)))) (|Field|) (|UnivariatePolynomialCategory| |#1|)) (T |PolynomialInterpolationAlgorithms|)) 
((|LagrangeInterpolation| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|Field|)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|PolynomialInterpolationAlgorithms| *4 *2))))) 
(CATEGORY |package| (SIGNATURE |LagrangeInterpolation| (|#2| (|List| |#1|) (|List| |#1|)))) 
((|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) 17) (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) 13))) 
(((|PolynomialInterpolation| |#1| |#2|) (CATEGORY |package| (SIGNATURE |interpolate| ((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|))) (SIGNATURE |interpolate| ((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)))) (|Symbol|) (|Field|)) (T |PolynomialInterpolation|)) 
((|interpolate| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *5)) (|isDomain| *1 (|PolynomialInterpolation| *4 *5)) (|ofType| *4 (|Symbol|)))) (|interpolate| (*1 *2 *2 *3 *3) (AND (|isDomain| *2 (|UnivariatePolynomial| *4 *5)) (|isDomain| *3 (|List| *5)) (|ofType| *4 (|Symbol|)) (|ofCategory| *5 (|Field|)) (|isDomain| *1 (|PolynomialInterpolation| *4 *5))))) 
(CATEGORY |package| (SIGNATURE |interpolate| ((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|))) (SIGNATURE |interpolate| ((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)))) 
((~= (((|Boolean|) $ $) 7)) (|setParam!| (((|Void|) $ (|List| |#2|)) 19)) (|setFoundPlacesToEmpty| (((|List| $)) 14)) (|setDegree!| (((|Void|) $ (|PositiveInteger|)) 18)) (|reduce| (((|Divisor| $) (|List| $)) 23)) (|localParam| (((|List| |#2|) $) 20)) (|leaf?| (((|Boolean|) $) 17)) (|latex| (((|String|) $) 9)) (|itsALeaf!| (((|Void|) $) 16)) (|hash| (((|SingleInteger|) $) 10)) (|foundPlaces| (((|List| $)) 15)) (|elt| ((|#1| $ (|Integer|)) 13)) (|degree| (((|PositiveInteger|) $) 12)) (|create| (($ (|List| |#1|)) 22) (($ (|Symbol|)) 21)) (|coerce| (((|OutputForm|) $) 11)) (= (((|Boolean|) $ $) 6)) (- (((|Divisor| $) $ $) 28) (((|Divisor| $) (|Divisor| $) $) 27) (((|Divisor| $) $ (|Divisor| $)) 26) (((|Divisor| $) $) 25)) (+ (((|Divisor| $) $ $) 31) (((|Divisor| $) (|Divisor| $) $) 30) (((|Divisor| $) $ (|Divisor| $)) 29)) (* (((|Divisor| $) (|Integer|) $) 24))) 
(((|PlacesCategory| |#1| |#2|) (|Category|) (|Field|) (|LocalPowerSeriesCategory| |t#1|)) (T |PlacesCategory|)) 
((+ (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|LocalPowerSeriesCategory| *3)) (|isDomain| *2 (|Divisor| *1)) (|ofCategory| *1 (|PlacesCategory| *3 *4)))) (+ (*1 *2 *2 *1) (AND (|isDomain| *2 (|Divisor| *1)) (|ofCategory| *1 (|PlacesCategory| *3 *4)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|LocalPowerSeriesCategory| *3)))) (+ (*1 *2 *1 *2) (AND (|isDomain| *2 (|Divisor| *1)) (|ofCategory| *1 (|PlacesCategory| *3 *4)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|LocalPowerSeriesCategory| *3)))) (- (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|LocalPowerSeriesCategory| *3)) (|isDomain| *2 (|Divisor| *1)) (|ofCategory| *1 (|PlacesCategory| *3 *4)))) (- (*1 *2 *2 *1) (AND (|isDomain| *2 (|Divisor| *1)) (|ofCategory| *1 (|PlacesCategory| *3 *4)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|LocalPowerSeriesCategory| *3)))) (- (*1 *2 *1 *2) (AND (|isDomain| *2 (|Divisor| *1)) (|ofCategory| *1 (|PlacesCategory| *3 *4)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|LocalPowerSeriesCategory| *3)))) (- (*1 *2 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|LocalPowerSeriesCategory| *3)) (|isDomain| *2 (|Divisor| *1)) (|ofCategory| *1 (|PlacesCategory| *3 *4)))) (* (*1 *2 *3 *1) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|LocalPowerSeriesCategory| *4)) (|isDomain| *2 (|Divisor| *1)) (|ofCategory| *1 (|PlacesCategory| *4 *5)))) (|reduce| (*1 *2 *3) (AND (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|PlacesCategory| *4 *5)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|LocalPowerSeriesCategory| *4)) (|isDomain| *2 (|Divisor| *1)))) (|create| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *1 (|PlacesCategory| *3 *4)) (|ofCategory| *4 (|LocalPowerSeriesCategory| *3)))) (|create| (*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *3 (|Field|)) (|ofCategory| *1 (|PlacesCategory| *3 *4)) (|ofCategory| *4 (|LocalPowerSeriesCategory| *3)))) (|localParam| (*1 *2 *1) (AND (|ofCategory| *1 (|PlacesCategory| *3 *4)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|LocalPowerSeriesCategory| *3)) (|isDomain| *2 (|List| *4)))) (|setParam!| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *5)) (|ofCategory| *1 (|PlacesCategory| *4 *5)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|LocalPowerSeriesCategory| *4)) (|isDomain| *2 (|Void|)))) (|setDegree!| (*1 *2 *1 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *1 (|PlacesCategory| *4 *5)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|LocalPowerSeriesCategory| *4)) (|isDomain| *2 (|Void|)))) (|leaf?| (*1 *2 *1) (AND (|ofCategory| *1 (|PlacesCategory| *3 *4)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|LocalPowerSeriesCategory| *3)) (|isDomain| *2 (|Boolean|)))) (|itsALeaf!| (*1 *2 *1) (AND (|ofCategory| *1 (|PlacesCategory| *3 *4)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|LocalPowerSeriesCategory| *3)) (|isDomain| *2 (|Void|)))) (|foundPlaces| (*1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|LocalPowerSeriesCategory| *3)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|PlacesCategory| *3 *4)))) (|setFoundPlacesToEmpty| (*1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|LocalPowerSeriesCategory| *3)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|PlacesCategory| *3 *4)))) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|PlacesCategory| *2 *4)) (|ofCategory| *4 (|LocalPowerSeriesCategory| *2)) (|ofCategory| *2 (|Field|))))) 
(|Join| (|SetCategoryWithDegree|) (CATEGORY |domain| (SIGNATURE + ((|Divisor| $) $ $)) (SIGNATURE + ((|Divisor| $) (|Divisor| $) $)) (SIGNATURE + ((|Divisor| $) $ (|Divisor| $))) (SIGNATURE - ((|Divisor| $) $ $)) (SIGNATURE - ((|Divisor| $) (|Divisor| $) $)) (SIGNATURE - ((|Divisor| $) $ (|Divisor| $))) (SIGNATURE - ((|Divisor| $) $)) (SIGNATURE * ((|Divisor| $) (|Integer|) $)) (SIGNATURE |reduce| ((|Divisor| $) (|List| $))) (SIGNATURE |create| ($ (|List| |t#1|))) (SIGNATURE |create| ($ (|Symbol|))) (SIGNATURE |localParam| ((|List| |t#2|) $)) (SIGNATURE |setParam!| ((|Void|) $ (|List| |t#2|))) (SIGNATURE |setDegree!| ((|Void|) $ (|PositiveInteger|))) (SIGNATURE |leaf?| ((|Boolean|) $)) (SIGNATURE |itsALeaf!| ((|Void|) $)) (SIGNATURE |foundPlaces| ((|List| $))) (SIGNATURE |setFoundPlacesToEmpty| ((|List| $))) (SIGNATURE |elt| (|t#1| $ (|Integer|))))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|SetCategoryWithDegree|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|setParam!| (((|Void|) $ (|List| (|NeitherSparseOrDensePowerSeries| |#1|))) NIL)) (|setFoundPlacesToEmpty| (((|List| $)) NIL)) (|setDegree!| (((|Void|) $ (|PositiveInteger|)) NIL)) (|reduce| (((|Divisor| $) (|List| $)) NIL)) (|localParam| (((|List| (|NeitherSparseOrDensePowerSeries| |#1|)) $) NIL)) (|leaf?| (((|Boolean|) $) NIL)) (|latex| (((|String|) $) NIL)) (|itsALeaf!| (((|Void|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|foundPlaces| (((|List| $)) NIL)) (|elt| ((|#1| $ (|Integer|)) NIL)) (|degree| (((|PositiveInteger|) $) NIL)) (|create| (($ (|List| |#1|)) NIL) (($ (|Symbol|)) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (= (((|Boolean|) $ $) NIL)) (- (((|Divisor| $) $ $) NIL) (((|Divisor| $) (|Divisor| $) $) NIL) (((|Divisor| $) $ (|Divisor| $)) NIL) (((|Divisor| $) $) NIL)) (+ (((|Divisor| $) $ $) NIL) (((|Divisor| $) (|Divisor| $) $) NIL) (((|Divisor| $) $ (|Divisor| $)) NIL)) (* (((|Divisor| $) (|Integer|) $) NIL))) 
(((|Places| |#1|) (|PlacesCategory| |#1| (|NeitherSparseOrDensePowerSeries| |#1|)) (|Field|)) (T |Places|)) 
NIL 
(|PlacesCategory| |#1| (|NeitherSparseOrDensePowerSeries| |#1|)) 
((~= (((|Boolean|) $ $) NIL)) (|setParam!| (((|Void|) $ (|List| (|NeitherSparseOrDensePowerSeries| (|PseudoAlgebraicClosureOfFiniteField| |#1|)))) NIL)) (|setFoundPlacesToEmpty| (((|List| $)) NIL)) (|setDegree!| (((|Void|) $ (|PositiveInteger|)) NIL)) (|reduce| (((|Divisor| $) (|List| $)) NIL)) (|localParam| (((|List| (|NeitherSparseOrDensePowerSeries| (|PseudoAlgebraicClosureOfFiniteField| |#1|))) $) NIL)) (|leaf?| (((|Boolean|) $) NIL)) (|latex| (((|String|) $) NIL)) (|itsALeaf!| (((|Void|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|foundPlaces| (((|List| $)) NIL)) (|elt| (((|PseudoAlgebraicClosureOfFiniteField| |#1|) $ (|Integer|)) NIL)) (|degree| (((|PositiveInteger|) $) NIL)) (|create| (($ (|List| (|PseudoAlgebraicClosureOfFiniteField| |#1|))) NIL) (($ (|Symbol|)) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (= (((|Boolean|) $ $) NIL)) (- (((|Divisor| $) $ $) NIL) (((|Divisor| $) (|Divisor| $) $) NIL) (((|Divisor| $) $ (|Divisor| $)) NIL) (((|Divisor| $) $) NIL)) (+ (((|Divisor| $) $ $) NIL) (((|Divisor| $) (|Divisor| $) $) NIL) (((|Divisor| $) $ (|Divisor| $)) NIL)) (* (((|Divisor| $) (|Integer|) $) NIL))) 
(((|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|) (|PlacesCategory| (|PseudoAlgebraicClosureOfFiniteField| |#1|) (|NeitherSparseOrDensePowerSeries| (|PseudoAlgebraicClosureOfFiniteField| |#1|))) (|FiniteFieldCategory|)) (T |PlacesOverPseudoAlgebraicClosureOfFiniteField|)) 
NIL 
(|PlacesCategory| (|PseudoAlgebraicClosureOfFiniteField| |#1|) (|NeitherSparseOrDensePowerSeries| (|PseudoAlgebraicClosureOfFiniteField| |#1|))) 
((~= (((|Boolean|) $ $) NIL)) (|setParam!| (((|Void|) $ (|List| |#2|)) 73)) (|setFoundPlacesToEmpty| (((|List| $)) 62)) (|setDegree!| (((|Void|) $ (|PositiveInteger|)) 71)) (|reduce| (((|Divisor| $) (|List| $)) 27)) (|localParam| (((|List| |#2|) $) 74)) (|leaf?| (((|Boolean|) $) 54)) (|latex| (((|String|) $) NIL)) (|itsALeaf!| (((|Void|) $) 57)) (|hash| (((|SingleInteger|) $) NIL)) (|foundPlaces| (((|List| $)) 59)) (|elt| ((|#1| $ (|Integer|)) 53)) (|degree| (((|PositiveInteger|) $) 42)) (|create| (($ (|List| |#1|)) 69) (($ (|Symbol|)) 70)) (|coerce| (((|OutputForm|) $) 45)) (= (((|Boolean|) $ $) 50)) (- (((|Divisor| $) $ $) 18) (((|Divisor| $) (|Divisor| $) $) 30) (((|Divisor| $) $ (|Divisor| $)) 31) (((|Divisor| $) $) 33)) (+ (((|Divisor| $) $ $) 16) (((|Divisor| $) (|Divisor| $) $) 28) (((|Divisor| $) $ (|Divisor| $)) 29)) (* (((|Divisor| $) (|Integer|) $) 21))) 
(((|Plcs| |#1| |#2|) (|PlacesCategory| |#1| |#2|) (|Field|) (|LocalPowerSeriesCategory| |#1|)) (T |Plcs|)) 
NIL 
(|PlacesCategory| |#1| |#2|) 
((|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) 137)) (|sqfree| ((|#4| |#4|) 153)) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) 116)) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) 73)) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) 57)) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) 53)) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) 149)) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) 130) (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) 129) (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) 128) (((|Integer|) (|Matrix| |#4|) (|String|)) 125) (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) 124) (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) 123) (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) 122) (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) 121) (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) 120) (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) 118) (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) 117) (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) 114)) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) 66)) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) 150)) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) 127)) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) 85)) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) 83)) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) 82)) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) 17) (((|Boolean|) (|List| |#4|)) 13)) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) 69)) (|factorset| (((|List| |#4|) |#4|) 47)) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) 112) (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) 54) (((|Fraction| (|Polynomial| |#1|)) |#4|) 109)) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) 89)) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) 81)) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) 98)) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) 46))) 
(((|ParametricLinearEquations| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |psolve| ((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|))) (SIGNATURE |psolve| ((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)))) (SIGNATURE |psolve| ((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|))) (SIGNATURE |psolve| ((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|))) (SIGNATURE |psolve| ((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|))) (SIGNATURE |psolve| ((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|))) (SIGNATURE |psolve| ((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|))) (SIGNATURE |psolve| ((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|))) (SIGNATURE |psolve| ((|Integer|) (|Matrix| |#4|) (|String|))) (SIGNATURE |psolve| ((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|))) (SIGNATURE |psolve| ((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|))) (SIGNATURE |psolve| ((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|))) (SIGNATURE |wrregime| ((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|))) (SIGNATURE |rdregime| ((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|))) (SIGNATURE |bsolve| ((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|))) (SIGNATURE |dmp2rfi| ((|Fraction| (|Polynomial| |#1|)) |#4|)) (SIGNATURE |dmp2rfi| ((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|))) (SIGNATURE |dmp2rfi| ((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|))) (SIGNATURE |se2rfi| ((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|)))) (SIGNATURE |pr2dmp| (|#4| 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(|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (SIGNATURE |factorset| ((|List| |#4|) |#4|)) (SIGNATURE |maxrank| ((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))))) (SIGNATURE |minrank| ((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))))) (SIGNATURE |minset| ((|List| (|List| |#4|)) (|List| (|List| |#4|)))) (SIGNATURE |nextSublist| ((|List| (|List| (|Integer|))) (|Integer|) (|Integer|))) (SIGNATURE |overset?| ((|Boolean|) (|List| |#4|) (|List| (|List| |#4|)))) (SIGNATURE |ParCond| ((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| 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|ParametricLinearEquations|)) 
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(|ConvertibleTo| (|Symbol|)))) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|isDomain| *1 (|ParametricLinearEquations| *3 *4 *5 *6)))) (|minrank| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| *7) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| *7))))) (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5)) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7)))) (|maxrank| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| *7) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| *7))))) (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5)) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7)))) (|factorset| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *4 *6 *5)))) (|B1solve| (*1 *2 *3) (AND (|isDomain| *3 (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| *4)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| *4)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| *4)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| *4))))))) (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7)) (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5)))) (|redpps| (*1 *2 *2 *3) (AND (|isDomain| *2 (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| *4)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| *4))))))) (|isDomain| *3 (|List| *7)) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5)) (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7)))) (|ParCondList| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Matrix| *8)) (|ofCategory| *8 (|PolynomialCategory| *5 *7 *6)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *6 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| *8) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| *8))))) (|isDomain| *1 (|ParametricLinearEquations| *5 *6 *7 *8)) (|isDomain| *4 (|NonNegativeInteger|)))) (|hasoln| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5)) (|isDomain| *2 (|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| *7)) (|:| |n0| (|List| *7)))) (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7)) (|isDomain| *3 (|List| *7)))) (|pr2dmp| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| *4)) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *2 (|PolynomialCategory| *4 *6 *5)) (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *2)) (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)))) (|se2rfi| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|List| (|Fraction| (|Polynomial| *4)))) (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7)) (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5)))) (|dmp2rfi| (*1 *2 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5)) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|List| (|Fraction| (|Polynomial| *4)))) (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7)))) (|dmp2rfi| (*1 *2 *3) (AND (|isDomain| *3 (|Matrix| *7)) (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5)) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Matrix| (|Fraction| (|Polynomial| *4)))) (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7)))) (|dmp2rfi| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Fraction| (|Polynomial| *4))) (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *4 *6 *5)))) (|bsolve| (*1 *2 *3 *4 *5 *6 *7) (AND (|isDomain| *3 (|Matrix| *11)) (|isDomain| *4 (|List| 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((|translateToOrigin| ((|#2| |#2| |#5|) 39) ((|#2| |#2| |#5| (|Integer|)) 20)) (|pointInIdeal?| (((|Boolean|) (|List| |#2|) |#5|) 23)) (|multiplicity| (((|NonNegativeInteger|) |#2| |#5| (|Integer|)) 42) (((|NonNegativeInteger|) |#2| |#5|) 41)) (|minimalForm| ((|#2| |#2| |#5| (|Integer|)) 45) ((|#2| |#2| |#5|) 44)) (|eval| ((|#1| |#2| |#5|) 21))) 
(((|PolynomialPackageForCurve| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |pointInIdeal?| ((|Boolean|) (|List| |#2|) |#5|)) (SIGNATURE |eval| (|#1| |#2| |#5|)) (SIGNATURE |translateToOrigin| (|#2| |#2| |#5| (|Integer|))) (SIGNATURE |translateToOrigin| (|#2| |#2| |#5|)) (SIGNATURE |minimalForm| (|#2| |#2| |#5|)) (SIGNATURE |minimalForm| (|#2| |#2| |#5| (|Integer|))) (SIGNATURE |multiplicity| ((|NonNegativeInteger|) |#2| |#5|)) (SIGNATURE |multiplicity| ((|NonNegativeInteger|) |#2| |#5| (|Integer|)))) (|Field|) (|FiniteAbelianMonoidRing| |#1| |#3|) (|DirectProductCategory| |#4| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|ProjectiveSpaceCategory| |#1|)) (T |PolynomialPackageForCurve|)) 
((|multiplicity| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|Integer|)) (|ofCategory| *6 (|Field|)) (|ofCategory| *7 (|DirectProductCategory| *8 *2)) (|ofType| *8 *2) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|PolynomialPackageForCurve| *6 *3 *7 *8 *4)) (|ofCategory| *3 (|FiniteAbelianMonoidRing| *6 *7)) (|ofCategory| *4 (|ProjectiveSpaceCategory| *6)))) (|multiplicity| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|DirectProductCategory| *7 *2)) (|ofType| *7 *2) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|PolynomialPackageForCurve| *5 *3 *6 *7 *4)) (|ofCategory| *3 (|FiniteAbelianMonoidRing| *5 *6)) (|ofCategory| *4 (|ProjectiveSpaceCategory| *5)))) (|minimalForm| (*1 *2 *2 *3 *4) (AND (|isDomain| *4 (|Integer|)) (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|DirectProductCategory| *7 (|NonNegativeInteger|))) (|ofType| *7 (|NonNegativeInteger|)) (|isDomain| *1 (|PolynomialPackageForCurve| *5 *2 *6 *7 *3)) (|ofCategory| *2 (|FiniteAbelianMonoidRing| *5 *6)) (|ofCategory| *3 (|ProjectiveSpaceCategory| *5)))) (|minimalForm| (*1 *2 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|DirectProductCategory| *6 (|NonNegativeInteger|))) (|ofType| *6 (|NonNegativeInteger|)) (|isDomain| *1 (|PolynomialPackageForCurve| *4 *2 *5 *6 *3)) (|ofCategory| *2 (|FiniteAbelianMonoidRing| *4 *5)) (|ofCategory| *3 (|ProjectiveSpaceCategory| *4)))) (|translateToOrigin| (*1 *2 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|DirectProductCategory| *6 (|NonNegativeInteger|))) (|ofType| *6 (|NonNegativeInteger|)) (|isDomain| *1 (|PolynomialPackageForCurve| *4 *2 *5 *6 *3)) (|ofCategory| *2 (|FiniteAbelianMonoidRing| *4 *5)) (|ofCategory| *3 (|ProjectiveSpaceCategory| *4)))) (|translateToOrigin| (*1 *2 *2 *3 *4) (AND (|isDomain| *4 (|Integer|)) (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|DirectProductCategory| *7 (|NonNegativeInteger|))) (|ofType| *7 (|NonNegativeInteger|)) (|isDomain| *1 (|PolynomialPackageForCurve| *5 *2 *6 *7 *3)) (|ofCategory| *2 (|FiniteAbelianMonoidRing| *5 *6)) (|ofCategory| *3 (|ProjectiveSpaceCategory| *5)))) (|eval| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|DirectProductCategory| *6 (|NonNegativeInteger|))) (|ofType| *6 (|NonNegativeInteger|)) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|PolynomialPackageForCurve| *2 *3 *5 *6 *4)) (|ofCategory| *3 (|FiniteAbelianMonoidRing| *2 *5)) (|ofCategory| *4 (|ProjectiveSpaceCategory| *2)))) (|pointInIdeal?| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *6 (|FiniteAbelianMonoidRing| *5 *7)) (|ofCategory| *7 (|DirectProductCategory| *8 (|NonNegativeInteger|))) (|ofType| *8 (|NonNegativeInteger|)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PolynomialPackageForCurve| *5 *6 *7 *8 *4)) (|ofCategory| *4 (|ProjectiveSpaceCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |pointInIdeal?| ((|Boolean|) (|List| |#2|) |#5|)) (SIGNATURE |eval| (|#1| |#2| |#5|)) (SIGNATURE |translateToOrigin| (|#2| |#2| |#5| (|Integer|))) (SIGNATURE |translateToOrigin| (|#2| |#2| |#5|)) (SIGNATURE |minimalForm| (|#2| |#2| |#5|)) (SIGNATURE |minimalForm| (|#2| |#2| |#5| (|Integer|))) (SIGNATURE |multiplicity| ((|NonNegativeInteger|) |#2| |#5|)) (SIGNATURE |multiplicity| ((|NonNegativeInteger|) |#2| |#5| (|Integer|)))) 
((|optional| ((|#2| |#2|) 25)) (|multiple| ((|#2| |#2|) 26)) (|constant| ((|#2| |#2|) 24)) (|assert| ((|#2| |#2| (|String|)) 23))) 
(((|FunctionSpaceAssertions| |#1| |#2|) (CATEGORY |package| (SIGNATURE |assert| (|#2| |#2| (|String|))) (SIGNATURE |constant| (|#2| |#2|)) (SIGNATURE |optional| (|#2| |#2|)) (SIGNATURE |multiple| (|#2| |#2|))) (|OrderedSet|) (|FunctionSpace| |#1|)) (T |FunctionSpaceAssertions|)) 
((|multiple| (*1 *2 *2) (AND (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|FunctionSpaceAssertions| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|optional| (*1 *2 *2) (AND (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|FunctionSpaceAssertions| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|constant| (*1 *2 *2) (AND (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|FunctionSpaceAssertions| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|assert| (*1 *2 *2 *3) (AND (|isDomain| *3 (|String|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|FunctionSpaceAssertions| *4 *2)) (|ofCategory| *2 (|FunctionSpace| *4))))) 
(CATEGORY |package| (SIGNATURE |assert| (|#2| |#2| (|String|))) (SIGNATURE |constant| (|#2| |#2|)) (SIGNATURE |optional| (|#2| |#2|)) (SIGNATURE |multiple| (|#2| |#2|))) 
((|optional| (((|Expression| (|Integer|)) (|Symbol|)) 15)) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) 13)) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) 11)) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|String|)) 18))) 
(((|PatternMatchAssertions|) (CATEGORY |package| (SIGNATURE |assert| ((|Expression| (|Integer|)) (|Symbol|) (|String|))) (SIGNATURE |constant| ((|Expression| (|Integer|)) (|Symbol|))) (SIGNATURE |optional| ((|Expression| (|Integer|)) (|Symbol|))) (SIGNATURE |multiple| ((|Expression| (|Integer|)) (|Symbol|))))) (T |PatternMatchAssertions|)) 
((|multiple| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Expression| (|Integer|))) (|isDomain| *1 (|PatternMatchAssertions|)))) (|optional| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Expression| (|Integer|))) (|isDomain| *1 (|PatternMatchAssertions|)))) (|constant| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Expression| (|Integer|))) (|isDomain| *1 (|PatternMatchAssertions|)))) (|assert| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|String|)) (|isDomain| *2 (|Expression| (|Integer|))) (|isDomain| *1 (|PatternMatchAssertions|))))) 
(CATEGORY |package| (SIGNATURE |assert| ((|Expression| (|Integer|)) (|Symbol|) (|String|))) (SIGNATURE |constant| ((|Expression| (|Integer|)) (|Symbol|))) (SIGNATURE |optional| ((|Expression| (|Integer|)) (|Symbol|))) (SIGNATURE |multiple| ((|Expression| (|Integer|)) (|Symbol|)))) 
((|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) 24)) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) 12))) 
(((|PatternMatchPushDown| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |fixPredicate| ((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|))) (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)))) (|SetCategory|) (|PatternMatchable| |#1|) (|Join| (|SetCategory|) (|RetractableTo| |#2|))) (T |PatternMatchPushDown|)) 
((|patternMatch| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|PatternMatchResult| *5 *6)) (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|Join| (|SetCategory|) (|RetractableTo| *3))) (|ofCategory| *3 (|PatternMatchable| *5)) (|isDomain| *1 (|PatternMatchPushDown| *5 *3 *6)))) (|fixPredicate| (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *6)) (|ofCategory| *6 (|Join| (|SetCategory|) (|RetractableTo| *5))) (|ofCategory| *5 (|PatternMatchable| *4)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Mapping| (|Boolean|) *5)) (|isDomain| *1 (|PatternMatchPushDown| *4 *5 *6))))) 
(CATEGORY |package| (SIGNATURE |fixPredicate| ((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|))) (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)))) 
((|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) 29))) 
(((|PatternMatchFunctionSpace| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)))) (|SetCategory|) (|Join| (|IntegralDomain|) (|OrderedSet|) (|PatternMatchable| |#1|)) (|Join| (|FunctionSpace| |#2|) (|ConvertibleTo| (|Pattern| |#1|)) (|PatternMatchable| |#1|) (|RetractableTo| (|Kernel| $)))) (T |PatternMatchFunctionSpace|)) 
((|patternMatch| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|PatternMatchResult| *5 *3)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *3 (|Join| (|FunctionSpace| *6) (|ConvertibleTo| *4) (|PatternMatchable| *5) (|RetractableTo| (|Kernel| $)))) (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *6 (|Join| (|IntegralDomain|) (|OrderedSet|) (|PatternMatchable| *5))) (|isDomain| *1 (|PatternMatchFunctionSpace| *5 *6 *3))))) 
(CATEGORY |package| (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)))) 
((|patternMatch| (((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)) 12))) 
(((|PatternMatchIntegerNumberSystem| |#1|) (CATEGORY |package| (SIGNATURE |patternMatch| ((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)))) (|IntegerNumberSystem|)) (T |PatternMatchIntegerNumberSystem|)) 
((|patternMatch| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|PatternMatchResult| (|Integer|) *3)) (|isDomain| *4 (|Pattern| (|Integer|))) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *1 (|PatternMatchIntegerNumberSystem| *3))))) 
(CATEGORY |package| (SIGNATURE |patternMatch| ((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)))) 
((|patternMatch| (((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)) 52))) 
(((|PatternMatchKernel| |#1| |#2|) (CATEGORY |package| (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)))) (|SetCategory|) (|Join| (|OrderedSet|) (|RetractableTo| (|Kernel| $)) (|ConvertibleTo| (|Pattern| |#1|)) (|PatternMatchable| |#1|))) (T |PatternMatchKernel|)) 
((|patternMatch| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|PatternMatchResult| *5 *6)) (|isDomain| *3 (|Kernel| *6)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|Join| (|OrderedSet|) (|RetractableTo| (|Kernel| $)) (|ConvertibleTo| *4) (|PatternMatchable| *5))) (|isDomain| *4 (|Pattern| *5)) (|isDomain| *1 (|PatternMatchKernel| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)))) 
((|patternMatch| (((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)) 14))) 
(((|PatternMatchListAggregate| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |patternMatch| ((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)))) (|SetCategory|) (|PatternMatchable| |#1|) (|ListAggregate| |#2|)) (T |PatternMatchListAggregate|)) 
((|patternMatch| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|PatternMatchListResult| *5 *6 *3)) (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|PatternMatchable| *5)) (|ofCategory| *3 (|ListAggregate| *6)) (|isDomain| *1 (|PatternMatchListAggregate| *5 *6 *3))))) 
(CATEGORY |package| (SIGNATURE |patternMatch| ((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)))) 
((|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) 17 (|has| |#3| (|PatternMatchable| |#1|))) (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) 16))) 
(((|PatternMatchPolynomialCategory| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)))) (IF (|has| |#3| (|PatternMatchable| |#1|)) (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) |noBranch|)) (|SetCategory|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|Join| (|Ring|) (|OrderedSet|) (|PatternMatchable| |#1|)) (|Join| (|PolynomialCategory| |#4| |#2| |#3|) (|ConvertibleTo| (|Pattern| |#1|)))) (T |PatternMatchPolynomialCategory|)) 
((|patternMatch| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|PatternMatchResult| *5 *3)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *3 (|Join| (|PolynomialCategory| *8 *6 *7) (|ConvertibleTo| *4))) (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *7 (|PatternMatchable| *5)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|Join| (|Ring|) (|OrderedSet|) (|PatternMatchable| *5))) (|isDomain| *1 (|PatternMatchPolynomialCategory| *5 *6 *7 *8 *3)))) (|patternMatch| (*1 *2 *3 *4 *2 *5) (AND (|isDomain| *5 (|Mapping| (|PatternMatchResult| *6 *3) *8 (|Pattern| *6) (|PatternMatchResult| *6 *3))) (|ofCategory| *8 (|OrderedSet|)) (|isDomain| *2 (|PatternMatchResult| *6 *3)) (|isDomain| *4 (|Pattern| *6)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *3 (|Join| (|PolynomialCategory| *9 *7 *8) (|ConvertibleTo| *4))) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *9 (|Join| (|Ring|) (|OrderedSet|) (|PatternMatchable| *6))) (|isDomain| *1 (|PatternMatchPolynomialCategory| *6 *7 *8 *9 *3))))) 
(CATEGORY |package| (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)))) (IF (|has| |#3| (|PatternMatchable| |#1|)) (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) |noBranch|)) 
((|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) 11) ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) 12))) 
(((|FunctionSpaceAttachPredicates| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |suchThat| (|#2| |#2| (|Mapping| (|Boolean|) |#3|))) (SIGNATURE |suchThat| (|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))))) (|OrderedSet|) (|FunctionSpace| |#1|) (|Type|)) (T |FunctionSpaceAttachPredicates|)) 
((|suchThat| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| (|Mapping| (|Boolean|) *5))) (|ofCategory| *5 (|Type|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|FunctionSpaceAttachPredicates| *4 *2 *5)) (|ofCategory| *2 (|FunctionSpace| *4)))) (|suchThat| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *5)) (|ofCategory| *5 (|Type|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|FunctionSpaceAttachPredicates| *4 *2 *5)) (|ofCategory| *2 (|FunctionSpace| *4))))) 
(CATEGORY |package| (SIGNATURE |suchThat| (|#2| |#2| (|Mapping| (|Boolean|) |#3|))) (SIGNATURE |suchThat| (|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))))) 
((|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) 16) (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) 13))) 
(((|AttachPredicates| |#1|) (CATEGORY |package| (SIGNATURE |suchThat| ((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|))) (SIGNATURE |suchThat| ((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))))) (|Type|)) (T |AttachPredicates|)) 
((|suchThat| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|List| (|Mapping| (|Boolean|) *5))) (|ofCategory| *5 (|Type|)) (|isDomain| *2 (|Expression| (|Integer|))) (|isDomain| *1 (|AttachPredicates| *5)))) (|suchThat| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|Mapping| (|Boolean|) *5)) (|ofCategory| *5 (|Type|)) (|isDomain| *2 (|Expression| (|Integer|))) (|isDomain| *1 (|AttachPredicates| *5))))) 
(CATEGORY |package| (SIGNATURE |suchThat| ((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|))) (SIGNATURE |suchThat| ((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))))) 
((|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) 25))) 
(((|PatternMatchQuotientFieldCategory| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)))) (|SetCategory|) (|Join| (|IntegralDomain|) (|PatternMatchable| |#1|) (|ConvertibleTo| (|Pattern| |#1|))) (|QuotientFieldCategory| |#2|)) (T |PatternMatchQuotientFieldCategory|)) 
((|patternMatch| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|PatternMatchResult| *5 *3)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *3 (|QuotientFieldCategory| *6)) (|ofCategory| *6 (|Join| (|IntegralDomain|) (|PatternMatchable| *5) (|ConvertibleTo| *4))) (|isDomain| *4 (|Pattern| *5)) (|isDomain| *1 (|PatternMatchQuotientFieldCategory| *5 *6 *3))))) 
(CATEGORY |package| (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)))) 
((|patternMatch| (((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))) 17))) 
(((|PatternMatchSymbol| |#1|) (CATEGORY |package| (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))))) (|SetCategory|)) (T |PatternMatchSymbol|)) 
((|patternMatch| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|PatternMatchResult| *5 (|Symbol|))) (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *5 (|SetCategory|)) (|isDomain| *1 (|PatternMatchSymbol| *5))))) 
(CATEGORY |package| (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))))) 
((|patternMatchTimes| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) 33)) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) 32))) 
(((|PatternMatchTools| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)))) (SIGNATURE |patternMatchTimes| ((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))))) (|SetCategory|) (|Join| (|Ring|) (|OrderedSet|)) (|Join| (|Ring|) (|ConvertibleTo| (|Pattern| |#1|)) (|RetractableTo| |#2|))) (T |PatternMatchTools|)) 
((|patternMatchTimes| (*1 *2 *3 *4 *2 *5) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|List| (|Pattern| *6))) (|isDomain| *5 (|Mapping| (|PatternMatchResult| *6 *8) *8 (|Pattern| *6) (|PatternMatchResult| *6 *8))) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *8 (|Join| (|Ring|) (|ConvertibleTo| (|Pattern| *6)) (|RetractableTo| *7))) (|isDomain| *2 (|PatternMatchResult| *6 *8)) (|ofCategory| *7 (|Join| (|Ring|) (|OrderedSet|))) (|isDomain| *1 (|PatternMatchTools| *6 *7 *8)))) (|patternMatch| (*1 *2 *3 *4 *5 *2 *6) (AND (|isDomain| *4 (|List| (|Pattern| *7))) (|isDomain| *5 (|Mapping| *9 (|List| *9))) (|isDomain| *6 (|Mapping| (|PatternMatchResult| *7 *9) *9 (|Pattern| *7) (|PatternMatchResult| *7 *9))) (|ofCategory| *7 (|SetCategory|)) (|ofCategory| *9 (|Join| (|Ring|) (|ConvertibleTo| (|Pattern| *7)) (|RetractableTo| *8))) (|isDomain| *2 (|PatternMatchResult| *7 *9)) (|isDomain| *3 (|List| *9)) (|ofCategory| *8 (|Join| (|Ring|) (|OrderedSet|))) (|isDomain| *1 (|PatternMatchTools| *7 *8 *9))))) 
(CATEGORY |package| (SIGNATURE |patternMatch| ((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)))) (SIGNATURE |patternMatchTimes| ((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))))) 
((|legendre| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) 61)) (|laguerre| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) 64)) (|hermite| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) 58)) (|fixedDivisor| (((|Integer|) (|SparseUnivariatePolynomial| (|Integer|))) 53)) (|euler| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) 47)) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) 36)) (|chebyshevU| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) 66)) (|chebyshevT| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) 65)) (|bernoulli| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) 49))) 
(((|PolynomialNumberTheoryFunctions|) (CATEGORY |package| (SIGNATURE |bernoulli| ((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |chebyshevT| ((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|))) (SIGNATURE |chebyshevU| ((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|))) (SIGNATURE |cyclotomic| ((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|))) (SIGNATURE |euler| ((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |fixedDivisor| ((|Integer|) (|SparseUnivariatePolynomial| (|Integer|)))) (SIGNATURE |hermite| ((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|))) (SIGNATURE |laguerre| ((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|))) (SIGNATURE |legendre| ((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|))))) (T |PolynomialNumberTheoryFunctions|)) 
((|legendre| (*1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|PolynomialNumberTheoryFunctions|)) (|isDomain| *3 (|Integer|)))) (|laguerre| (*1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *1 (|PolynomialNumberTheoryFunctions|)) (|isDomain| *3 (|Integer|)))) (|hermite| (*1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *1 (|PolynomialNumberTheoryFunctions|)) (|isDomain| *3 (|Integer|)))) (|fixedDivisor| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PolynomialNumberTheoryFunctions|)))) (|euler| (*1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|PolynomialNumberTheoryFunctions|)) (|isDomain| *3 (|Integer|)))) (|cyclotomic| (*1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *1 (|PolynomialNumberTheoryFunctions|)) (|isDomain| *3 (|Integer|)))) (|chebyshevU| (*1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *1 (|PolynomialNumberTheoryFunctions|)) (|isDomain| *3 (|Integer|)))) (|chebyshevT| (*1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *1 (|PolynomialNumberTheoryFunctions|)) (|isDomain| *3 (|Integer|)))) (|bernoulli| (*1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|PolynomialNumberTheoryFunctions|)) (|isDomain| *3 (|Integer|))))) 
(CATEGORY |package| (SIGNATURE |bernoulli| ((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |chebyshevT| ((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|))) (SIGNATURE |chebyshevU| ((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|))) (SIGNATURE |cyclotomic| ((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|))) (SIGNATURE |euler| ((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|))) (SIGNATURE |fixedDivisor| ((|Integer|) (|SparseUnivariatePolynomial| (|Integer|)))) (SIGNATURE |hermite| ((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|))) (SIGNATURE |laguerre| ((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|))) (SIGNATURE |legendre| ((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)))) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|zero| (($ (|NonNegativeInteger|)) NIL (|has| |#1| (|AbelianMonoid|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) NIL) (((|Boolean|) $) NIL (|has| |#1| (|OrderedSet|)))) (|sort!| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $) NIL (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|has| |#1| (|OrderedSet|))))) (|sort| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) NIL) (($ $) NIL (|has| |#1| (|OrderedSet|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setelt| ((|#1| $ (|Integer|) |#1|) 11 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) NIL T CONST)) (|reverse!| (($ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) NIL)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|remove| (($ |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| ((|#1| $ (|Integer|) |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#1| $ (|Integer|)) NIL)) (|position| (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) NIL) (((|Integer|) |#1| $) NIL (|has| |#1| (|SetCategory|))) (((|Integer|) |#1| $ (|Integer|)) NIL (|has| |#1| (|SetCategory|)))) (|point| (($ (|List| |#1|)) 13)) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|outerProduct| (((|Matrix| |#1|) $ $) NIL (|has| |#1| (|Ring|)))) (|new| (($ (|NonNegativeInteger|) |#1|) 8)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) 10 (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|merge| (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) NIL) (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|maxIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL) (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL)) (|magnitude| ((|#1| $) NIL (AND (|has| |#1| (|RadicalCategory|)) (|has| |#1| (|Ring|))))) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|length| ((|#1| $) NIL (AND (|has| |#1| (|RadicalCategory|)) (|has| |#1| (|Ring|))))) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|insert| (($ |#1| $ (|Integer|)) NIL) (($ $ $ (|Integer|)) NIL)) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|first| ((|#1| $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) NIL)) (|fill!| (($ $ |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|extend| (($ $ (|List| |#1|)) 24)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|entry?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|entries| (((|List| |#1|) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#1| $ (|Integer|) |#1|) NIL) ((|#1| $ (|Integer|)) 18) (($ $ (|UniversalSegment| (|Integer|))) NIL)) (|dot| ((|#1| $ $) NIL (|has| |#1| (|Ring|)))) (|dimension| (((|PositiveInteger|) $) 16)) (|delete| (($ $ (|Integer|)) NIL) (($ $ (|UniversalSegment| (|Integer|))) NIL)) (|cross| (($ $ $) 22)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copyInto!| (($ $ $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| (|InputForm|)))) (($ (|List| |#1|)) 17)) (|construct| (($ (|List| |#1|)) NIL)) (|concat| (($ $ |#1|) NIL) (($ |#1| $) NIL) (($ $ $) 23) (($ (|List| $)) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (- (($ $) NIL (|has| |#1| (|AbelianGroup|))) (($ $ $) NIL (|has| |#1| (|AbelianGroup|)))) (+ (($ $ $) NIL (|has| |#1| (|AbelianSemiGroup|)))) (* (($ (|Integer|) $) NIL (|has| |#1| (|AbelianGroup|))) (($ |#1| $) NIL (|has| |#1| (|Monoid|))) (($ $ |#1|) NIL (|has| |#1| (|Monoid|)))) (|#| (((|NonNegativeInteger|) $) 14 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|Point| |#1|) (|PointCategory| |#1|) (|Ring|)) (T |Point|)) 
NIL 
(|PointCategory| |#1|) 
((|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) 17)) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) 29)) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) 22)) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) 53)) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) 26)) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) 44))) 
(((|PolToPol| |#1| |#2|) (CATEGORY |package| (SIGNATURE |dmpToHdmp| ((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|))) (SIGNATURE |hdmpToDmp| ((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) (SIGNATURE |pToHdmp| ((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|))) (SIGNATURE |hdmpToP| ((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) (SIGNATURE |dmpToP| ((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|))) (SIGNATURE |pToDmp| ((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)))) (|List| (|Symbol|)) (|Ring|)) (T |PolToPol|)) 
((|pToDmp| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| *5)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|DistributedMultivariatePolynomial| *4 *5)) (|isDomain| *1 (|PolToPol| *4 *5)) (|ofType| *4 (|List| (|Symbol|))))) (|dmpToP| (*1 *2 *3) (AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *4 *5)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Polynomial| *5)) (|isDomain| *1 (|PolToPol| *4 *5)))) (|hdmpToP| (*1 *2 *3) (AND (|isDomain| *3 (|HomogeneousDistributedMultivariatePolynomial| *4 *5)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Polynomial| *5)) (|isDomain| *1 (|PolToPol| *4 *5)))) (|pToHdmp| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| *5)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|HomogeneousDistributedMultivariatePolynomial| *4 *5)) (|isDomain| *1 (|PolToPol| *4 *5)) (|ofType| *4 (|List| (|Symbol|))))) (|hdmpToDmp| (*1 *2 *3) (AND (|isDomain| *3 (|HomogeneousDistributedMultivariatePolynomial| *4 *5)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|DistributedMultivariatePolynomial| *4 *5)) (|isDomain| *1 (|PolToPol| *4 *5)))) (|dmpToHdmp| (*1 *2 *3) (AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *4 *5)) (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|HomogeneousDistributedMultivariatePolynomial| *4 *5)) (|isDomain| *1 (|PolToPol| *4 *5))))) 
(CATEGORY |package| (SIGNATURE |dmpToHdmp| ((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|))) (SIGNATURE |hdmpToDmp| ((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) (SIGNATURE |pToHdmp| ((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|))) (SIGNATURE |hdmpToP| ((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) (SIGNATURE |dmpToP| ((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|))) (SIGNATURE |pToDmp| ((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)))) 
((|sylvesterSequence| (((|List| |#2|) |#2| |#2|) 10)) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) 37 (|has| |#1| (|OrderedRing|)))) (|sturmSequence| (((|List| |#2|) |#2|) 11)) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) 36 (|has| |#1| (|OrderedRing|)))) (|boundOfCauchy| ((|#1| |#2|) 32 (|has| |#1| (|OrderedRing|))))) 
(((|RealPolynomialUtilitiesPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |sylvesterSequence| ((|List| |#2|) |#2| |#2|)) (SIGNATURE |sturmSequence| ((|List| |#2|) |#2|)) (IF (|has| |#1| (|OrderedRing|)) (PROGN (SIGNATURE |boundOfCauchy| (|#1| |#2|)) (SIGNATURE |sturmVariationsOf| ((|NonNegativeInteger|) (|List| |#1|))) (SIGNATURE |lazyVariations| ((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)))) |noBranch|)) (|Field|) (|UnivariatePolynomialCategory| |#1|)) (T |RealPolynomialUtilitiesPackage|)) 
((|lazyVariations| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|Integer|)) (|ofCategory| *5 (|OrderedRing|)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *5 *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)))) (|sturmVariationsOf| (*1 *2 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|OrderedRing|)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *4 *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)))) (|boundOfCauchy| (*1 *2 *3) (AND (|ofCategory| *2 (|Field|)) (|ofCategory| *2 (|OrderedRing|)) (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|sturmSequence| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|sylvesterSequence| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |sylvesterSequence| ((|List| |#2|) |#2| |#2|)) (SIGNATURE |sturmSequence| ((|List| |#2|) |#2|)) (IF (|has| |#1| (|OrderedRing|)) (PROGN (SIGNATURE |boundOfCauchy| (|#1| |#2|)) (SIGNATURE |sturmVariationsOf| ((|NonNegativeInteger|) (|List| |#1|))) (SIGNATURE |lazyVariations| ((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)))) |noBranch|)) 
((|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) 18))) 
(((|PolynomialFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)))) (|Ring|) (|Ring|)) (T |PolynomialFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Polynomial| *5)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|Ring|)) (|isDomain| *2 (|Polynomial| *6)) (|isDomain| *1 (|PolynomialFunctions2| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |map| ((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)))) 
((|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) 18))) 
(((|PolynomialToUnivariatePolynomial| |#1| |#2|) (CATEGORY |package| (SIGNATURE |univariate| ((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)))) (|Symbol|) (|Ring|)) (T |PolynomialToUnivariatePolynomial|)) 
((|univariate| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Variable| *5)) (|ofType| *5 (|Symbol|)) (|ofCategory| *6 (|Ring|)) (|isDomain| *2 (|UnivariatePolynomial| *5 (|Polynomial| *6))) (|isDomain| *1 (|PolynomialToUnivariatePolynomial| *5 *6)) (|isDomain| *3 (|Polynomial| *6))))) 
(CATEGORY |package| (SIGNATURE |univariate| ((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)))) 
((|totalDegree| (((|NonNegativeInteger|) $) 69) (((|NonNegativeInteger|) $ (|List| |#4|)) 72)) (|squareFreePart| (($ $) 169)) (|squareFree| (((|Factored| $) $) 161)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 112)) (|retractIfCan| (((|Union| |#2| "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL) (((|Union| (|Integer|) "failed") $) NIL) (((|Union| |#4| "failed") $) 58)) (|retract| ((|#2| $) NIL) (((|Fraction| (|Integer|)) $) NIL) (((|Integer|) $) NIL) ((|#4| $) 57)) (|resultant| (($ $ $ |#4|) 74)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| $) (|Vector| $)) 102) (((|Matrix| |#2|) (|Matrix| $)) 95)) (|primitivePart| (($ $) 177) (($ $ |#4|) 180)) (|primitiveMonomials| (((|List| $) $) 61)) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) 195) (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) 189)) (|monomials| (((|List| $) $) 27)) (|monomial| (($ |#2| |#3|) NIL) (($ $ |#4| (|NonNegativeInteger|)) NIL) (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) 55)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) 158)) (|isTimes| (((|Union| (|List| $) "failed") $) 41)) (|isPlus| (((|Union| (|List| $) "failed") $) 30)) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) 45)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 105)) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 118)) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 116)) (|factor| (((|Factored| $) $) 136)) (|eval| (($ $ (|List| (|Equation| $))) 20) (($ $ (|Equation| $)) NIL) (($ $ $ $) NIL) (($ $ (|List| $) (|List| $)) NIL) (($ $ |#4| |#2|) NIL) (($ $ (|List| |#4|) (|List| |#2|)) NIL) (($ $ |#4| $) NIL) (($ $ (|List| |#4|) (|List| $)) NIL)) (|discriminant| (($ $ |#4|) 76)) (|convert| (((|Pattern| (|Float|)) $) 209) (((|Pattern| (|Integer|)) $) 202) (((|InputForm|) $) 217)) (|content| ((|#2| $) NIL) (($ $ |#4|) 171)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 150)) (|coefficient| ((|#2| $ |#3|) NIL) (($ $ |#4| (|NonNegativeInteger|)) 50) (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) 53)) (|charthRoot| (((|Union| $ "failed") $) 152)) (< (((|Boolean|) $ $) 183))) 
(((|PolynomialCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |squareFree| ((|Factored| |#1|) |#1|)) (SIGNATURE |squareFreePart| (|#1| |#1|)) (SIGNATURE |charthRoot| ((|Union| |#1| "failed") |#1|)) (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |convert| ((|Pattern| (|Integer|)) |#1|)) (SIGNATURE |convert| ((|Pattern| (|Float|)) |#1|)) (SIGNATURE |patternMatch| ((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|))) (SIGNATURE |patternMatch| ((|PatternMatchResult| (|Float|) |#1|) |#1| (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) |#1|))) (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) (SIGNATURE |factorPolynomial| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |factorSquareFreePolynomial| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |conditionP| ((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|))) (SIGNATURE |primitivePart| (|#1| |#1| |#4|)) (SIGNATURE |content| (|#1| |#1| |#4|)) (SIGNATURE |discriminant| (|#1| |#1| |#4|)) (SIGNATURE |resultant| (|#1| |#1| |#1| |#4|)) (SIGNATURE |primitiveMonomials| ((|List| |#1|) |#1|)) (SIGNATURE |totalDegree| ((|NonNegativeInteger|) |#1| (|List| |#4|))) (SIGNATURE |totalDegree| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |isExpt| ((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") |#1|)) (SIGNATURE |isTimes| ((|Union| (|List| |#1|) "failed") |#1|)) (SIGNATURE |isPlus| ((|Union| (|List| |#1|) "failed") |#1|)) (SIGNATURE |monomial| (|#1| |#1| (|List| |#4|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |monomial| (|#1| |#1| |#4| (|NonNegativeInteger|))) (SIGNATURE |monicDivide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1| |#4|)) (SIGNATURE |monomials| ((|List| |#1|) |#1|)) (SIGNATURE |coefficient| (|#1| |#1| (|List| |#4|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |coefficient| (|#1| |#1| |#4| (|NonNegativeInteger|))) (SIGNATURE |reducedSystem| ((|Matrix| |#2|) (|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Matrix| (|Integer|)) (|Matrix| |#1|))) (SIGNATURE |retract| (|#4| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#4| "failed") |#1|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#4|) (|List| |#1|))) (SIGNATURE |eval| (|#1| |#1| |#4| |#1|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#4|) (|List| |#2|))) (SIGNATURE |eval| (|#1| |#1| |#4| |#2|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#1|) (|List| |#1|))) (SIGNATURE |eval| (|#1| |#1| |#1| |#1|)) (SIGNATURE |eval| (|#1| |#1| (|Equation| |#1|))) (SIGNATURE |eval| (|#1| |#1| (|List| (|Equation| |#1|)))) (SIGNATURE |monomial| (|#1| |#2| |#3|)) (SIGNATURE |coefficient| (|#2| |#1| |#3|)) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |content| (|#2| |#1|)) (SIGNATURE |primitivePart| (|#1| |#1|))) (|PolynomialCategory| |#2| |#3| |#4|) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|)) (T |PolynomialCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |squareFree| ((|Factored| |#1|) |#1|)) (SIGNATURE |squareFreePart| (|#1| |#1|)) (SIGNATURE |charthRoot| ((|Union| |#1| "failed") |#1|)) (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |convert| ((|Pattern| (|Integer|)) |#1|)) (SIGNATURE |convert| ((|Pattern| (|Float|)) |#1|)) (SIGNATURE |patternMatch| ((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|))) (SIGNATURE |patternMatch| ((|PatternMatchResult| (|Float|) |#1|) |#1| (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) |#1|))) (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) (SIGNATURE |factorPolynomial| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |factorSquareFreePolynomial| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |conditionP| ((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|))) (SIGNATURE |primitivePart| (|#1| |#1| |#4|)) (SIGNATURE |content| (|#1| |#1| |#4|)) (SIGNATURE |discriminant| (|#1| |#1| |#4|)) (SIGNATURE |resultant| (|#1| |#1| |#1| |#4|)) (SIGNATURE |primitiveMonomials| ((|List| |#1|) |#1|)) (SIGNATURE |totalDegree| ((|NonNegativeInteger|) |#1| (|List| |#4|))) (SIGNATURE |totalDegree| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |isExpt| ((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") |#1|)) (SIGNATURE |isTimes| ((|Union| (|List| |#1|) "failed") |#1|)) (SIGNATURE |isPlus| ((|Union| (|List| |#1|) "failed") |#1|)) (SIGNATURE |monomial| (|#1| |#1| (|List| |#4|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |monomial| (|#1| |#1| |#4| (|NonNegativeInteger|))) (SIGNATURE |monicDivide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1| |#4|)) (SIGNATURE |monomials| ((|List| |#1|) |#1|)) (SIGNATURE |coefficient| (|#1| |#1| (|List| |#4|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |coefficient| (|#1| |#1| |#4| (|NonNegativeInteger|))) (SIGNATURE |reducedSystem| ((|Matrix| |#2|) (|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Matrix| (|Integer|)) (|Matrix| |#1|))) (SIGNATURE |retract| (|#4| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#4| "failed") |#1|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#4|) (|List| |#1|))) (SIGNATURE |eval| (|#1| |#1| |#4| |#1|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#4|) (|List| |#2|))) (SIGNATURE |eval| (|#1| |#1| |#4| |#2|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#1|) (|List| |#1|))) (SIGNATURE |eval| (|#1| |#1| |#1| |#1|)) (SIGNATURE |eval| (|#1| |#1| (|Equation| |#1|))) (SIGNATURE |eval| (|#1| |#1| (|List| (|Equation| |#1|)))) (SIGNATURE |monomial| (|#1| |#2| |#3|)) (SIGNATURE |coefficient| (|#2| |#1| |#3|)) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |content| (|#2| |#1|)) (SIGNATURE |primitivePart| (|#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|variables| (((|List| |#3|) $) 109)) (|univariate| (((|SparseUnivariatePolynomial| $) $ |#3|) 124) (((|SparseUnivariatePolynomial| |#1|) $) 123)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 85 (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) 86 (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) 88 (|has| |#1| (|IntegralDomain|)))) (|totalDegree| (((|NonNegativeInteger|) $) 111) (((|NonNegativeInteger|) $ (|List| |#3|)) 110)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 99 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) 97 (|has| |#1| (|GcdDomain|)))) (|squareFree| (((|Factored| $) $) 96 (|has| |#1| (|GcdDomain|)))) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 102 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 163) (((|Union| (|Fraction| (|Integer|)) "failed") $) 161 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Integer|) "failed") $) 159 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| |#3| "failed") $) 135)) (|retract| ((|#1| $) 164) (((|Fraction| (|Integer|)) $) 160 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Integer|) $) 158 (|has| |#1| (|RetractableTo| (|Integer|)))) ((|#3| $) 134)) (|resultant| (($ $ $ |#3|) 107 (|has| |#1| (|CommutativeRing|)))) (|reductum| (($ $) 153)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) 133 (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) 132 (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) 131) (((|Matrix| |#1|) (|Matrix| $)) 130)) (|recip| (((|Union| $ "failed") $) 33)) (|primitivePart| (($ $) 175 (|has| |#1| (|GcdDomain|))) (($ $ |#3|) 104 (|has| |#1| (|GcdDomain|)))) (|primitiveMonomials| (((|List| $) $) 108)) (|prime?| (((|Boolean|) $) 95 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|pomopo!| (($ $ |#1| |#2| $) 171)) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) 82 (AND (|has| |#3| (|PatternMatchable| (|Float|))) (|has| |#1| (|PatternMatchable| (|Float|))))) (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) 81 (AND (|has| |#3| (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Integer|)))))) (|one?| (((|Boolean|) $) 30)) (|numberOfMonomials| (((|NonNegativeInteger|) $) 168)) (|multivariate| (($ (|SparseUnivariatePolynomial| |#1|) |#3|) 116) (($ (|SparseUnivariatePolynomial| $) |#3|) 115)) (|monomials| (((|List| $) $) 125)) (|monomial?| (((|Boolean|) $) 151)) (|monomial| (($ |#1| |#2|) 152) (($ $ |#3| (|NonNegativeInteger|)) 118) (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) 117)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) 119)) (|minimumDegree| ((|#2| $) 169) (((|NonNegativeInteger|) $ |#3|) 121) (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) 120)) (|min| (($ $ $) 77 (|has| |#1| (|OrderedSet|)))) (|max| (($ $ $) 76 (|has| |#1| (|OrderedSet|)))) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) 170)) (|map| (($ (|Mapping| |#1| |#1|) $) 150)) (|mainVariable| (((|Union| |#3| "failed") $) 122)) (|leadingMonomial| (($ $) 148)) (|leadingCoefficient| ((|#1| $) 147)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 89 (|has| |#1| (|GcdDomain|)))) (|lcm| (($ (|List| $)) 93 (|has| |#1| (|GcdDomain|))) (($ $ $) 92 (|has| |#1| (|GcdDomain|)))) (|latex| (((|String|) $) 9)) (|isTimes| (((|Union| (|List| $) "failed") $) 113)) (|isPlus| (((|Union| (|List| $) "failed") $) 114)) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) 112)) (|hash| (((|SingleInteger|) $) 10)) (|ground?| (((|Boolean|) $) 165)) (|ground| ((|#1| $) 166)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 94 (|has| |#1| (|GcdDomain|)))) (|gcd| (($ (|List| $)) 91 (|has| |#1| (|GcdDomain|))) (($ $ $) 90 (|has| |#1| (|GcdDomain|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 101 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 100 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) 98 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|exquo| (((|Union| $ "failed") $ |#1|) 173 (|has| |#1| (|IntegralDomain|))) (((|Union| $ "failed") $ $) 84 (|has| |#1| (|IntegralDomain|)))) (|eval| (($ $ (|List| (|Equation| $))) 144) (($ $ (|Equation| $)) 143) (($ $ $ $) 142) (($ $ (|List| $) (|List| $)) 141) (($ $ |#3| |#1|) 140) (($ $ (|List| |#3|) (|List| |#1|)) 139) (($ $ |#3| $) 138) (($ $ (|List| |#3|) (|List| $)) 137)) (|discriminant| (($ $ |#3|) 106 (|has| |#1| (|CommutativeRing|)))) (|differentiate| (($ $ |#3|) 41) (($ $ (|List| |#3|)) 40) (($ $ |#3| (|NonNegativeInteger|)) 39) (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) 38)) (|degree| ((|#2| $) 149) (((|NonNegativeInteger|) $ |#3|) 129) (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) 128)) (|convert| (((|Pattern| (|Float|)) $) 80 (AND (|has| |#3| (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))))) (((|Pattern| (|Integer|)) $) 79 (AND (|has| |#3| (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))))) (((|InputForm|) $) 78 (AND (|has| |#3| (|ConvertibleTo| (|InputForm|))) (|has| |#1| (|ConvertibleTo| (|InputForm|)))))) (|content| ((|#1| $) 174 (|has| |#1| (|GcdDomain|))) (($ $ |#3|) 105 (|has| |#1| (|GcdDomain|)))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 103 (|and| (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))))) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ |#1|) 162) (($ |#3|) 136) (($ $) 83 (|has| |#1| (|IntegralDomain|))) (($ (|Fraction| (|Integer|))) 70 (OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) (|coefficients| (((|List| |#1|) $) 167)) (|coefficient| ((|#1| $ |#2|) 154) (($ $ |#3| (|NonNegativeInteger|)) 127) (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) 126)) (|charthRoot| (((|Union| $ "failed") $) 71 (OR (|and| (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) 172 (|has| |#1| (|CommutativeRing|)))) (|associates?| (((|Boolean|) $ $) 87 (|has| |#1| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $ |#3|) 37) (($ $ (|List| |#3|)) 36) (($ $ |#3| (|NonNegativeInteger|)) 35) (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) 34)) (>= (((|Boolean|) $ $) 74 (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) 73 (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 75 (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) 72 (|has| |#1| (|OrderedSet|)))) (/ (($ $ |#1|) 155 (|has| |#1| (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ (|Fraction| (|Integer|))) 157 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ (|Fraction| (|Integer|)) $) 156 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ |#1| $) 146) (($ $ |#1|) 145))) 
(((|PolynomialCategory| |#1| |#2| |#3|) (|Category|) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|)) (T |PolynomialCategory|)) 
((|primitivePart| (*1 *1 *1) (AND (|ofCategory| *1 (|PolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|)))) (|degree| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|PolynomialCategory| *4 *5 *3)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|degree| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| (|NonNegativeInteger|))))) (|coefficient| (*1 *1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *2)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|coefficient| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *6)) (|isDomain| *3 (|List| (|NonNegativeInteger|))) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)))) (|monomials| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5)))) (|univariate| (*1 *2 *1 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *3)))) (|univariate| (*1 *2 *1) (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|mainVariable| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|minimumDegree| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|PolynomialCategory| *4 *5 *3)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|minimumDegree| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| (|NonNegativeInteger|))))) (|monicDivide| (*1 *2 *1 *1 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *3)))) (|monomial| (*1 *1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *2)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|monomial| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *6)) (|isDomain| *3 (|List| (|NonNegativeInteger|))) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)))) (|multivariate| (*1 *1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *3)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)))) (|multivariate| (*1 *1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *3)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)))) (|isPlus| (*1 *2 *1) (|partial| AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5)))) (|isTimes| (*1 *2 *1) (|partial| AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5)))) (|isExpt| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |var| *5) (|:| |exponent| (|NonNegativeInteger|)))))) (|totalDegree| (*1 *2 *1) (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|totalDegree| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|variables| (*1 *2 *1) (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *5)))) (|primitiveMonomials| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5)))) (|resultant| (*1 *1 *1 *1 *2) (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|)))) (|discriminant| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|)))) (|content| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|GcdDomain|)))) (|primitivePart| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|GcdDomain|)))) (|squareFreePart| (*1 *1 *1) (AND (|ofCategory| *1 (|PolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|)))) (|squareFree| (*1 *2 *1) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Factored| *1)) (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5))))) 
(|Join| (|PartialDifferentialRing| |t#3|) (|FiniteAbelianMonoidRing| |t#1| |t#2|) (|Evalable| $) (|InnerEvalable| |t#3| |t#1|) (|InnerEvalable| |t#3| $) (|RetractableTo| |t#3|) (|FullyLinearlyExplicitRingOver| |t#1|) (CATEGORY |domain| (SIGNATURE |degree| ((|NonNegativeInteger|) $ |t#3|)) (SIGNATURE |degree| ((|List| (|NonNegativeInteger|)) $ (|List| |t#3|))) (SIGNATURE |coefficient| ($ $ |t#3| (|NonNegativeInteger|))) (SIGNATURE |coefficient| ($ $ (|List| |t#3|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |monomials| ((|List| $) $)) (SIGNATURE |univariate| ((|SparseUnivariatePolynomial| $) $ |t#3|)) (SIGNATURE |univariate| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |mainVariable| ((|Union| |t#3| "failed") $)) (SIGNATURE |minimumDegree| ((|NonNegativeInteger|) $ |t#3|)) (SIGNATURE |minimumDegree| ((|List| (|NonNegativeInteger|)) $ (|List| |t#3|))) (SIGNATURE |monicDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |t#3|)) (SIGNATURE |monomial| ($ $ |t#3| (|NonNegativeInteger|))) (SIGNATURE |monomial| ($ $ (|List| |t#3|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |multivariate| ($ (|SparseUnivariatePolynomial| |t#1|) |t#3|)) (SIGNATURE |multivariate| ($ (|SparseUnivariatePolynomial| $) |t#3|)) (SIGNATURE |isPlus| ((|Union| (|List| $) "failed") $)) (SIGNATURE |isTimes| ((|Union| (|List| $) "failed") $)) (SIGNATURE |isExpt| ((|Union| (|Record| (|:| |var| |t#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $)) (SIGNATURE |totalDegree| ((|NonNegativeInteger|) $)) (SIGNATURE |totalDegree| ((|NonNegativeInteger|) $ (|List| |t#3|))) (SIGNATURE |variables| ((|List| |t#3|) $)) (SIGNATURE |primitiveMonomials| ((|List| $) $)) (IF (|has| |t#1| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|InputForm|))) (IF (|has| |t#3| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |noBranch|) |noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (IF (|has| |t#3| (|ConvertibleTo| (|Pattern| (|Integer|)))) (ATTRIBUTE (|ConvertibleTo| (|Pattern| (|Integer|)))) |noBranch|) |noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|Pattern| (|Float|)))) (IF (|has| |t#3| (|ConvertibleTo| (|Pattern| (|Float|)))) (ATTRIBUTE (|ConvertibleTo| (|Pattern| (|Float|)))) |noBranch|) |noBranch|) (IF (|has| |t#1| (|PatternMatchable| (|Integer|))) (IF (|has| |t#3| (|PatternMatchable| (|Integer|))) (ATTRIBUTE (|PatternMatchable| (|Integer|))) |noBranch|) |noBranch|) (IF (|has| |t#1| (|PatternMatchable| (|Float|))) (IF (|has| |t#3| (|PatternMatchable| (|Float|))) (ATTRIBUTE (|PatternMatchable| (|Float|))) |noBranch|) |noBranch|) (IF (|has| |t#1| (|CommutativeRing|)) (PROGN (SIGNATURE |resultant| ($ $ $ |t#3|)) (SIGNATURE |discriminant| ($ $ |t#3|))) |noBranch|) (IF (|has| |t#1| (|GcdDomain|)) (PROGN (ATTRIBUTE (|GcdDomain|)) (SIGNATURE |content| ($ $ |t#3|)) (SIGNATURE |primitivePart| ($ $)) (SIGNATURE |primitivePart| ($ $ |t#3|)) (SIGNATURE |squareFree| ((|Factored| $) $)) (SIGNATURE |squareFreePart| ($ $))) |noBranch|) (IF (|has| |t#1| (ATTRIBUTE |canonicalUnitNormal|)) (ATTRIBUTE |canonicalUnitNormal|) |noBranch|) (IF (|has| |t#1| (|PolynomialFactorizationExplicit|)) (ATTRIBUTE (|PolynomialFactorizationExplicit|)) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| |#2|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|ConvertibleTo| (|InputForm|)) AND (|has| |#1| (|ConvertibleTo| (|InputForm|))) (|has| |#3| (|ConvertibleTo| (|InputForm|)))) ((|ConvertibleTo| (|Pattern| (|Float|))) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#3| (|ConvertibleTo| (|Pattern| (|Float|))))) ((|ConvertibleTo| (|Pattern| (|Integer|))) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Pattern| (|Integer|))))) ((|EntireRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|Evalable| $) . T) ((|FiniteAbelianMonoidRing| |#1| |#2|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|GcdDomain|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|GcdDomain|))) ((|InnerEvalable| |#3| |#1|) . T) ((|InnerEvalable| |#3| $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|LeftModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|GcdDomain|))) ((|LinearlyExplicitRingOver| (|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|Monoid|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|PartialDifferentialRing| |#3|) . T) ((|PatternMatchable| (|Float|)) AND (|has| |#1| (|PatternMatchable| (|Float|))) (|has| |#3| (|PatternMatchable| (|Float|)))) ((|PatternMatchable| (|Integer|)) AND (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#3| (|PatternMatchable| (|Integer|)))) ((|PolynomialFactorizationExplicit|) |has| |#1| (|PolynomialFactorizationExplicit|)) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RetractableTo| |#3|) . T) ((|RightModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|PolynomialFactorizationExplicit|))) 
((|variables| (((|List| |#2|) |#5|) 36)) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) 23) (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) 16)) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) 30)) (|mainVariable| (((|Union| |#2| "failed") |#5|) 61)) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) 55)) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) 45)) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) 57)) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) 48))) 
(((|PolynomialCategoryQuotientFunctions| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |variables| ((|List| |#2|) |#5|)) (SIGNATURE |mainVariable| ((|Union| |#2| "failed") |#5|)) (SIGNATURE |univariate| ((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|)) (SIGNATURE |multivariate| (|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|)) (SIGNATURE |univariate| ((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|))) (SIGNATURE |isPlus| ((|Union| (|List| |#5|) "failed") |#5|)) (SIGNATURE |isTimes| ((|Union| (|List| |#5|) "failed") |#5|)) (SIGNATURE |isExpt| ((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|)) (SIGNATURE |isPower| ((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|Ring|) (|PolynomialCategory| |#3| |#1| |#2|) (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#4|)) (SIGNATURE |numer| (|#4| $)) (SIGNATURE |denom| (|#4| $))))) (T |PolynomialCategoryQuotientFunctions|)) 
((|isPower| (*1 *2 *3) (|partial| AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|isDomain| *2 (|Record| (|:| |val| *3) (|:| |exponent| (|Integer|)))) (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *4 *5 *6 *7 *3)) (|ofCategory| *3 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ *7)) (SIGNATURE |numer| (*7 $)) (SIGNATURE |denom| (*7 $))))))) (|isExpt| (*1 *2 *3) (|partial| AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|isDomain| *2 (|Record| (|:| |var| *5) (|:| |exponent| (|Integer|)))) (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *4 *5 *6 *7 *3)) (|ofCategory| *3 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ *7)) (SIGNATURE |numer| (*7 $)) (SIGNATURE |denom| (*7 $))))))) (|isTimes| (*1 *2 *3) (|partial| AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *4 *5 *6 *7 *3)) (|ofCategory| *3 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ *7)) (SIGNATURE |numer| (*7 $)) (SIGNATURE |denom| (*7 $))))))) (|isPlus| (*1 *2 *3) (|partial| AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *4 *5 *6 *7 *3)) (|ofCategory| *3 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ *7)) (SIGNATURE |numer| (*7 $)) (SIGNATURE |denom| (*7 $))))))) (|univariate| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ *7)) (SIGNATURE |numer| (*7 $)) (SIGNATURE |denom| (*7 $))))) (|ofCategory| *7 (|PolynomialCategory| *6 *5 *4)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *6 (|Ring|)) (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *5 *4 *6 *7 *3)))) (|multivariate| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|SparseUnivariatePolynomial| *2))) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *2 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ *7)) (SIGNATURE |numer| (*7 $)) (SIGNATURE |denom| (*7 $))))) (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *5 *4 *6 *7 *2)) (|ofCategory| *7 (|PolynomialCategory| *6 *5 *4)))) (|univariate| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *7 (|PolynomialCategory| *6 *5 *4)) (|isDomain| *2 (|Fraction| (|SparseUnivariatePolynomial| *3))) (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *5 *4 *6 *7 *3)) (|ofCategory| *3 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ *7)) (SIGNATURE |numer| (*7 $)) (SIGNATURE |denom| (*7 $))))))) (|mainVariable| (*1 *2 *3) (|partial| AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|PolynomialCategory| *5 *4 *2)) (|ofCategory| *2 (|OrderedSet|)) (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *4 *2 *5 *6 *3)) (|ofCategory| *3 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ *6)) (SIGNATURE |numer| (*6 $)) (SIGNATURE |denom| (*6 $))))))) (|variables| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *4 *5 *6 *7 *3)) (|ofCategory| *3 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ *7)) (SIGNATURE |numer| (*7 $)) (SIGNATURE |denom| (*7 $)))))))) 
(CATEGORY |package| (SIGNATURE |variables| ((|List| |#2|) |#5|)) (SIGNATURE |mainVariable| ((|Union| |#2| "failed") |#5|)) (SIGNATURE |univariate| ((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|)) (SIGNATURE |multivariate| (|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|)) (SIGNATURE |univariate| ((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|))) (SIGNATURE |isPlus| ((|Union| (|List| |#5|) "failed") |#5|)) (SIGNATURE |isTimes| ((|Union| (|List| |#5|) "failed") |#5|)) (SIGNATURE |isExpt| ((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|)) (SIGNATURE |isPower| ((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|))) 
((|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) 23))) 
(((|PolynomialCategoryLifting| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |map| (|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|Ring|) (|PolynomialCategory| |#3| |#1| |#2|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE + ($ $ $)) (SIGNATURE * ($ $ $)) (SIGNATURE ** ($ $ (|NonNegativeInteger|)))))) (T |PolynomialCategoryLifting|)) 
((|map| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *2 *7)) (|isDomain| *4 (|Mapping| *2 *8)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|Ring|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE + ($ $ $)) (SIGNATURE * ($ $ $)) (SIGNATURE ** ($ $ (|NonNegativeInteger|)))))) (|isDomain| *1 (|PolynomialCategoryLifting| *6 *7 *8 *5 *2)) (|ofCategory| *5 (|PolynomialCategory| *8 *6 *7))))) 
(CATEGORY |package| (SIGNATURE |map| (|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|variables| (((|List| (|Symbol|)) $) 15)) (|univariate| (((|SparseUnivariatePolynomial| $) $ (|Symbol|)) 21) (((|SparseUnivariatePolynomial| |#1|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|totalDegree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|List| (|Symbol|))) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL (|has| |#1| (|GcdDomain|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#1| (|GcdDomain|)))) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 8) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Symbol|) "failed") $) NIL)) (|retract| ((|#1| $) NIL) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Symbol|) $) NIL)) (|resultant| (($ $ $ (|Symbol|)) NIL (|has| |#1| (|CommutativeRing|)))) (|reductum| (($ $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| |#1|) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|primitivePart| (($ $) NIL (|has| |#1| (|GcdDomain|))) (($ $ (|Symbol|)) NIL (|has| |#1| (|GcdDomain|)))) (|primitiveMonomials| (((|List| $) $) NIL)) (|prime?| (((|Boolean|) $) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|pomopo!| (($ $ |#1| (|IndexedExponents| (|Symbol|)) $) NIL)) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (AND (|has| (|Symbol|) (|PatternMatchable| (|Float|))) (|has| |#1| (|PatternMatchable| (|Float|))))) (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (AND (|has| (|Symbol|) (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Integer|)))))) (|one?| (((|Boolean|) $) NIL)) (|numberOfMonomials| (((|NonNegativeInteger|) $) NIL)) (|multivariate| (($ (|SparseUnivariatePolynomial| |#1|) (|Symbol|)) NIL) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) NIL)) (|monomials| (((|List| $) $) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monomial| (($ |#1| (|IndexedExponents| (|Symbol|))) NIL) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ (|Symbol|)) NIL)) (|minimumDegree| (((|IndexedExponents| (|Symbol|)) $) NIL) (((|NonNegativeInteger|) $ (|Symbol|)) NIL) (((|List| (|NonNegativeInteger|)) $ (|List| (|Symbol|))) NIL)) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|mapExponents| (($ (|Mapping| (|IndexedExponents| (|Symbol|)) (|IndexedExponents| (|Symbol|))) $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|mainVariable| (((|Union| (|Symbol|) "failed") $) 19)) (|leadingMonomial| (($ $) NIL)) (|leadingCoefficient| ((|#1| $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| |#1| (|GcdDomain|)))) (|lcm| (($ (|List| $)) NIL (|has| |#1| (|GcdDomain|))) (($ $ $) NIL (|has| |#1| (|GcdDomain|)))) (|latex| (((|String|) $) NIL)) (|isTimes| (((|Union| (|List| $) "failed") $) NIL)) (|isPlus| (((|Union| (|List| $) "failed") $) NIL)) (|isExpt| (((|Union| (|Record| (|:| |var| (|Symbol|)) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) NIL)) (|integrate| (($ $ (|Symbol|)) 29 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|hash| (((|SingleInteger|) $) NIL)) (|ground?| (((|Boolean|) $) NIL)) (|ground| ((|#1| $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|GcdDomain|)))) (|gcd| (($ (|List| $)) NIL (|has| |#1| (|GcdDomain|))) (($ $ $) NIL (|has| |#1| (|GcdDomain|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|exquo| (((|Union| $ "failed") $ |#1|) NIL (|has| |#1| (|IntegralDomain|))) (((|Union| $ "failed") $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|eval| (($ $ (|List| (|Equation| $))) NIL) (($ $ (|Equation| $)) NIL) (($ $ $ $) NIL) (($ $ (|List| $) (|List| $)) NIL) (($ $ (|Symbol|) |#1|) NIL) (($ $ (|List| (|Symbol|)) (|List| |#1|)) NIL) (($ $ (|Symbol|) $) NIL) (($ $ (|List| (|Symbol|)) (|List| $)) NIL)) (|discriminant| (($ $ (|Symbol|)) NIL (|has| |#1| (|CommutativeRing|)))) (|differentiate| (($ $ (|Symbol|)) NIL) (($ $ (|List| (|Symbol|))) NIL) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL)) (|degree| (((|IndexedExponents| (|Symbol|)) $) NIL) (((|NonNegativeInteger|) $ (|Symbol|)) NIL) (((|List| (|NonNegativeInteger|)) $ (|List| (|Symbol|))) NIL)) (|convert| (((|Pattern| (|Float|)) $) NIL (AND (|has| (|Symbol|) (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))))) (((|Pattern| (|Integer|)) $) NIL (AND (|has| (|Symbol|) (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))))) (((|InputForm|) $) NIL (AND (|has| (|Symbol|) (|ConvertibleTo| (|InputForm|))) (|has| |#1| (|ConvertibleTo| (|InputForm|)))))) (|content| ((|#1| $) NIL (|has| |#1| (|GcdDomain|))) (($ $ (|Symbol|)) NIL (|has| |#1| (|GcdDomain|)))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))))) (|coerce| (((|OutputForm|) $) 25) (($ (|Integer|)) NIL) (($ |#1|) NIL) (($ (|Symbol|)) 27) (($ (|Fraction| (|Integer|))) NIL (OR (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))))) (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|coefficients| (((|List| |#1|) $) NIL)) (|coefficient| ((|#1| $ (|IndexedExponents| (|Symbol|))) NIL) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|CommutativeRing|)))) (|associates?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($ $ (|Symbol|)) NIL) (($ $ (|List| (|Symbol|))) NIL) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL)) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (/ (($ $ |#1|) NIL (|has| |#1| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ |#1| $) NIL) (($ $ |#1|) NIL))) 
(((|Polynomial| |#1|) (|Join| (|PolynomialCategory| |#1| (|IndexedExponents| (|Symbol|)) (|Symbol|)) (CATEGORY |domain| (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ (|Symbol|))) |noBranch|))) (|Ring|)) (T |Polynomial|)) 
((|integrate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|Polynomial| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *3 (|Ring|))))) 
(|Join| (|PolynomialCategory| |#1| (|IndexedExponents| (|Symbol|)) (|Symbol|)) (CATEGORY |domain| (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ (|Symbol|))) |noBranch|))) 
((|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) 37)) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) 33)) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) 52)) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) 62 (|has| |#3| (|GcdDomain|))))) 
(((|PolynomialRoots| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |rroot| ((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|))) (SIGNATURE |qroot| ((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|))) (IF (|has| |#3| (|GcdDomain|)) (SIGNATURE |froot| ((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|))) |noBranch|) (SIGNATURE |nthr| ((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|IntegralDomain|) (|PolynomialCategory| |#3| |#1| |#2|) (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |numer| (|#4| $)) (SIGNATURE |denom| (|#4| $)) (SIGNATURE |coerce| ($ |#4|))))) (T |PolynomialRoots|)) 
((|nthr| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|IntegralDomain|)) (|ofCategory| *3 (|PolynomialCategory| *7 *5 *6)) (|isDomain| *2 (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| *3) (|:| |radicand| (|List| *3)))) (|isDomain| *1 (|PolynomialRoots| *5 *6 *7 *3 *8)) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *8 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |numer| (*3 $)) (SIGNATURE |denom| (*3 $)) (SIGNATURE |coerce| ($ *3))))))) (|froot| (*1 *2 *3 *4) (AND (|ofCategory| *7 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|IntegralDomain|)) (|ofCategory| *8 (|PolynomialCategory| *7 *5 *6)) (|isDomain| *2 (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| *3) (|:| |radicand| *3))) (|isDomain| *1 (|PolynomialRoots| *5 *6 *7 *8 *3)) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *3 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |numer| (*8 $)) (SIGNATURE |denom| (*8 $)) (SIGNATURE |coerce| ($ *8))))))) (|qroot| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|Integer|))) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|IntegralDomain|)) (|ofCategory| *8 (|PolynomialCategory| *7 *5 *6)) (|isDomain| *2 (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| *9) (|:| |radicand| *9))) (|isDomain| *1 (|PolynomialRoots| *5 *6 *7 *8 *9)) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *9 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |numer| (*8 $)) (SIGNATURE |denom| (*8 $)) (SIGNATURE |coerce| ($ *8))))))) (|rroot| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *7 (|PolynomialCategory| *3 *5 *6)) (|isDomain| *2 (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| *8) (|:| |radicand| *8))) (|isDomain| *1 (|PolynomialRoots| *5 *6 *3 *7 *8)) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *8 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |numer| (*7 $)) (SIGNATURE |denom| (*7 $)) (SIGNATURE |coerce| ($ *7)))))))) 
(CATEGORY |package| (SIGNATURE |rroot| ((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|))) (SIGNATURE |qroot| ((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|))) (IF (|has| |#3| (|GcdDomain|)) (SIGNATURE |froot| ((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|))) |noBranch|) (SIGNATURE |nthr| ((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)))) 
((|vectorcombination| (((|Void|) (|U32Vector|) (|Integer|) (|U32Vector|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) 33)) (|vectoraddmul| (((|Void|) (|U32Vector|) (|U32Vector|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) 27)) (|truncatedmultiplication| (((|U32Vector|) (|U32Vector|) (|U32Vector|) (|Integer|) (|Integer|)) 45)) (|truncatedmuladd| (((|Void|) (|U32Vector|) (|U32Vector|) (|U32Vector|) (|Integer|) (|Integer|)) 44)) (|tomodpa| (((|U32Vector|) (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) 26)) (|resultant| (((|Integer|) (|U32Vector|) (|U32Vector|) (|Integer|)) 54)) (|remainder!| (((|Void|) (|U32Vector|) (|U32Vector|) (|Integer|)) 36)) (|pow| (((|U32Vector|) (|U32Vector|) (|PositiveInteger|) (|NonNegativeInteger|) (|Integer|)) 48)) (|mulbyscalar| (((|Void|) (|U32Vector|) (|Integer|) (|Integer|) (|Integer|)) 31)) (|mulbybinomial| (((|Void|) (|U32Vector|) (|Integer|) (|Integer|) (|Integer|)) 28) (((|Void|) (|U32Vector|) (|Integer|) (|Integer|)) 30)) (|mul| (((|U32Vector|) (|U32Vector|) (|U32Vector|) (|Integer|)) 41)) (|lcm| (((|U32Vector|) (|PrimitiveArray| (|U32Vector|)) (|Integer|) (|Integer|) (|Integer|)) 42)) (|gcd| (((|U32Vector|) (|PrimitiveArray| (|U32Vector|)) (|Integer|) (|Integer|) (|Integer|)) 40) (((|U32Vector|) (|U32Vector|) (|U32Vector|) (|Integer|)) 38)) (|extendedgcd| (((|List| (|U32Vector|)) (|U32Vector|) (|U32Vector|) (|Integer|)) 53)) (|evalat| (((|Integer|) (|U32Vector|) (|Integer|) (|Integer|) (|Integer|)) 15)) (|divide!| (((|Void|) (|U32Vector|) (|U32Vector|) (|U32Vector|) (|Integer|)) 35)) (|differentiate| (((|U32Vector|) (|U32Vector|) (|NonNegativeInteger|) (|Integer|)) 51) (((|U32Vector|) (|U32Vector|) (|Integer|)) 50)) (|degree| (((|Integer|) (|U32Vector|)) 32)) (|copyslice| (((|Void|) (|U32Vector|) (|U32Vector|) (|Integer|) (|Integer|)) 12)) (|copyfirst| (((|Void|) (|U32Vector|) (|U32Vector|) (|Integer|)) 11))) 
(((|U32VectorPolynomialOperations|) (CATEGORY |package| (SIGNATURE |copyfirst| ((|Void|) (|U32Vector|) (|U32Vector|) (|Integer|))) (SIGNATURE |copyslice| ((|Void|) (|U32Vector|) (|U32Vector|) (|Integer|) (|Integer|))) (SIGNATURE |evalat| ((|Integer|) (|U32Vector|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |vectoraddmul| ((|Void|) (|U32Vector|) (|U32Vector|) (|Integer|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |mulbybinomial| ((|Void|) (|U32Vector|) (|Integer|) (|Integer|))) (SIGNATURE |mulbybinomial| ((|Void|) (|U32Vector|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |mulbyscalar| ((|Void|) (|U32Vector|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |mul| ((|U32Vector|) (|U32Vector|) (|U32Vector|) (|Integer|))) (SIGNATURE |truncatedmultiplication| ((|U32Vector|) (|U32Vector|) (|U32Vector|) (|Integer|) (|Integer|))) (SIGNATURE |truncatedmuladd| ((|Void|) (|U32Vector|) (|U32Vector|) (|U32Vector|) (|Integer|) (|Integer|))) (SIGNATURE |pow| ((|U32Vector|) (|U32Vector|) (|PositiveInteger|) (|NonNegativeInteger|) (|Integer|))) (SIGNATURE |differentiate| ((|U32Vector|) (|U32Vector|) (|Integer|))) (SIGNATURE |differentiate| ((|U32Vector|) (|U32Vector|) (|NonNegativeInteger|) (|Integer|))) (SIGNATURE |divide!| ((|Void|) (|U32Vector|) (|U32Vector|) (|U32Vector|) (|Integer|))) (SIGNATURE |remainder!| ((|Void|) (|U32Vector|) (|U32Vector|) (|Integer|))) (SIGNATURE |vectorcombination| ((|Void|) (|U32Vector|) (|Integer|) (|U32Vector|) (|Integer|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |tomodpa| ((|U32Vector|) (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|))) (SIGNATURE |gcd| ((|U32Vector|) (|U32Vector|) (|U32Vector|) (|Integer|))) (SIGNATURE |gcd| ((|U32Vector|) (|PrimitiveArray| (|U32Vector|)) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |lcm| ((|U32Vector|) (|PrimitiveArray| (|U32Vector|)) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |degree| ((|Integer|) (|U32Vector|))) (SIGNATURE |extendedgcd| ((|List| (|U32Vector|)) (|U32Vector|) (|U32Vector|) (|Integer|))) (SIGNATURE |resultant| ((|Integer|) (|U32Vector|) (|U32Vector|) (|Integer|))))) (T |U32VectorPolynomialOperations|)) 
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(((|PlottablePlaneCurveCategory|) (|Category|)) (T |PlottablePlaneCurveCategory|)) 
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(((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (|#| (((|NonNegativeInteger|) $) 8 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|PrimitiveArray| |#1|) (|OneDimensionalArrayAggregate| |#1|) (|Type|)) (T |PrimitiveArray|)) 
NIL 
(|OneDimensionalArrayAggregate| |#1|) 
((|integral| (($ $ (|SegmentBinding| $)) 7) (($ $ (|Symbol|)) 6))) 
(((|PrimitiveFunctionCategory|) (|Category|)) (T |PrimitiveFunctionCategory|)) 
((|integral| (*1 *1 *1 *2) (AND (|isDomain| *2 (|SegmentBinding| *1)) (|ofCategory| *1 (|PrimitiveFunctionCategory|)))) (|integral| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PrimitiveFunctionCategory|)) (|isDomain| *2 (|Symbol|))))) 
(|Join| (CATEGORY |domain| (SIGNATURE |integral| ($ $ (|Symbol|))) (SIGNATURE |integral| ($ $ (|SegmentBinding| $))))) 
((|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) 23) (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) 24) (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) 41))) 
(((|PrimitiveElement| |#1|) (CATEGORY |package| (SIGNATURE |primitiveElement| ((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|))) (SIGNATURE |primitiveElement| ((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)))) (SIGNATURE |primitiveElement| ((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)))) (|Join| (|Field|) (|CharacteristicZero|))) (T |PrimitiveElement|)) 
((|primitiveElement| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| (|Polynomial| *6))) (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *5 (|Symbol|)) (|ofCategory| *6 (|Join| (|Field|) (|CharacteristicZero|))) (|isDomain| *2 (|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| *6))) (|:| |prim| (|SparseUnivariatePolynomial| *6)))) (|isDomain| *1 (|PrimitiveElement| *6)))) (|primitiveElement| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|))) (|isDomain| *2 (|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| *5))) (|:| |prim| (|SparseUnivariatePolynomial| *5)))) (|isDomain| *1 (|PrimitiveElement| *5)))) (|primitiveElement| (*1 *2 *3 *4 *3 *4) (AND (|isDomain| *3 (|Polynomial| *5)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|))) (|isDomain| *2 (|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| *5)))) (|isDomain| *1 (|PrimitiveElement| *5))))) 
(CATEGORY |package| (SIGNATURE |primitiveElement| ((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|))) (SIGNATURE |primitiveElement| ((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)))) (SIGNATURE |primitiveElement| ((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)))) 
((|primes| (((|List| |#1|) |#1| |#1|) 42)) (|prime?| (((|Boolean|) |#1|) 39)) (|prevPrime| ((|#1| |#1|) 64)) (|nextPrime| ((|#1| |#1|) 63))) 
(((|IntegerPrimesPackage| |#1|) (CATEGORY |package| (SIGNATURE |prime?| ((|Boolean|) |#1|)) (SIGNATURE |nextPrime| (|#1| |#1|)) (SIGNATURE |prevPrime| (|#1| |#1|)) (SIGNATURE |primes| ((|List| |#1|) |#1| |#1|))) (|IntegerNumberSystem|)) (T |IntegerPrimesPackage|)) 
((|primes| (*1 *2 *3 *3) (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|IntegerPrimesPackage| *3)) (|ofCategory| *3 (|IntegerNumberSystem|)))) (|prevPrime| (*1 *2 *2) (AND (|isDomain| *1 (|IntegerPrimesPackage| *2)) (|ofCategory| *2 (|IntegerNumberSystem|)))) (|nextPrime| (*1 *2 *2) (AND (|isDomain| *1 (|IntegerPrimesPackage| *2)) (|ofCategory| *2 (|IntegerNumberSystem|)))) (|prime?| (*1 *2 *3) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|IntegerPrimesPackage| *3)) (|ofCategory| *3 (|IntegerNumberSystem|))))) 
(CATEGORY |package| (SIGNATURE |prime?| ((|Boolean|) |#1|)) (SIGNATURE |nextPrime| (|#1| |#1|)) (SIGNATURE |prevPrime| (|#1| |#1|)) (SIGNATURE |primes| ((|List| |#1|) |#1| |#1|))) 
((|print| (((|Void|) (|OutputForm|)) 9))) 
(((|PrintPackage|) (CATEGORY |package| (SIGNATURE |print| ((|Void|) (|OutputForm|))))) (T |PrintPackage|)) 
((|print| (*1 *2 *3) (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|PrintPackage|))))) 
(CATEGORY |package| (SIGNATURE |print| ((|Void|) (|OutputForm|)))) 
((|singularPointsWithRestriction| (((|List| |#5|) |#3| (|List| |#3|)) 70)) (|singularPoints| (((|List| |#5|) |#3|) 45)) (|rationalPoints| (((|List| |#5|) |#3| (|PositiveInteger|)) 58)) (|algebraicSet| (((|List| |#5|) (|List| |#3|)) 48))) 
(((|ProjectiveAlgebraicSetPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |singularPointsWithRestriction| ((|List| |#5|) |#3| (|List| |#3|))) (SIGNATURE |singularPoints| ((|List| |#5|) |#3|)) (SIGNATURE |algebraicSet| ((|List| |#5|) (|List| |#3|))) (SIGNATURE |rationalPoints| ((|List| |#5|) |#3| (|PositiveInteger|)))) (|Field|) (|List| (|Symbol|)) (|PolynomialCategory| |#1| |#4| (|OrderedVariableList| |#2|)) (|DirectProductCategory| (|#| |#2|) (|NonNegativeInteger|)) (|ProjectiveSpaceCategory| |#1|)) (T |ProjectiveAlgebraicSetPackage|)) 
((|rationalPoints| (*1 *2 *3 *4) (AND (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|ofCategory| *7 (|DirectProductCategory| (|#| *6) (|NonNegativeInteger|))) (|isDomain| *2 (|List| *8)) (|isDomain| *1 (|ProjectiveAlgebraicSetPackage| *5 *6 *3 *7 *8)) (|ofCategory| *3 (|PolynomialCategory| *5 *7 (|OrderedVariableList| *6))) (|ofCategory| *8 (|ProjectiveSpaceCategory| *5)))) (|algebraicSet| (*1 *2 *3) (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *6 (|PolynomialCategory| *4 *7 (|OrderedVariableList| *5))) (|ofCategory| *7 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|isDomain| *2 (|List| *8)) (|isDomain| *1 (|ProjectiveAlgebraicSetPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|ProjectiveSpaceCategory| *4)))) (|singularPoints| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|))) (|isDomain| *2 (|List| *7)) (|isDomain| *1 (|ProjectiveAlgebraicSetPackage| *4 *5 *3 *6 *7)) (|ofCategory| *3 (|PolynomialCategory| *4 *6 (|OrderedVariableList| *5))) (|ofCategory| *7 (|ProjectiveSpaceCategory| *4)))) (|singularPointsWithRestriction| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *3)) (|ofCategory| *3 (|PolynomialCategory| *5 *7 (|OrderedVariableList| *6))) (|ofCategory| *7 (|DirectProductCategory| (|#| *6) (|NonNegativeInteger|))) (|ofCategory| *5 (|Field|)) (|ofType| *6 (|List| (|Symbol|))) (|isDomain| *2 (|List| *8)) (|isDomain| *1 (|ProjectiveAlgebraicSetPackage| *5 *6 *3 *7 *8)) (|ofCategory| *8 (|ProjectiveSpaceCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |singularPointsWithRestriction| ((|List| |#5|) |#3| (|List| |#3|))) (SIGNATURE |singularPoints| ((|List| |#5|) |#3|)) (SIGNATURE |algebraicSet| ((|List| |#5|) (|List| |#3|))) (SIGNATURE |rationalPoints| ((|List| |#5|) |#3| (|PositiveInteger|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 62 (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) 63 (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) 28)) (|retract| (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) NIL)) (|reductum| (($ $) 24)) (|recip| (((|Union| $ "failed") $) 35)) (|primitivePart| (($ $) NIL (|has| |#1| (|GcdDomain|)))) (|pomopo!| (($ $ |#1| |#2| $) 47)) (|one?| (((|Boolean|) $) NIL)) (|numberOfMonomials| (((|NonNegativeInteger|) $) 16)) (|monomial?| (((|Boolean|) $) NIL)) (|monomial| (($ |#1| |#2|) NIL)) (|minimumDegree| ((|#2| $) 19)) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|leadingMonomial| (($ $) 23)) (|leadingCoefficient| ((|#1| $) 21)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|ground?| (((|Boolean|) $) 40)) (|ground| ((|#1| $) NIL)) (|fmecg| (($ $ |#2| |#1| $) 71 (AND (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#1| (|IntegralDomain|))))) (|exquo| (((|Union| $ "failed") $ $) 73 (|has| |#1| (|IntegralDomain|))) (((|Union| $ "failed") $ |#1|) 69 (|has| |#1| (|IntegralDomain|)))) (|degree| ((|#2| $) 17)) (|content| ((|#1| $) NIL (|has| |#1| (|GcdDomain|)))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) 39) (($ $) NIL (|has| |#1| (|IntegralDomain|))) (($ |#1|) 34) (($ (|Fraction| (|Integer|))) NIL (OR (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))))) (|coefficients| (((|List| |#1|) $) NIL)) (|coefficient| ((|#1| $ |#2|) 31)) (|charthRoot| (((|Union| $ "failed") $) NIL (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) 15)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) 58 (|has| |#1| (|CommutativeRing|)))) (|associates?| (((|Boolean|) $ $) 68 (|has| |#1| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) 54) (($ $ (|NonNegativeInteger|)) 55)) (|Zero| (($) 22 T CONST)) (|One| (($) 12 T CONST)) (= (((|Boolean|) $ $) 67)) (/ (($ $ |#1|) 74 (|has| |#1| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) 53) (($ $ (|NonNegativeInteger|)) 51)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 50) (($ $ |#1|) 49) (($ |#1| $) 48) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) 
(((|PolynomialRing| |#1| |#2|) (|Join| (|FiniteAbelianMonoidRing| |#1| |#2|) (CATEGORY |domain| (IF (|has| |#1| (|IntegralDomain|)) (IF (|has| |#2| (|CancellationAbelianMonoid|)) (SIGNATURE |fmecg| ($ $ |#2| |#1| $)) |noBranch|) |noBranch|) (IF (|has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (ATTRIBUTE |canonicalUnitNormal|) |noBranch|))) (|Ring|) (|OrderedAbelianMonoid|)) (T |PolynomialRing|)) 
((|fmecg| (*1 *1 *1 *2 *3 *1) (AND (|isDomain| *1 (|PolynomialRing| *3 *2)) (|ofCategory| *2 (|CancellationAbelianMonoid|)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|))))) 
(|Join| (|FiniteAbelianMonoidRing| |#1| |#2|) (CATEGORY |domain| (IF (|has| |#1| (|IntegralDomain|)) (IF (|has| |#2| (|CancellationAbelianMonoid|)) (SIGNATURE |fmecg| ($ $ |#2| |#1| $)) |noBranch|) |noBranch|) (IF (|has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (ATTRIBUTE |canonicalUnitNormal|) |noBranch|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL (OR (AND (|has| |#1| (|AbelianGroup|)) (|has| |#2| (|AbelianGroup|))) (AND (|has| |#1| (|AbelianMonoid|)) (|has| |#2| (|AbelianMonoid|))) (AND (|has| |#1| (|CancellationAbelianMonoid|)) (|has| |#2| (|CancellationAbelianMonoid|))) (AND (|has| |#1| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedAbelianMonoidSup|)))))) (|sup| (($ $ $) 63 (AND (|has| |#1| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedAbelianMonoidSup|))))) (|subtractIfCan| (((|Union| $ "failed") $ $) 50 (OR (AND (|has| |#1| (|AbelianGroup|)) (|has| |#2| (|AbelianGroup|))) (AND (|has| |#1| (|CancellationAbelianMonoid|)) (|has| |#2| (|CancellationAbelianMonoid|))) (AND (|has| |#1| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedAbelianMonoidSup|)))))) (|size| (((|NonNegativeInteger|)) 34 (AND (|has| |#1| (|Finite|)) (|has| |#2| (|Finite|))))) (|selectsecond| ((|#2| $) 21)) (|selectfirst| ((|#1| $) 20)) (|sample| (($) NIL (OR (AND (|has| |#1| (|AbelianGroup|)) (|has| |#2| (|AbelianGroup|))) (AND (|has| |#1| (|AbelianMonoid|)) (|has| |#2| (|AbelianMonoid|))) (AND (|has| |#1| (|CancellationAbelianMonoid|)) (|has| |#2| (|CancellationAbelianMonoid|))) (AND (|has| |#1| (|Group|)) (|has| |#2| (|Group|))) (AND (|has| |#1| (|Monoid|)) (|has| |#2| (|Monoid|))) (AND (|has| |#1| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedAbelianMonoidSup|)))) CONST)) (|recip| (((|Union| $ "failed") $) NIL (OR (AND (|has| |#1| (|Group|)) (|has| |#2| (|Group|))) (AND (|has| |#1| (|Monoid|)) (|has| |#2| (|Monoid|)))))) (|random| (($) NIL (AND (|has| |#1| (|Finite|)) (|has| |#2| (|Finite|))))) (|one?| (((|Boolean|) $) NIL (OR (AND (|has| |#1| (|Group|)) (|has| |#2| (|Group|))) (AND (|has| |#1| (|Monoid|)) (|has| |#2| (|Monoid|)))))) (|min| (($ $ $) NIL (OR (AND (|has| |#1| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedAbelianMonoidSup|))) (AND (|has| |#1| (|OrderedSet|)) (|has| |#2| (|OrderedSet|)))))) (|max| (($ $ $) NIL (OR (AND (|has| |#1| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedAbelianMonoidSup|))) (AND (|has| |#1| (|OrderedSet|)) (|has| |#2| (|OrderedSet|)))))) (|makeprod| (($ |#1| |#2|) 19)) (|lookup| (((|PositiveInteger|) $) NIL (AND (|has| |#1| (|Finite|)) (|has| |#2| (|Finite|))))) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 37 (AND (|has| |#1| (|Group|)) (|has| |#2| (|Group|))))) (|index| (($ (|PositiveInteger|)) NIL (AND (|has| |#1| (|Finite|)) (|has| |#2| (|Finite|))))) (|hash| (((|SingleInteger|) $) NIL)) (|enumerate| (((|List| $)) NIL (AND (|has| |#1| (|Finite|)) (|has| |#2| (|Finite|))))) (|conjugate| (($ $ $) NIL (AND (|has| |#1| (|Group|)) (|has| |#2| (|Group|))))) (|commutator| (($ $ $) NIL (AND (|has| |#1| (|Group|)) (|has| |#2| (|Group|))))) (|coerce| (((|OutputForm|) $) 14)) (^ (($ $ (|Integer|)) NIL (AND (|has| |#1| (|Group|)) (|has| |#2| (|Group|)))) (($ $ (|NonNegativeInteger|)) NIL (OR (AND (|has| |#1| (|Group|)) (|has| |#2| (|Group|))) (AND (|has| |#1| (|Monoid|)) (|has| |#2| (|Monoid|))))) (($ $ (|PositiveInteger|)) NIL (OR (AND (|has| |#1| (|Group|)) (|has| |#2| (|Group|))) (AND (|has| |#1| (|Monoid|)) (|has| |#2| (|Monoid|)))))) (|Zero| (($) 40 (OR (AND (|has| |#1| (|AbelianGroup|)) (|has| |#2| (|AbelianGroup|))) (AND (|has| |#1| (|AbelianMonoid|)) (|has| |#2| (|AbelianMonoid|))) (AND (|has| |#1| (|CancellationAbelianMonoid|)) (|has| |#2| (|CancellationAbelianMonoid|))) (AND (|has| |#1| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedAbelianMonoidSup|)))) CONST)) (|One| (($) 24 (OR (AND (|has| |#1| (|Group|)) (|has| |#2| (|Group|))) (AND (|has| |#1| (|Monoid|)) (|has| |#2| (|Monoid|)))) CONST)) (>= (((|Boolean|) $ $) NIL (OR (AND (|has| |#1| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedAbelianMonoidSup|))) (AND (|has| |#1| (|OrderedSet|)) (|has| |#2| (|OrderedSet|)))))) (> (((|Boolean|) $ $) NIL (OR (AND (|has| |#1| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedAbelianMonoidSup|))) (AND (|has| |#1| (|OrderedSet|)) (|has| |#2| (|OrderedSet|)))))) (= (((|Boolean|) $ $) 18)) (<= (((|Boolean|) $ $) NIL (OR (AND (|has| |#1| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedAbelianMonoidSup|))) (AND (|has| |#1| (|OrderedSet|)) (|has| |#2| (|OrderedSet|)))))) (< (((|Boolean|) $ $) 66 (OR (AND (|has| |#1| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedAbelianMonoidSup|))) (AND (|has| |#1| (|OrderedSet|)) (|has| |#2| (|OrderedSet|)))))) (/ (($ $ $) NIL (AND (|has| |#1| (|Group|)) (|has| |#2| (|Group|))))) (- (($ $ $) 56 (AND (|has| |#1| (|AbelianGroup|)) (|has| |#2| (|AbelianGroup|)))) (($ $) 53 (AND (|has| |#1| (|AbelianGroup|)) (|has| |#2| (|AbelianGroup|))))) (+ (($ $ $) 43 (OR (AND (|has| |#1| (|AbelianGroup|)) (|has| |#2| (|AbelianGroup|))) (AND (|has| |#1| (|AbelianMonoid|)) (|has| |#2| (|AbelianMonoid|))) (AND (|has| |#1| (|CancellationAbelianMonoid|)) (|has| |#2| (|CancellationAbelianMonoid|))) (AND (|has| |#1| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedAbelianMonoidSup|)))))) (** (($ $ (|Integer|)) NIL (AND (|has| |#1| (|Group|)) (|has| |#2| (|Group|)))) (($ $ (|NonNegativeInteger|)) 31 (OR (AND (|has| |#1| (|Group|)) (|has| |#2| (|Group|))) (AND (|has| |#1| (|Monoid|)) (|has| |#2| (|Monoid|))))) (($ $ (|PositiveInteger|)) NIL (OR (AND (|has| |#1| (|Group|)) (|has| |#2| (|Group|))) (AND (|has| |#1| (|Monoid|)) (|has| |#2| (|Monoid|)))))) (* (($ (|Integer|) $) 60 (AND (|has| |#1| (|AbelianGroup|)) (|has| |#2| (|AbelianGroup|)))) (($ (|NonNegativeInteger|) $) 46 (OR (AND (|has| |#1| (|AbelianGroup|)) (|has| |#2| (|AbelianGroup|))) (AND (|has| |#1| (|AbelianMonoid|)) (|has| |#2| (|AbelianMonoid|))) (AND (|has| |#1| (|CancellationAbelianMonoid|)) (|has| |#2| (|CancellationAbelianMonoid|))) (AND (|has| |#1| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedAbelianMonoidSup|))))) (($ (|PositiveInteger|) $) NIL (OR (AND (|has| |#1| (|AbelianGroup|)) (|has| |#2| (|AbelianGroup|))) (AND (|has| |#1| (|AbelianMonoid|)) (|has| |#2| (|AbelianMonoid|))) (AND (|has| |#1| (|CancellationAbelianMonoid|)) (|has| |#2| (|CancellationAbelianMonoid|))) (AND (|has| |#1| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|OrderedAbelianMonoidSup|))))) (($ $ $) 27 (OR (AND (|has| |#1| (|Group|)) (|has| |#2| (|Group|))) (AND (|has| |#1| (|Monoid|)) (|has| |#2| (|Monoid|))))))) 
(((|Product| |#1| |#2|) (|Join| (|SetCategory|) (CATEGORY |domain| (IF (|has| |#1| (|Finite|)) (IF (|has| |#2| (|Finite|)) (ATTRIBUTE (|Finite|)) |noBranch|) |noBranch|) (IF (|has| |#1| (|Monoid|)) (IF (|has| |#2| (|Monoid|)) (ATTRIBUTE (|Monoid|)) |noBranch|) |noBranch|) (IF (|has| |#1| (|AbelianMonoid|)) (IF (|has| |#2| (|AbelianMonoid|)) (ATTRIBUTE (|AbelianMonoid|)) |noBranch|) |noBranch|) (IF (|has| |#1| (|CancellationAbelianMonoid|)) (IF (|has| |#2| (|CancellationAbelianMonoid|)) (ATTRIBUTE (|CancellationAbelianMonoid|)) |noBranch|) |noBranch|) (IF (|has| |#1| (|Group|)) (IF (|has| |#2| (|Group|)) (ATTRIBUTE (|Group|)) |noBranch|) |noBranch|) (IF (|has| |#1| (|AbelianGroup|)) (IF (|has| |#2| (|AbelianGroup|)) (ATTRIBUTE (|AbelianGroup|)) |noBranch|) |noBranch|) (IF (|has| |#1| (|OrderedAbelianMonoidSup|)) (IF (|has| |#2| (|OrderedAbelianMonoidSup|)) (ATTRIBUTE (|OrderedAbelianMonoidSup|)) |noBranch|) |noBranch|) (IF (|has| |#1| (|OrderedSet|)) (IF (|has| |#2| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |noBranch|) |noBranch|) (SIGNATURE |makeprod| ($ |#1| |#2|)) (SIGNATURE |selectfirst| (|#1| $)) (SIGNATURE |selectsecond| (|#2| $)))) (|SetCategory|) (|SetCategory|)) (T |Product|)) 
((|makeprod| (*1 *1 *2 *3) (AND (|isDomain| *1 (|Product| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|selectfirst| (*1 *2 *1) (AND (|ofCategory| *2 (|SetCategory|)) (|isDomain| *1 (|Product| *2 *3)) (|ofCategory| *3 (|SetCategory|)))) (|selectsecond| (*1 *2 *1) (AND (|ofCategory| *2 (|SetCategory|)) (|isDomain| *1 (|Product| *3 *2)) (|ofCategory| *3 (|SetCategory|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (IF (|has| |#1| (|Finite|)) (IF (|has| |#2| (|Finite|)) (ATTRIBUTE (|Finite|)) |noBranch|) |noBranch|) (IF (|has| |#1| (|Monoid|)) (IF (|has| |#2| (|Monoid|)) (ATTRIBUTE (|Monoid|)) |noBranch|) |noBranch|) (IF (|has| |#1| (|AbelianMonoid|)) (IF (|has| |#2| (|AbelianMonoid|)) (ATTRIBUTE (|AbelianMonoid|)) |noBranch|) |noBranch|) (IF (|has| |#1| (|CancellationAbelianMonoid|)) (IF (|has| |#2| (|CancellationAbelianMonoid|)) (ATTRIBUTE (|CancellationAbelianMonoid|)) |noBranch|) |noBranch|) (IF (|has| |#1| (|Group|)) (IF (|has| |#2| (|Group|)) (ATTRIBUTE (|Group|)) |noBranch|) |noBranch|) (IF (|has| |#1| (|AbelianGroup|)) (IF (|has| |#2| (|AbelianGroup|)) (ATTRIBUTE (|AbelianGroup|)) |noBranch|) |noBranch|) (IF (|has| |#1| (|OrderedAbelianMonoidSup|)) (IF (|has| |#2| (|OrderedAbelianMonoidSup|)) (ATTRIBUTE (|OrderedAbelianMonoidSup|)) |noBranch|) |noBranch|) (IF (|has| |#1| (|OrderedSet|)) (IF (|has| |#2| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |noBranch|) |noBranch|) (SIGNATURE |makeprod| ($ |#1| |#2|)) (SIGNATURE |selectfirst| (|#1| $)) (SIGNATURE |selectsecond| (|#2| $)))) 
((~= (((|Boolean|) $ $) NIL)) (|setelt| ((|#1| $ (|Integer|) |#1|) NIL)) (|removeConjugate| (((|List| $) (|List| $) (|NonNegativeInteger|)) NIL) (((|List| $) (|List| $)) NIL)) (|rational?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL) (((|Boolean|) $) NIL)) (|projectivePoint| (($ (|List| |#1|)) NIL)) (|pointValue| (((|List| |#1|) $) NIL)) (|orbit| (((|List| $) $) NIL) (((|List| $) $ (|NonNegativeInteger|)) NIL)) (|list| (((|List| |#1|) $) NIL)) (|latex| (((|String|) $) NIL)) (|lastNonNull| (((|Integer|) $) NIL)) (|lastNonNul| (((|Integer|) $) NIL)) (|homogenize| (($ $ (|Integer|)) NIL) (($ $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|elt| ((|#1| $ (|Integer|)) NIL)) (|degree| (((|PositiveInteger|) $) NIL)) (|definingField| ((|#1| $) NIL)) (|conjugate| (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (((|List| |#1|) $) NIL) (($ (|List| |#1|)) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|ProjectivePlane| |#1|) (|ProjectiveSpaceCategory| |#1|) (|Field|)) (T |ProjectivePlane|)) 
NIL 
(|ProjectiveSpaceCategory| |#1|) 
((~= (((|Boolean|) $ $) NIL)) (|setelt| (((|PseudoAlgebraicClosureOfFiniteField| |#1|) $ (|Integer|) (|PseudoAlgebraicClosureOfFiniteField| |#1|)) NIL)) (|removeConjugate| (((|List| $) (|List| $) (|NonNegativeInteger|)) NIL) (((|List| $) (|List| $)) NIL)) (|rational?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL) (((|Boolean|) $) NIL)) (|projectivePoint| (($ (|List| (|PseudoAlgebraicClosureOfFiniteField| |#1|))) NIL)) (|pointValue| (((|List| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) $) NIL)) (|orbit| (((|List| $) $) NIL) (((|List| $) $ (|NonNegativeInteger|)) NIL)) (|list| (((|List| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) $) NIL)) (|latex| (((|String|) $) NIL)) (|lastNonNull| (((|Integer|) $) NIL)) (|lastNonNul| (((|Integer|) $) NIL)) (|homogenize| (($ $ (|Integer|)) NIL) (($ $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|elt| (((|PseudoAlgebraicClosureOfFiniteField| |#1|) $ (|Integer|)) NIL)) (|degree| (((|PositiveInteger|) $) NIL)) (|definingField| (((|PseudoAlgebraicClosureOfFiniteField| |#1|) $) NIL)) (|conjugate| (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (((|List| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) $) NIL) (($ (|List| (|PseudoAlgebraicClosureOfFiniteField| |#1|))) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|) (|ProjectiveSpaceCategory| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) (|FiniteFieldCategory|)) (T |ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField|)) 
NIL 
(|ProjectiveSpaceCategory| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) 
((~= (((|Boolean|) $ $) NIL)) (|setelt| ((|#2| $ (|Integer|) |#2|) NIL)) (|removeConjugate| (((|List| $) (|List| $) (|NonNegativeInteger|)) 41) (((|List| $) (|List| $)) 42)) (|rational?| (((|Boolean|) $ (|NonNegativeInteger|)) 38) (((|Boolean|) $) 40)) (|projectivePoint| (($ (|List| |#2|)) 25)) (|pointValue| (((|List| |#2|) $) 27)) (|orbit| (((|List| $) $) 50) (((|List| $) $ (|NonNegativeInteger|)) 47)) (|list| (((|List| |#2|) $) 26)) (|latex| (((|String|) $) NIL)) (|lastNonNull| (((|Integer|) $) 59)) (|lastNonNul| (((|Integer|) $) 62)) (|homogenize| (($ $ (|Integer|)) 36) (($ $) 52)) (|hash| (((|SingleInteger|) $) NIL)) (|elt| ((|#2| $ (|Integer|)) 32)) (|degree| (((|PositiveInteger|) $) 16)) (|definingField| ((|#2| $) 22)) (|conjugate| (($ $ (|NonNegativeInteger|)) 30) (($ $) 49)) (|coerce| (((|OutputForm|) $) 19) (((|List| |#2|) $) 24) (($ (|List| |#2|)) 58)) (= (((|Boolean|) $ $) 37))) 
(((|ProjectiveSpace| |#1| |#2|) (|ProjectiveSpaceCategory| |#2|) (|NonNegativeInteger|) (|Field|)) (T |ProjectiveSpace|)) 
NIL 
(|ProjectiveSpaceCategory| |#2|) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|sample| (($) 7 T CONST)) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|merge!| (($ $ $) 40)) (|merge| (($ $ $) 41)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|max| ((|#1| $) 42)) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|inspect| ((|#1| $) 36)) (|insert!| (($ |#1| $) 37)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|extract!| ((|#1| $) 38)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|bag| (($ (|List| |#1|)) 39)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|PriorityQueueAggregate| |#1|) (|Category|) (|OrderedSet|)) (T |PriorityQueueAggregate|)) 
((|max| (*1 *2 *1) (AND (|ofCategory| *1 (|PriorityQueueAggregate| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|merge| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|PriorityQueueAggregate| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|merge!| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|PriorityQueueAggregate| *2)) (|ofCategory| *2 (|OrderedSet|))))) 
(|Join| (|BagAggregate| |t#1|) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (SIGNATURE |max| (|t#1| $)) (SIGNATURE |merge| ($ $ $)) (SIGNATURE |merge!| ($ $ $)))) 
(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) 84)) (|subResultantGcd| ((|#2| |#2| |#2|) 82)) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) 86)) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) 88)) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) 106 (|has| |#1| (|GcdDomain|)))) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) 45)) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) 63)) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) 65)) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) 77)) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) 70)) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) 96)) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) 73)) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) 81)) (|resultantnaif| ((|#1| |#2| |#2|) 41)) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) 104 (|has| |#1| (|GcdDomain|)))) (|resultantReduit| ((|#1| |#2| |#2|) 102 (|has| |#1| (|GcdDomain|)))) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) 43)) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) 62)) (|resultant| ((|#1| |#2| |#2|) 60)) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) 35)) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) 52)) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) 75)) (|lastSubResultant| ((|#2| |#2| |#2|) 74)) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) 68)) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) 66)) (|gcd| ((|#2| |#2| |#2|) 110 (|has| |#1| (|GcdDomain|)))) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) 21)) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) 38)) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) 94)) (|discriminant| ((|#1| |#2|) 91)) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) 72)) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) 71)) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) 79)) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) 49)) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) 48)) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) 16))) 
(((|PseudoRemainderSequence| |#1| |#2|) (CATEGORY |package| (SIGNATURE |resultant| (|#1| |#2| |#2|)) (SIGNATURE |resultantEuclidean| ((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|)) (SIGNATURE |semiResultantEuclidean2| ((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|)) (SIGNATURE |semiResultantEuclidean1| ((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|)) (SIGNATURE |indiceSubResultant| (|#2| |#2| |#2| (|NonNegativeInteger|))) (SIGNATURE |indiceSubResultantEuclidean| ((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|))) (SIGNATURE |semiIndiceSubResultantEuclidean| ((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|))) (SIGNATURE |degreeSubResultant| (|#2| |#2| |#2| (|NonNegativeInteger|))) (SIGNATURE |degreeSubResultantEuclidean| ((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|))) (SIGNATURE |semiDegreeSubResultantEuclidean| ((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|))) (SIGNATURE |lastSubResultant| (|#2| |#2| |#2|)) (SIGNATURE |lastSubResultantEuclidean| ((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|)) (SIGNATURE |semiLastSubResultantEuclidean| ((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|)) (SIGNATURE |subResultantGcd| (|#2| |#2| |#2|)) (SIGNATURE |subResultantGcdEuclidean| ((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|)) (SIGNATURE |semiSubResultantGcdEuclidean2| ((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|)) (SIGNATURE |semiSubResultantGcdEuclidean1| ((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|)) (SIGNATURE |discriminant| (|#1| |#2|)) (SIGNATURE |discriminantEuclidean| ((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|)) (SIGNATURE |semiDiscriminantEuclidean| ((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|)) (SIGNATURE |chainSubResultants| ((|List| |#2|) |#2| |#2|)) (SIGNATURE |schema| ((|List| (|NonNegativeInteger|)) |#2| |#2|)) (IF (|has| |#1| (|GcdDomain|)) (PROGN (SIGNATURE |resultantReduit| (|#1| |#2| |#2|)) (SIGNATURE |resultantReduitEuclidean| ((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|)) (SIGNATURE |semiResultantReduitEuclidean| ((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|)) (SIGNATURE |gcd| (|#2| |#2| |#2|))) |noBranch|) (SIGNATURE * ((|Vector| |#2|) |#1| (|Vector| |#2|))) (SIGNATURE |exquo| ((|Vector| |#2|) (|Vector| |#2|) |#1|)) (SIGNATURE |pseudoDivide| ((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|)) (SIGNATURE |divide| ((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|)) (SIGNATURE |Lazard| (|#1| |#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |Lazard2| (|#2| |#2| |#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |nextsousResultant2| (|#2| |#2| |#2| |#2| |#1|)) (SIGNATURE |resultantnaif| (|#1| |#2| |#2|)) (SIGNATURE |resultantEuclideannaif| ((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|)) (SIGNATURE |semiResultantEuclideannaif| ((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|))) (|IntegralDomain|) (|UnivariatePolynomialCategory| |#1|)) (T |PseudoRemainderSequence|)) 
((|semiResultantEuclideannaif| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef2| *3) (|:| |resultant| *4))) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|resultantEuclideannaif| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef1| *3) (|:| |coef2| *3) (|:| |resultant| *4))) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|resultantnaif| (*1 *2 *3 *3) (AND (|ofCategory| *2 (|IntegralDomain|)) (|isDomain| *1 (|PseudoRemainderSequence| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|nextsousResultant2| (*1 *2 *2 *2 *2 *3) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|PseudoRemainderSequence| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|Lazard2| (*1 *2 *2 *3 *3 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|PseudoRemainderSequence| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|Lazard| (*1 *2 *2 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *2 (|IntegralDomain|)) (|isDomain| *1 (|PseudoRemainderSequence| *2 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)))) (|divide| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|pseudoDivide| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef| *4) (|:| |quotient| *3) (|:| |remainder| *3))) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|exquo| (*1 *2 *2 *3) (AND (|isDomain| *2 (|Vector| *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|PseudoRemainderSequence| *3 *4)))) (* (*1 *2 *3 *2) (AND (|isDomain| *2 (|Vector| *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|PseudoRemainderSequence| *3 *4)))) (|gcd| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|PseudoRemainderSequence| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|semiResultantReduitEuclidean| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef2| *3) (|:| |resultantReduit| *4))) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|resultantReduitEuclidean| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef1| *3) (|:| |coef2| *3) (|:| |resultantReduit| *4))) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|resultantReduit| (*1 *2 *3 *3) (AND (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|GcdDomain|)) (|isDomain| *1 (|PseudoRemainderSequence| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|schema| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| (|NonNegativeInteger|))) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|chainSubResultants| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|semiDiscriminantEuclidean| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef2| *3) (|:| |discriminant| *4))) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|discriminantEuclidean| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef1| *3) (|:| |coef2| *3) (|:| |discriminant| *4))) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|discriminant| (*1 *2 *3) (AND (|ofCategory| *2 (|IntegralDomain|)) (|isDomain| *1 (|PseudoRemainderSequence| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|semiSubResultantGcdEuclidean1| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef1| *3) (|:| |gcd| *3))) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|semiSubResultantGcdEuclidean2| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef2| *3) (|:| |gcd| *3))) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|subResultantGcdEuclidean| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef1| *3) (|:| |coef2| *3) (|:| |gcd| *3))) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|subResultantGcd| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|PseudoRemainderSequence| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|semiLastSubResultantEuclidean| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef2| *3) (|:| |subResultant| *3))) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|lastSubResultantEuclidean| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3))) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|lastSubResultant| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|PseudoRemainderSequence| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|semiDegreeSubResultantEuclidean| (*1 *2 *3 *3 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef2| *3) (|:| |subResultant| *3))) (|isDomain| *1 (|PseudoRemainderSequence| *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|degreeSubResultantEuclidean| (*1 *2 *3 *3 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3))) (|isDomain| *1 (|PseudoRemainderSequence| *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|degreeSubResultant| (*1 *2 *2 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *1 (|PseudoRemainderSequence| *4 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)))) (|semiIndiceSubResultantEuclidean| (*1 *2 *3 *3 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef2| *3) (|:| |subResultant| *3))) (|isDomain| *1 (|PseudoRemainderSequence| *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|indiceSubResultantEuclidean| (*1 *2 *3 *3 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3))) (|isDomain| *1 (|PseudoRemainderSequence| *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|indiceSubResultant| (*1 *2 *2 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *1 (|PseudoRemainderSequence| *4 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)))) (|semiResultantEuclidean1| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef1| *3) (|:| |resultant| *4))) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|semiResultantEuclidean2| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef2| *3) (|:| |resultant| *4))) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|resultantEuclidean| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |coef1| *3) (|:| |coef2| *3) (|:| |resultant| *4))) (|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|resultant| (*1 *2 *3 *3) (AND (|ofCategory| *2 (|IntegralDomain|)) (|isDomain| *1 (|PseudoRemainderSequence| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(CATEGORY |package| (SIGNATURE |resultant| (|#1| |#2| |#2|)) (SIGNATURE |resultantEuclidean| ((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|)) (SIGNATURE |semiResultantEuclidean2| ((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|)) (SIGNATURE |semiResultantEuclidean1| ((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|)) (SIGNATURE |indiceSubResultant| (|#2| |#2| |#2| (|NonNegativeInteger|))) (SIGNATURE |indiceSubResultantEuclidean| ((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|))) (SIGNATURE |semiIndiceSubResultantEuclidean| ((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|))) (SIGNATURE |degreeSubResultant| (|#2| |#2| |#2| (|NonNegativeInteger|))) (SIGNATURE |degreeSubResultantEuclidean| ((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|))) (SIGNATURE |semiDegreeSubResultantEuclidean| ((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|))) (SIGNATURE |lastSubResultant| (|#2| |#2| |#2|)) (SIGNATURE |lastSubResultantEuclidean| ((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|)) (SIGNATURE |semiLastSubResultantEuclidean| ((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|)) (SIGNATURE |subResultantGcd| (|#2| |#2| |#2|)) (SIGNATURE |subResultantGcdEuclidean| ((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|)) (SIGNATURE |semiSubResultantGcdEuclidean2| ((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|)) (SIGNATURE |semiSubResultantGcdEuclidean1| ((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|)) (SIGNATURE |discriminant| (|#1| |#2|)) (SIGNATURE |discriminantEuclidean| ((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|)) (SIGNATURE |semiDiscriminantEuclidean| ((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|)) (SIGNATURE |chainSubResultants| ((|List| |#2|) |#2| |#2|)) (SIGNATURE |schema| ((|List| (|NonNegativeInteger|)) |#2| |#2|)) (IF (|has| |#1| (|GcdDomain|)) (PROGN (SIGNATURE |resultantReduit| (|#1| |#2| |#2|)) (SIGNATURE |resultantReduitEuclidean| ((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|)) (SIGNATURE |semiResultantReduitEuclidean| ((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|)) (SIGNATURE |gcd| (|#2| |#2| |#2|))) |noBranch|) (SIGNATURE * ((|Vector| |#2|) |#1| (|Vector| |#2|))) (SIGNATURE |exquo| ((|Vector| |#2|) (|Vector| |#2|) |#1|)) (SIGNATURE |pseudoDivide| ((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|)) (SIGNATURE |divide| ((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|)) (SIGNATURE |Lazard| (|#1| |#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |Lazard2| (|#2| |#2| |#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |nextsousResultant2| (|#2| |#2| |#2| |#2| |#1|)) (SIGNATURE |resultantnaif| (|#1| |#2| |#2|)) (SIGNATURE |resultantEuclideannaif| ((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|)) (SIGNATURE |semiResultantEuclideannaif| ((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|))) 
((~= (((|Boolean|) $ $) 7)) (|setelt| ((|#1| $ (|Integer|) |#1|) 14)) (|removeConjugate| (((|List| $) (|List| $) (|NonNegativeInteger|)) 22) (((|List| $) (|List| $)) 21)) (|rational?| (((|Boolean|) $ (|NonNegativeInteger|)) 20) (((|Boolean|) $) 19)) (|projectivePoint| (($ (|List| |#1|)) 30)) (|pointValue| (((|List| |#1|) $) 13)) (|orbit| (((|List| $) $) 26) (((|List| $) $ (|NonNegativeInteger|)) 25)) (|list| (((|List| |#1|) $) 16)) (|latex| (((|String|) $) 9)) (|lastNonNull| (((|Integer|) $) 17)) (|lastNonNul| (((|Integer|) $) 32)) (|homogenize| (($ $ (|Integer|)) 31) (($ $) 18)) (|hash| (((|SingleInteger|) $) 10)) (|elt| ((|#1| $ (|Integer|)) 15)) (|degree| (((|PositiveInteger|) $) 12)) (|definingField| ((|#1| $) 29)) (|conjugate| (($ $ (|NonNegativeInteger|)) 24) (($ $) 23)) (|coerce| (((|OutputForm|) $) 11) (((|List| |#1|) $) 28) (($ (|List| |#1|)) 27)) (= (((|Boolean|) $ $) 6))) 
(((|ProjectiveSpaceCategory| |#1|) (|Category|) (|Field|)) (T |ProjectiveSpaceCategory|)) 
((|lastNonNul| (*1 *2 *1) (AND (|ofCategory| *1 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Integer|)))) (|homogenize| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *3 (|Field|)))) (|projectivePoint| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *1 (|ProjectiveSpaceCategory| *3)))) (|definingField| (*1 *2 *1) (AND (|ofCategory| *1 (|ProjectiveSpaceCategory| *2)) (|ofCategory| *2 (|Field|)))) (|coerce| (*1 *2 *1) (AND (|ofCategory| *1 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|List| *3)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *1 (|ProjectiveSpaceCategory| *3)))) (|orbit| (*1 *2 *1) (AND (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|ProjectiveSpaceCategory| *3)))) (|orbit| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|ProjectiveSpaceCategory| *4)))) (|conjugate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *3 (|Field|)))) (|conjugate| (*1 *1 *1) (AND (|ofCategory| *1 (|ProjectiveSpaceCategory| *2)) (|ofCategory| *2 (|Field|)))) (|removeConjugate| (*1 *2 *2 *3) (AND (|isDomain| *2 (|List| *1)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *4 (|Field|)))) (|removeConjugate| (*1 *2 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *3 (|Field|)))) (|rational?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|ProjectiveSpaceCategory| *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|Boolean|)))) (|rational?| (*1 *2 *1) (AND (|ofCategory| *1 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Boolean|)))) (|homogenize| (*1 *1 *1) (AND (|ofCategory| *1 (|ProjectiveSpaceCategory| *2)) (|ofCategory| *2 (|Field|)))) (|lastNonNull| (*1 *2 *1) (AND (|ofCategory| *1 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Integer|)))) (|list| (*1 *2 *1) (AND (|ofCategory| *1 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|List| *3)))) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|ProjectiveSpaceCategory| *2)) (|ofCategory| *2 (|Field|)))) (|setelt| (*1 *2 *1 *3 *2) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|ProjectiveSpaceCategory| *2)) (|ofCategory| *2 (|Field|)))) (|pointValue| (*1 *2 *1) (AND (|ofCategory| *1 (|ProjectiveSpaceCategory| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|List| *3))))) 
(|Join| (|SetCategoryWithDegree|) (CATEGORY |domain| (SIGNATURE |lastNonNul| ((|Integer|) $)) (SIGNATURE |homogenize| ($ $ (|Integer|))) (SIGNATURE |projectivePoint| ($ (|List| |t#1|))) (SIGNATURE |definingField| (|t#1| $)) (SIGNATURE |coerce| ((|List| |t#1|) $)) (SIGNATURE |coerce| ($ (|List| |t#1|))) (SIGNATURE |orbit| ((|List| $) $)) (SIGNATURE |orbit| ((|List| $) $ (|NonNegativeInteger|))) (SIGNATURE |conjugate| ($ $ (|NonNegativeInteger|))) (SIGNATURE |conjugate| ($ $)) (SIGNATURE |removeConjugate| ((|List| $) (|List| $) (|NonNegativeInteger|))) (SIGNATURE |removeConjugate| ((|List| $) (|List| $))) (SIGNATURE |rational?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |homogenize| ($ $)) (SIGNATURE |lastNonNull| ((|Integer|) $)) (SIGNATURE |list| ((|List| |t#1|) $)) (SIGNATURE |elt| (|t#1| $ (|Integer|))) (SIGNATURE |setelt| (|t#1| $ (|Integer|) |t#1|)) (SIGNATURE |pointValue| ((|List| |t#1|) $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|SetCategoryWithDegree|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26)) (|sample| (($) NIL T CONST)) (|powers| (((|List| (|List| (|Integer|))) (|List| (|Integer|))) 28)) (|pdct| (((|Integer|) $) 44)) (|partition| (($ (|List| (|Integer|))) 17)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|convert| (((|List| (|Integer|)) $) 11)) (|conjugate| (($ $) 31)) (|coerce| (((|OutputForm|) $) 42) (((|List| (|Integer|)) $) 9)) (|Zero| (($) 7 T CONST)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 19)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 18)) (+ (($ $ $) 20)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) 24))) 
(((|Partition|) (|Join| (|OrderedCancellationAbelianMonoid|) (|ConvertibleTo| (|List| (|Integer|))) (CATEGORY |domain| (SIGNATURE |partition| ($ (|List| (|Integer|)))) (SIGNATURE |powers| ((|List| (|List| (|Integer|))) (|List| (|Integer|)))) (SIGNATURE |pdct| ((|Integer|) $)) (SIGNATURE |conjugate| ($ $)) (SIGNATURE |coerce| ((|List| (|Integer|)) $))))) (T |Partition|)) 
((|partition| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|Partition|)))) (|powers| (*1 *2 *3) (AND (|isDomain| *2 (|List| (|List| (|Integer|)))) (|isDomain| *1 (|Partition|)) (|isDomain| *3 (|List| (|Integer|))))) (|pdct| (*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Partition|)))) (|conjugate| (*1 *1 *1) (|isDomain| *1 (|Partition|))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|Partition|))))) 
(|Join| (|OrderedCancellationAbelianMonoid|) (|ConvertibleTo| (|List| (|Integer|))) (CATEGORY |domain| (SIGNATURE |partition| ($ (|List| (|Integer|)))) (SIGNATURE |powers| ((|List| (|List| (|Integer|))) (|List| (|Integer|)))) (SIGNATURE |pdct| ((|Integer|) $)) (SIGNATURE |conjugate| ($ $)) (SIGNATURE |coerce| ((|List| (|Integer|)) $)))) 
((/ (($ $ |#2|) 30)) (- (($ $) 22) (($ $ $) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 15) (($ $ $) NIL) (($ $ |#2|) 20) (($ |#2| $) 19) (($ (|Fraction| (|Integer|)) $) 26) (($ $ (|Fraction| (|Integer|))) 28))) 
(((|PowerSeriesCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE * (|#1| |#1| (|Fraction| (|Integer|)))) (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)) (SIGNATURE / (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|PowerSeriesCategory| |#2| |#3| |#4|) (|Ring|) (|OrderedAbelianMonoid|) (|OrderedSet|)) (T |PowerSeriesCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE * (|#1| |#1| (|Fraction| (|Integer|)))) (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)) (SIGNATURE / (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|variables| (((|List| |#3|) $) 70)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 50 (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) 51 (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) 53 (|has| |#1| (|IntegralDomain|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|reductum| (($ $) 59)) (|recip| (((|Union| $ "failed") $) 33)) (|pole?| (((|Boolean|) $) 69)) (|one?| (((|Boolean|) $) 30)) (|monomial?| (((|Boolean|) $) 61)) (|monomial| (($ |#1| |#2|) 60) (($ $ |#3| |#2|) 72) (($ $ (|List| |#3|) (|List| |#2|)) 71)) (|map| (($ (|Mapping| |#1| |#1|) $) 62)) (|leadingMonomial| (($ $) 64)) (|leadingCoefficient| ((|#1| $) 65)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|exquo| (((|Union| $ "failed") $ $) 49 (|has| |#1| (|IntegralDomain|)))) (|degree| ((|#2| $) 63)) (|complete| (($ $) 68)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ (|Fraction| (|Integer|))) 56 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $) 48 (|has| |#1| (|IntegralDomain|))) (($ |#1|) 46 (|has| |#1| (|CommutativeRing|)))) (|coefficient| ((|#1| $ |#2|) 58)) (|charthRoot| (((|Union| $ "failed") $) 47 (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 52 (|has| |#1| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (/ (($ $ |#1|) 57 (|has| |#1| (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 67) (($ |#1| $) 66) (($ (|Fraction| (|Integer|)) $) 55 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) 54 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) 
(((|PowerSeriesCategory| |#1| |#2| |#3|) (|Category|) (|Ring|) (|OrderedAbelianMonoid|) (|OrderedSet|)) (T |PowerSeriesCategory|)) 
((|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *2 *3 *4)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|Ring|)))) (|leadingMonomial| (*1 *1 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *4 (|OrderedSet|)))) (|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *3 *2 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|monomial| (*1 *1 *1 *2 *3) (AND (|ofCategory| *1 (|PowerSeriesCategory| *4 *3 *2)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|OrderedSet|)))) (|monomial| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *6)) (|isDomain| *3 (|List| *5)) (|ofCategory| *1 (|PowerSeriesCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoid|)) (|ofCategory| *6 (|OrderedSet|)))) (|variables| (*1 *2 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *5)))) (|pole?| (*1 *2 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|complete| (*1 *1 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *4 (|OrderedSet|))))) 
(|Join| (|AbelianMonoidRing| |t#1| |t#2|) (CATEGORY |domain| (SIGNATURE |monomial| ($ $ |t#3| |t#2|)) (SIGNATURE |monomial| ($ $ (|List| |t#3|) (|List| |t#2|))) (SIGNATURE |leadingMonomial| ($ $)) (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |degree| (|t#2| $)) (SIGNATURE |variables| ((|List| |t#3|) $)) (SIGNATURE |pole?| ((|Boolean|) $)) (SIGNATURE |complete| ($ $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| |#2|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|Module| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|RightModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|zRange| (((|Segment| (|DoubleFloat|)) $) 7)) (|yRange| (((|Segment| (|DoubleFloat|)) $) 8)) (|xRange| (((|Segment| (|DoubleFloat|)) $) 9)) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) 10)) (|coerce| (((|OutputForm|) $) 6))) 
(((|PlottableSpaceCurveCategory|) (|Category|)) (T |PlottableSpaceCurveCategory|)) 
((|listBranches| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottableSpaceCurveCategory|)) (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|))))))) (|xRange| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottableSpaceCurveCategory|)) (|isDomain| *2 (|Segment| (|DoubleFloat|))))) (|yRange| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottableSpaceCurveCategory|)) (|isDomain| *2 (|Segment| (|DoubleFloat|))))) (|zRange| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottableSpaceCurveCategory|)) (|isDomain| *2 (|Segment| (|DoubleFloat|)))))) 
(|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |listBranches| ((|List| (|List| (|Point| (|DoubleFloat|)))) $)) (SIGNATURE |xRange| ((|Segment| (|DoubleFloat|)) $)) (SIGNATURE |yRange| ((|Segment| (|DoubleFloat|)) $)) (SIGNATURE |zRange| ((|Segment| (|DoubleFloat|)) $)))) 
(((|CoercibleTo| (|OutputForm|)) . T)) 
((|variables| (((|List| |#4|) $) 23)) (|trivialIdeal?| (((|Boolean|) $) 47)) (|triangular?| (((|Boolean|) $) 46)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) 35)) (|roughUnitIdeal?| (((|Boolean|) $) 48)) (|roughSubIdeal?| (((|Boolean|) $ $) 54)) (|roughEqualIdeals?| (((|Boolean|) $ $) 57)) (|roughBase?| (((|Boolean|) $) 52)) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) 89)) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) 86)) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) 80)) (|mainVariables| (((|List| |#4|) $) 27)) (|mainVariable?| (((|Boolean|) |#4| $) 29)) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) 72)) (|collectUpper| (($ $ |#4|) 32)) (|collectUnder| (($ $ |#4|) 31)) (|collect| (($ $ |#4|) 33)) (= (((|Boolean|) $ $) 39))) 
(((|PolynomialSetCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |domain| (SIGNATURE |triangular?| ((|Boolean|) |#1|)) (SIGNATURE |rewriteIdealWithRemainder| ((|List| |#5|) (|List| |#5|) |#1|)) (SIGNATURE |rewriteIdealWithHeadRemainder| ((|List| |#5|) (|List| |#5|) |#1|)) (SIGNATURE |remainder| ((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| |#1|)) (SIGNATURE |headRemainder| ((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| |#1|)) (SIGNATURE |roughUnitIdeal?| ((|Boolean|) |#1|)) (SIGNATURE |roughEqualIdeals?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |roughSubIdeal?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |roughBase?| ((|Boolean|) |#1|)) (SIGNATURE |trivialIdeal?| ((|Boolean|) |#1|)) (SIGNATURE |sort| ((|Record| (|:| |under| |#1|) (|:| |floor| |#1|) (|:| |upper| |#1|)) |#1| |#4|)) (SIGNATURE |collectUpper| (|#1| |#1| |#4|)) (SIGNATURE |collect| (|#1| |#1| |#4|)) (SIGNATURE |collectUnder| (|#1| |#1| |#4|)) (SIGNATURE |mainVariable?| ((|Boolean|) |#4| |#1|)) (SIGNATURE |mainVariables| ((|List| |#4|) |#1|)) (SIGNATURE |variables| ((|List| |#4|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|))) (|PolynomialSetCategory| |#2| |#3| |#4| |#5|) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#2| |#3| |#4|)) (T |PolynomialSetCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |triangular?| ((|Boolean|) |#1|)) (SIGNATURE |rewriteIdealWithRemainder| ((|List| |#5|) (|List| |#5|) |#1|)) (SIGNATURE |rewriteIdealWithHeadRemainder| ((|List| |#5|) (|List| |#5|) |#1|)) (SIGNATURE |remainder| ((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| |#1|)) (SIGNATURE |headRemainder| ((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| |#1|)) (SIGNATURE |roughUnitIdeal?| ((|Boolean|) |#1|)) (SIGNATURE |roughEqualIdeals?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |roughSubIdeal?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |roughBase?| ((|Boolean|) |#1|)) (SIGNATURE |trivialIdeal?| ((|Boolean|) |#1|)) (SIGNATURE |sort| ((|Record| (|:| |under| |#1|) (|:| |floor| |#1|) (|:| |upper| |#1|)) |#1| |#4|)) (SIGNATURE |collectUpper| (|#1| |#1| |#4|)) (SIGNATURE |collect| (|#1| |#1| |#4|)) (SIGNATURE |collectUnder| (|#1| |#1| |#4|)) (SIGNATURE |mainVariable?| ((|Boolean|) |#4| |#1|)) (SIGNATURE |mainVariables| ((|List| |#4|) |#1|)) (SIGNATURE |variables| ((|List| |#4|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|variables| (((|List| |#3|) $) 32)) (|trivialIdeal?| (((|Boolean|) $) 25)) (|triangular?| (((|Boolean|) $) 16 (|has| |#1| (|IntegralDomain|)))) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 26)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 43)) (|select| (($ (|Mapping| (|Boolean|) |#4|) $) 64 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) 44 T CONST)) (|roughUnitIdeal?| (((|Boolean|) $) 21 (|has| |#1| (|IntegralDomain|)))) (|roughSubIdeal?| (((|Boolean|) $ $) 23 (|has| |#1| (|IntegralDomain|)))) (|roughEqualIdeals?| (((|Boolean|) $ $) 22 (|has| |#1| (|IntegralDomain|)))) (|roughBase?| (((|Boolean|) $) 24 (|has| |#1| (|IntegralDomain|)))) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) 17 (|has| |#1| (|IntegralDomain|)))) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) 18 (|has| |#1| (|IntegralDomain|)))) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 35)) (|retract| (($ (|List| |#4|)) 34)) (|removeDuplicates| (($ $) 67 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove| (($ |#4| $) 66 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#4|) $) 63 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 19 (|has| |#1| (|IntegralDomain|)))) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 65 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 62 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 61 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|parts| (((|List| |#4|) $) 51 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|mvar| ((|#3| $) 33)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 42)) (|members| (((|List| |#4|) $) 52 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#4| $) 54 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#4| |#4|) $) 47 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#4| |#4|) $) 46)) (|mainVariables| (((|List| |#3|) $) 31)) (|mainVariable?| (((|Boolean|) |#3| $) 30)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 41)) (|latex| (((|String|) $) 9)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 20 (|has| |#1| (|IntegralDomain|)))) (|hash| (((|SingleInteger|) $) 10)) (|find| (((|Union| |#4| "failed") (|Mapping| (|Boolean|) |#4|) $) 60)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) 49 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 58 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ |#4| |#4|) 57 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|Equation| |#4|)) 56 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|List| (|Equation| |#4|))) 55 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 37)) (|empty?| (((|Boolean|) $) 40)) (|empty| (($) 39)) (|count| (((|NonNegativeInteger|) |#4| $) 53 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#4|) $) 50 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) 38)) (|convert| (((|InputForm|) $) 68 (|has| |#4| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#4|)) 59)) (|collectUpper| (($ $ |#3|) 27)) (|collectUnder| (($ $ |#3|) 29)) (|collect| (($ $ |#3|) 28)) (|coerce| (((|OutputForm|) $) 11) (((|List| |#4|) $) 36)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) 48 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 6)) (|#| (((|NonNegativeInteger|) $) 45 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) (|Category|) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |t#1| |t#2| |t#3|)) (T |PolynomialSetCategory|)) 
((|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)))) (|mvar| (*1 *2 *1) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *2 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *2 (|OrderedSet|)))) (|variables| (*1 *2 *1) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|List| *5)))) (|mainVariables| (*1 *2 *1) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|List| *5)))) (|mainVariable?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|PolynomialSetCategory| *4 *5 *3 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *4 *5 *3)) (|isDomain| *2 (|Boolean|)))) (|collectUnder| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *2 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *5 (|RecursivePolynomialCategory| *3 *4 *2)))) (|collect| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *2 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *5 (|RecursivePolynomialCategory| *3 *4 *2)))) (|collectUpper| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *2 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *5 (|RecursivePolynomialCategory| *3 *4 *2)))) (|sort| (*1 *2 *1 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *4 *5 *3)) (|isDomain| *2 (|Record| (|:| |under| *1) (|:| |floor| *1) (|:| |upper| *1))) (|ofCategory| *1 (|PolynomialSetCategory| *4 *5 *3 *6)))) (|trivialIdeal?| (*1 *2 *1) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Boolean|)))) (|roughBase?| (*1 *2 *1) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|)))) (|roughSubIdeal?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|)))) (|roughEqualIdeals?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|)))) (|roughUnitIdeal?| (*1 *2 *1) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|)))) (|headRemainder| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|PolynomialSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| *4))))) (|remainder| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|PolynomialSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |rnum| *4) (|:| |polnum| *3) (|:| |den| *4))))) (|rewriteIdealWithHeadRemainder| (*1 *2 *2 *1) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|IntegralDomain|)))) (|rewriteIdealWithRemainder| (*1 *2 *2 *1) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|IntegralDomain|)))) (|triangular?| (*1 *2 *1) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|))))) 
(|Join| (|SetCategory|) (|Collection| |t#4|) (|CoercibleTo| (|List| |t#4|)) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|List| |t#4|))) (SIGNATURE |retract| ($ (|List| |t#4|))) (SIGNATURE |mvar| (|t#3| $)) (SIGNATURE |variables| ((|List| |t#3|) $)) (SIGNATURE |mainVariables| ((|List| |t#3|) $)) (SIGNATURE |mainVariable?| ((|Boolean|) |t#3| $)) (SIGNATURE |collectUnder| ($ $ |t#3|)) (SIGNATURE |collect| ($ $ |t#3|)) (SIGNATURE |collectUpper| ($ $ |t#3|)) (SIGNATURE |sort| ((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |t#3|)) (SIGNATURE |trivialIdeal?| ((|Boolean|) $)) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |roughBase?| ((|Boolean|) $)) (SIGNATURE |roughSubIdeal?| ((|Boolean|) $ $)) (SIGNATURE |roughEqualIdeals?| ((|Boolean|) $ $)) (SIGNATURE |roughUnitIdeal?| ((|Boolean|) $)) (SIGNATURE |headRemainder| ((|Record| (|:| |num| |t#4|) (|:| |den| |t#1|)) |t#4| $)) (SIGNATURE |remainder| ((|Record| (|:| |rnum| |t#1|) (|:| |polnum| |t#4|) (|:| |den| |t#1|)) |t#4| $)) (SIGNATURE |rewriteIdealWithHeadRemainder| ((|List| |t#4|) (|List| |t#4|) $)) (SIGNATURE |rewriteIdealWithRemainder| ((|List| |t#4|) (|List| |t#4|) $)) (SIGNATURE |triangular?| ((|Boolean|) $))) |noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|SetCategory|) . T) ((|Type|) . T)) 
((|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) 114)) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) 103 (|has| |#1| (|GcdDomain|))) (((|List| |#4|) (|List| |#4|)) 104 (|has| |#1| (|GcdDomain|)))) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) 34)) (|univariate?| (((|Boolean|) |#4|) 33)) (|squareFreeFactors| (((|List| |#4|) |#4|) 100 (|has| |#1| (|GcdDomain|)))) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) 19)) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) 21)) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) 22)) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) 72)) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) 84)) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) 107)) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) 106)) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) 47) (((|List| |#4|) (|List| |#4|) (|List| |#4|)) 49)) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) 48)) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) 110 (|has| |#1| (|GcdDomain|)))) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) 113 (|has| |#1| (|GcdDomain|)))) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) 112 (|has| |#1| (|GcdDomain|)))) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) 86) (((|List| |#4|) (|List| |#4|) (|List| |#4|)) 88) (((|List| |#4|) (|List| |#4|) |#4|) 117) (((|List| |#4|) |#4| |#4|) 115) (((|List| |#4|) (|List| |#4|)) 87)) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) 97 (AND (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|EuclideanDomain|))))) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) 40)) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) 61)) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) 52)) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) 28)) (|linear?| (((|Boolean|) |#4|) 27)) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) 96 (AND (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|EuclideanDomain|))))) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) 95 (AND (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|EuclideanDomain|))))) (|interReduce| (((|List| |#4|) (|List| |#4|)) 65)) (|crushedSet| (((|List| |#4|) (|List| |#4|)) 78)) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) 50)) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) 38)) (|bivariate?| (((|Boolean|) |#4|) 35))) 
(((|PolynomialSetUtilitiesPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |removeRedundantFactors| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |removeRedundantFactors| ((|List| |#4|) |#4| |#4|)) (SIGNATURE |removeSquaresIfCan| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |unprotectedRemoveRedundantFactors| ((|List| |#4|) |#4| |#4|)) (SIGNATURE |removeRedundantFactors| ((|List| |#4|) (|List| |#4|) |#4|)) (SIGNATURE |removeRedundantFactors| ((|List| |#4|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |removeRedundantFactors| ((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|)))) (SIGNATURE |certainlySubVariety?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |possiblyNewVariety?| ((|Boolean|) (|List| |#4|) (|List| (|List| |#4|)))) (SIGNATURE |probablyZeroDim?| ((|Boolean|) (|List| |#4|))) (SIGNATURE |selectPolynomials| ((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|))) (SIGNATURE |selectOrPolynomials| ((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|))) (SIGNATURE |selectAndPolynomials| ((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|))) (SIGNATURE |quasiMonicPolynomials| ((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|))) (SIGNATURE |univariate?| ((|Boolean|) |#4|)) (SIGNATURE |univariatePolynomials| ((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|))) (SIGNATURE |linear?| ((|Boolean|) |#4|)) (SIGNATURE |linearPolynomials| ((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|))) (SIGNATURE |bivariate?| ((|Boolean|) |#4|)) (SIGNATURE |bivariatePolynomials| ((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|))) (SIGNATURE |removeRoughlyRedundantFactorsInPols| ((|List| |#4|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |removeRoughlyRedundantFactorsInPols| ((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|))) (SIGNATURE |removeRoughlyRedundantFactorsInPol| (|#4| |#4| (|List| |#4|))) (SIGNATURE |interReduce| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |roughBasicSet| ((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|))) (SIGNATURE |crushedSet| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |rewriteSetByReducingWithParticularGenerators| ((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|))) (SIGNATURE |rewriteIdealWithQuasiMonicGenerators| ((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|))) (IF (|has| |#1| (|GcdDomain|)) (PROGN (SIGNATURE |squareFreeFactors| ((|List| |#4|) |#4|)) (SIGNATURE |univariatePolynomialsGcds| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |univariatePolynomialsGcds| ((|List| |#4|) (|List| |#4|) (|Boolean|))) (SIGNATURE |removeRoughlyRedundantFactorsInContents| ((|List| |#4|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |removeRedundantFactorsInContents| ((|List| |#4|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |removeRedundantFactorsInPols| ((|List| |#4|) (|List| |#4|) (|List| |#4|)))) |noBranch|) (IF (|has| |#1| (|EuclideanDomain|)) (IF (|has| |#1| (|CharacteristicZero|)) (PROGN (SIGNATURE |irreducibleFactors| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |lazyIrreducibleFactors| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |removeIrreducibleRedundantFactors| ((|List| |#4|) (|List| |#4|) (|List| |#4|)))) |noBranch|) |noBranch|)) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|)) (T |PolynomialSetUtilitiesPackage|)) 
((|removeIrreducibleRedundantFactors| (*1 *2 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|CharacteristicZero|)) (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *3 *4 *5 *6)))) (|lazyIrreducibleFactors| (*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|CharacteristicZero|)) (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *3 *4 *5 *6)))) (|irreducibleFactors| (*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|CharacteristicZero|)) (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *3 *4 *5 *6)))) (|removeRedundantFactorsInPols| (*1 *2 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *3 *4 *5 *6)))) (|removeRedundantFactorsInContents| (*1 *2 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *3 *4 *5 *6)))) (|removeRoughlyRedundantFactorsInContents| (*1 *2 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *3 *4 *5 *6)))) (|univariatePolynomialsGcds| (*1 *2 *2 *3) (AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|Boolean|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *7)))) (|univariatePolynomialsGcds| (*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *3 *4 *5 *6)))) (|squareFreeFactors| (*1 *2 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *3)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)))) (|rewriteIdealWithQuasiMonicGenerators| (*1 *2 *2 *3 *4) (AND (|isDomain| *2 (|List| *8)) (|isDomain| *3 (|Mapping| (|Boolean|) *8 *8)) (|isDomain| *4 (|Mapping| *8 *8 *8)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *5 *6 *7 *8)))) (|rewriteSetByReducingWithParticularGenerators| (*1 *2 *2 *3 *4 *5) (AND (|isDomain| *2 (|List| *9)) (|isDomain| *3 (|Mapping| (|Boolean|) *9)) (|isDomain| *4 (|Mapping| (|Boolean|) *9 *9)) (|isDomain| *5 (|Mapping| *9 *9 *9)) (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8)) (|ofCategory| *6 (|IntegralDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *6 *7 *8 *9)))) (|crushedSet| (*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *3 *4 *5 *6)))) (|roughBasicSet| (*1 *2 *3) (|partial| AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Record| (|:| |bas| (|GeneralTriangularSet| *4 *5 *6 *7)) (|:| |top| (|List| *7)))) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *7)) (|isDomain| *3 (|List| *7)))) (|interReduce| (*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *3 *4 *5 *6)))) (|removeRoughlyRedundantFactorsInPol| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *2)))) (|removeRoughlyRedundantFactorsInPols| (*1 *2 *2 *2 *3) (AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|Boolean|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *7)))) (|removeRoughlyRedundantFactorsInPols| (*1 *2 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *3 *4 *5 *6)))) (|bivariatePolynomials| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Record| (|:| |goodPols| (|List| *7)) (|:| |badPols| (|List| *7)))) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *7)) (|isDomain| *3 (|List| *7)))) (|bivariate?| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *3)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)))) (|linearPolynomials| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Record| (|:| |goodPols| (|List| *7)) (|:| |badPols| (|List| *7)))) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *7)) (|isDomain| *3 (|List| *7)))) (|linear?| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *3)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)))) (|univariatePolynomials| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Record| (|:| |goodPols| (|List| *7)) (|:| |badPols| (|List| *7)))) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *7)) (|isDomain| *3 (|List| *7)))) (|univariate?| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *3)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)))) (|quasiMonicPolynomials| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Record| (|:| |goodPols| (|List| *7)) (|:| |badPols| (|List| *7)))) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *7)) (|isDomain| *3 (|List| *7)))) (|selectAndPolynomials| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Mapping| (|Boolean|) *8))) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |goodPols| (|List| *8)) (|:| |badPols| (|List| *8)))) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *5 *6 *7 *8)) (|isDomain| *4 (|List| *8)))) (|selectOrPolynomials| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Mapping| (|Boolean|) *8))) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |goodPols| (|List| *8)) (|:| |badPols| (|List| *8)))) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *5 *6 *7 *8)) (|isDomain| *4 (|List| *8)))) (|selectPolynomials| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *8)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |goodPols| (|List| *8)) (|:| |badPols| (|List| *8)))) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *5 *6 *7 *8)) (|isDomain| *4 (|List| *8)))) (|probablyZeroDim?| (*1 *2 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *7)))) (|possiblyNewVariety?| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| (|List| *8))) (|isDomain| *3 (|List| *8)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *5 *6 *7 *8)))) (|certainlySubVariety?| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *7)))) (|removeRedundantFactors| (*1 *2 *2 *2 *3) (AND (|isDomain| *3 (|Mapping| (|List| *7) (|List| *7))) (|isDomain| *2 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *7)))) (|removeRedundantFactors| (*1 *2 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *3 *4 *5 *6)))) (|removeRedundantFactors| (*1 *2 *2 *3) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *3)))) (|unprotectedRemoveRedundantFactors| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *3)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)))) (|removeSquaresIfCan| (*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *3 *4 *5 *6)))) (|removeRedundantFactors| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *3)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)))) (|removeRedundantFactors| (*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *3 *4 *5 *6))))) 
(CATEGORY |package| (SIGNATURE |removeRedundantFactors| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |removeRedundantFactors| ((|List| |#4|) |#4| |#4|)) (SIGNATURE |removeSquaresIfCan| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |unprotectedRemoveRedundantFactors| ((|List| |#4|) |#4| |#4|)) (SIGNATURE |removeRedundantFactors| ((|List| |#4|) (|List| |#4|) |#4|)) (SIGNATURE |removeRedundantFactors| ((|List| |#4|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |removeRedundantFactors| ((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|)))) (SIGNATURE |certainlySubVariety?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |possiblyNewVariety?| ((|Boolean|) (|List| |#4|) (|List| (|List| |#4|)))) (SIGNATURE |probablyZeroDim?| ((|Boolean|) (|List| |#4|))) (SIGNATURE |selectPolynomials| ((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|))) (SIGNATURE |selectOrPolynomials| ((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|))) (SIGNATURE |selectAndPolynomials| ((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|))) (SIGNATURE |quasiMonicPolynomials| ((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|))) (SIGNATURE |univariate?| ((|Boolean|) |#4|)) (SIGNATURE |univariatePolynomials| ((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|))) (SIGNATURE |linear?| ((|Boolean|) |#4|)) (SIGNATURE |linearPolynomials| ((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|))) (SIGNATURE |bivariate?| ((|Boolean|) |#4|)) (SIGNATURE |bivariatePolynomials| ((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|))) (SIGNATURE |removeRoughlyRedundantFactorsInPols| ((|List| |#4|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |removeRoughlyRedundantFactorsInPols| ((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|))) (SIGNATURE |removeRoughlyRedundantFactorsInPol| (|#4| |#4| (|List| |#4|))) (SIGNATURE |interReduce| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |roughBasicSet| ((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|))) (SIGNATURE |crushedSet| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |rewriteSetByReducingWithParticularGenerators| ((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|))) (SIGNATURE |rewriteIdealWithQuasiMonicGenerators| ((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|))) (IF (|has| |#1| (|GcdDomain|)) (PROGN (SIGNATURE |squareFreeFactors| ((|List| |#4|) |#4|)) (SIGNATURE |univariatePolynomialsGcds| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |univariatePolynomialsGcds| ((|List| |#4|) (|List| |#4|) (|Boolean|))) (SIGNATURE |removeRoughlyRedundantFactorsInContents| ((|List| |#4|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |removeRedundantFactorsInContents| ((|List| |#4|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |removeRedundantFactorsInPols| ((|List| |#4|) (|List| |#4|) (|List| |#4|)))) |noBranch|) (IF (|has| |#1| (|EuclideanDomain|)) (IF (|has| |#1| (|CharacteristicZero|)) (PROGN (SIGNATURE |irreducibleFactors| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |lazyIrreducibleFactors| ((|List| |#4|) (|List| |#4|))) (SIGNATURE |removeIrreducibleRedundantFactors| ((|List| |#4|) (|List| |#4|) (|List| |#4|)))) |noBranch|) |noBranch|)) 
((|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) 19)) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) 35)) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) 16))) 
(((|PseudoLinearNormalForm| |#1|) (CATEGORY |package| (SIGNATURE |normalForm| ((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|))) (SIGNATURE |changeBase| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|))) (SIGNATURE |companionBlocks| ((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)))) (|Field|)) (T |PseudoLinearNormalForm|)) 
((|companionBlocks| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|List| (|Record| (|:| C (|Matrix| *5)) (|:| |g| (|Vector| *5))))) (|isDomain| *1 (|PseudoLinearNormalForm| *5)) (|isDomain| *3 (|Matrix| *5)) (|isDomain| *4 (|Vector| *5)))) (|changeBase| (*1 *2 *2 *2 *3 *4) (AND (|isDomain| *2 (|Matrix| *5)) (|isDomain| *3 (|Automorphism| *5)) (|isDomain| *4 (|Mapping| *5 *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *1 (|PseudoLinearNormalForm| *5)))) (|normalForm| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|Automorphism| *6)) (|isDomain| *5 (|Mapping| *6 *6)) (|ofCategory| *6 (|Field|)) (|isDomain| *2 (|Record| (|:| R (|Matrix| *6)) (|:| A (|Matrix| *6)) (|:| |Ainv| (|Matrix| *6)))) (|isDomain| *1 (|PseudoLinearNormalForm| *6)) (|isDomain| *3 (|Matrix| *6))))) 
(CATEGORY |package| (SIGNATURE |normalForm| ((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|))) (SIGNATURE |changeBase| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|))) (SIGNATURE |companionBlocks| ((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)))) 
((|squareFree| (((|Factored| |#4|) |#4|) 47))) 
(((|PolynomialSquareFree| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |squareFree| ((|Factored| |#4|) |#4|))) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|GcdDomain|) (|PolynomialCategory| |#3| |#2| |#1|)) (T |PolynomialSquareFree|)) 
((|squareFree| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|GcdDomain|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|PolynomialSquareFree| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *6 *5 *4))))) 
(CATEGORY |package| (SIGNATURE |squareFree| ((|Factored| |#4|) |#4|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|zero| (($ (|NonNegativeInteger|)) 105 (|has| |#1| (|AbelianMonoid|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) 91) (((|Boolean|) $) 85 (|has| |#1| (|OrderedSet|)))) (|sort!| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) 82 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $) 81 (AND (|has| |#1| (|OrderedSet|)) (|has| $ (ATTRIBUTE |shallowlyMutable|))))) (|sort| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) 92) (($ $) 86 (|has| |#1| (|OrderedSet|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setelt| ((|#1| $ (|Integer|) |#1|) 49 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) 53 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 70 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) 7 T CONST)) (|reverse!| (($ $) 83 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) 93)) (|removeDuplicates| (($ $) 73 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove| (($ |#1| $) 72 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#1|) $) 69 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 71 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 68 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 67 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| ((|#1| $ (|Integer|) |#1|) 50 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#1| $ (|Integer|)) 48)) (|position| (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) 90) (((|Integer|) |#1| $) 89 (|has| |#1| (|SetCategory|))) (((|Integer|) |#1| $ (|Integer|)) 88 (|has| |#1| (|SetCategory|)))) (|point| (($ (|List| |#1|)) 110)) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|outerProduct| (((|Matrix| |#1|) $ $) 98 (|has| |#1| (|Ring|)))) (|new| (($ (|NonNegativeInteger|) |#1|) 64)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|minIndex| (((|Integer|) $) 40 (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) 80 (|has| |#1| (|OrderedSet|)))) (|merge| (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) 94) (($ $ $) 87 (|has| |#1| (|OrderedSet|)))) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|maxIndex| (((|Integer|) $) 41 (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) 79 (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35) (($ (|Mapping| |#1| |#1| |#1|) $ $) 59)) (|magnitude| ((|#1| $) 95 (AND (|has| |#1| (|Ring|)) (|has| |#1| (|RadicalCategory|))))) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|length| ((|#1| $) 96 (AND (|has| |#1| (|Ring|)) (|has| |#1| (|RadicalCategory|))))) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|insert| (($ |#1| $ (|Integer|)) 55) (($ $ $ (|Integer|)) 54)) (|indices| (((|List| (|Integer|)) $) 43)) (|index?| (((|Boolean|) (|Integer|) $) 44)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|first| ((|#1| $) 39 (|has| (|Integer|) (|OrderedSet|)))) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) 66)) (|fill!| (($ $ |#1|) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|extend| (($ $ (|List| |#1|)) 107)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 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(((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|PointCategory| |#1|) (|Category|) (|Ring|)) (T |PointCategory|)) 
((|point| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|PointCategory| *3)))) (|dimension| (*1 *2 *1) (AND (|ofCategory| *1 (|PointCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|PositiveInteger|)))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|PointCategory| *3)))) (|cross| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|PointCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|extend| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *1 (|PointCategory| *3)) (|ofCategory| *3 (|Ring|))))) 
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(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| (|Integer|) |#1|) . T) ((|EltableAggregate| (|Integer|) |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteLinearAggregate| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| (|Integer|) |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|LinearAggregate| |#1|) . T) ((|OneDimensionalArrayAggregate| |#1|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|SetCategory|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|Type|) . T) ((|VectorCategory| |#1|) . T)) 
((|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) 17))) 
(((|PointFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)))) (|Ring|) (|Ring|)) (T |PointFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Point| *5)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|Ring|)) (|isDomain| *2 (|Point| *6)) (|isDomain| *1 (|PointFunctions2| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |map| ((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)))) 
((|zCoord| ((|#1| (|Point| |#1|)) 13)) (|yCoord| ((|#1| (|Point| |#1|)) 12)) (|xCoord| ((|#1| (|Point| |#1|)) 11)) (|thetaCoord| ((|#1| (|Point| |#1|)) 15)) (|shade| ((|#1| (|Point| |#1|)) 21)) (|rCoord| ((|#1| (|Point| |#1|)) 14)) (|phiCoord| ((|#1| (|Point| |#1|)) 16)) (|hue| ((|#1| (|Point| |#1|)) 20)) (|color| ((|#1| (|Point| |#1|)) 19))) 
(((|PointPackage| |#1|) (CATEGORY |package| (SIGNATURE |xCoord| (|#1| (|Point| |#1|))) (SIGNATURE |yCoord| (|#1| (|Point| |#1|))) (SIGNATURE |zCoord| (|#1| (|Point| |#1|))) (SIGNATURE |rCoord| (|#1| (|Point| |#1|))) (SIGNATURE |thetaCoord| (|#1| (|Point| |#1|))) (SIGNATURE |phiCoord| (|#1| (|Point| |#1|))) (SIGNATURE |color| (|#1| (|Point| |#1|))) (SIGNATURE |hue| (|#1| (|Point| |#1|))) (SIGNATURE |shade| (|#1| (|Point| |#1|)))) (|Ring|)) (T |PointPackage|)) 
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(CATEGORY |package| (SIGNATURE |xCoord| (|#1| (|Point| |#1|))) (SIGNATURE |yCoord| (|#1| (|Point| |#1|))) (SIGNATURE |zCoord| (|#1| (|Point| |#1|))) (SIGNATURE |rCoord| (|#1| (|Point| |#1|))) (SIGNATURE |thetaCoord| (|#1| (|Point| |#1|))) (SIGNATURE |phiCoord| (|#1| (|Point| |#1|))) (SIGNATURE |color| (|#1| (|Point| |#1|))) (SIGNATURE |hue| (|#1| (|Point| |#1|))) (SIGNATURE |shade| (|#1| (|Point| |#1|)))) 
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(((|PartialTranscendentalFunctions| |#1|) (|Category|) (|TranscendentalFunctionCategory|)) (T |PartialTranscendentalFunctions|)) 
((|acschIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|asechIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|acothIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|atanhIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|acoshIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|asinhIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|cschIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|sechIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|cothIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|tanhIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|coshIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|sinhIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|acscIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|asecIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|acotIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|atanIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|acosIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|asinIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|cscIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|secIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|cotIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|tanIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|cosIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|sinIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|logIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|expIfCan| (*1 *2 *2) (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|nthRootIfCan| (*1 *2 *2 *3) (|partial| AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|PartialTranscendentalFunctions| *2)) (|ofCategory| *2 (|TranscendentalFunctionCategory|))))) 
(|Join| (CATEGORY |package| (SIGNATURE |nthRootIfCan| ((|Union| |t#1| "failed") |t#1| (|NonNegativeInteger|))) (SIGNATURE |expIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |logIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |sinIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |cosIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |tanIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |cotIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |secIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |cscIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |asinIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |acosIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |atanIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |acotIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |asecIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |acscIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |sinhIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |coshIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |tanhIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |cothIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |sechIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |cschIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |asinhIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |acoshIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |atanhIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |acothIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |asechIfCan| ((|Union| |t#1| "failed") |t#1|)) (SIGNATURE |acschIfCan| ((|Union| |t#1| "failed") |t#1|)))) 
((|pushup| ((|#4| |#4| (|List| |#3|)) 55) ((|#4| |#4| |#3|) 54)) (|pushdown| ((|#4| |#4| (|List| |#3|)) 23) ((|#4| |#4| |#3|) 19)) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) 30))) 
(((|PushVariables| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |pushdown| (|#4| |#4| |#3|)) (SIGNATURE |pushdown| (|#4| |#4| (|List| |#3|))) (SIGNATURE |pushup| (|#4| |#4| |#3|)) (SIGNATURE |pushup| (|#4| |#4| (|List| |#3|))) (SIGNATURE |map| (|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|))) (|Ring|) (|OrderedAbelianMonoidSup|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") (|Symbol|))))) (|PolynomialCategory| (|Polynomial| |#1|) |#2| |#3|)) (T |PushVariables|)) 
((|map| (*1 *2 *3 *2) (AND (|isDomain| *3 (|Mapping| *2 (|Polynomial| *4))) (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|PolynomialCategory| (|Polynomial| *4) *5 *6)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") (|Symbol|)))))) (|isDomain| *1 (|PushVariables| *4 *5 *6 *2)))) (|pushup| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *6 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") (|Symbol|)))))) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|isDomain| *1 (|PushVariables| *4 *5 *6 *2)) (|ofCategory| *2 (|PolynomialCategory| (|Polynomial| *4) *5 *6)))) (|pushup| (*1 *2 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") (|Symbol|)))))) (|isDomain| *1 (|PushVariables| *4 *5 *3 *2)) (|ofCategory| *2 (|PolynomialCategory| (|Polynomial| *4) *5 *3)))) (|pushdown| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *6 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") (|Symbol|)))))) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|isDomain| *1 (|PushVariables| *4 *5 *6 *2)) (|ofCategory| *2 (|PolynomialCategory| (|Polynomial| *4) *5 *6)))) (|pushdown| (*1 *2 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") (|Symbol|)))))) (|isDomain| *1 (|PushVariables| *4 *5 *3 *2)) (|ofCategory| *2 (|PolynomialCategory| (|Polynomial| *4) *5 *3))))) 
(CATEGORY |package| (SIGNATURE |pushdown| (|#4| |#4| |#3|)) (SIGNATURE |pushdown| (|#4| |#4| (|List| |#3|))) (SIGNATURE |pushup| (|#4| |#4| |#3|)) (SIGNATURE |pushup| (|#4| |#4| (|List| |#3|))) (SIGNATURE |map| (|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|))) 
((|reducedDiscriminant| ((|#2| |#3|) 34)) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) 71)) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) 86))) 
(((|PAdicWildFunctionFieldIntegralBasis| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |integralBasis| ((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))))) (SIGNATURE |localIntegralBasis| ((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|)) (SIGNATURE |reducedDiscriminant| (|#2| |#3|))) (|FiniteFieldCategory|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| |#2|) (|MonogenicAlgebra| |#2| |#3|)) (T |PAdicWildFunctionFieldIntegralBasis|)) 
((|reducedDiscriminant| (*1 *2 *3) (AND (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|PAdicWildFunctionFieldIntegralBasis| *4 *2 *3 *5)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|ofCategory| *5 (|MonogenicAlgebra| *2 *3)))) (|localIntegralBasis| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Record| (|:| |basis| (|Matrix| *3)) (|:| |basisDen| *3) (|:| |basisInv| (|Matrix| *3)))) (|isDomain| *1 (|PAdicWildFunctionFieldIntegralBasis| *4 *3 *5 *6)) (|ofCategory| *6 (|MonogenicAlgebra| *3 *5)))) (|integralBasis| (*1 *2) (AND (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Record| (|:| |basis| (|Matrix| *4)) (|:| |basisDen| *4) (|:| |basisInv| (|Matrix| *4)))) (|isDomain| *1 (|PAdicWildFunctionFieldIntegralBasis| *3 *4 *5 *6)) (|ofCategory| *6 (|MonogenicAlgebra| *4 *5))))) 
(CATEGORY |package| (SIGNATURE |integralBasis| ((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))))) (SIGNATURE |localIntegralBasis| ((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|)) (SIGNATURE |reducedDiscriminant| (|#2| |#3|))) 
((|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) 64))) 
(((|QuasiAlgebraicSet2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |radicalSimplify| ((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))))) (|List| (|Symbol|)) (|NonNegativeInteger|)) (T |QuasiAlgebraicSet2|)) 
((|radicalSimplify| (*1 *2 *2) (AND (|isDomain| *2 (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| *3) (|DirectProduct| *4 (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| *3 (|Fraction| (|Integer|))))) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|NonNegativeInteger|)) (|isDomain| *1 (|QuasiAlgebraicSet2| *3 *4))))) 
(CATEGORY |package| (SIGNATURE |radicalSimplify| ((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))))) 
((~= (((|Boolean|) $ $) NIL)) (|status| (((|Union| (|Boolean|) "failed") $) 67)) (|simplify| (($ $) 35 (AND (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|EuclideanDomain|))))) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) 68)) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) 24)) (|latex| (((|String|) $) NIL)) (|idealSimplify| (($ $) 65)) (|hash| (((|SingleInteger|) $) NIL)) (|empty?| (((|Boolean|) $) 66)) (|empty| (($) 29)) (|definingInequation| ((|#4| $) 70)) (|definingEquations| (((|List| |#4|) $) 69)) (|coerce| (((|OutputForm|) $) 64)) (= (((|Boolean|) $ $) NIL))) 
(((|QuasiAlgebraicSet| |#1| |#2| |#3| |#4|) (|Join| (|SetCategory|) (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |empty| ($)) (SIGNATURE |quasiAlgebraicSet| ($ (|List| |#4|) |#4|)) (SIGNATURE |status| ((|Union| (|Boolean|) "failed") $)) (SIGNATURE |setStatus| ($ $ (|Union| (|Boolean|) "failed"))) (SIGNATURE |empty?| ((|Boolean|) $)) (SIGNATURE |definingEquations| ((|List| |#4|) $)) (SIGNATURE |definingInequation| (|#4| $)) (SIGNATURE |idealSimplify| ($ $)) (IF (|has| |#1| (|EuclideanDomain|)) (IF (|has| |#1| (|CharacteristicZero|)) (SIGNATURE |simplify| ($ $)) |noBranch|) |noBranch|))) (|GcdDomain|) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|PolynomialCategory| |#1| |#3| |#2|)) (T |QuasiAlgebraicSet|)) 
((|empty| (*1 *1) (AND (|ofCategory| *2 (|GcdDomain|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|isDomain| *1 (|QuasiAlgebraicSet| *2 *3 *4 *5)) (|ofCategory| *5 (|PolynomialCategory| *2 *4 *3)))) (|quasiAlgebraicSet| (*1 *1 *2 *3) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|PolynomialCategory| *4 *6 *5)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *1 (|QuasiAlgebraicSet| *4 *5 *6 *3)))) (|status| (*1 *2 *1) (|partial| AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|QuasiAlgebraicSet| *3 *4 *5 *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *5 *4)))) (|setStatus| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Union| (|Boolean|) "failed")) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|isDomain| *1 (|QuasiAlgebraicSet| *3 *4 *5 *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *5 *4)))) (|empty?| (*1 *2 *1) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|QuasiAlgebraicSet| *3 *4 *5 *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *5 *4)))) (|definingEquations| (*1 *2 *1) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|List| *6)) (|isDomain| *1 (|QuasiAlgebraicSet| *3 *4 *5 *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *5 *4)))) (|definingInequation| (*1 *2 *1) (AND (|ofCategory| *2 (|PolynomialCategory| *3 *5 *4)) (|isDomain| *1 (|QuasiAlgebraicSet| *3 *4 *5 *2)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)))) (|idealSimplify| (*1 *1 *1) (AND (|ofCategory| *2 (|GcdDomain|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|isDomain| *1 (|QuasiAlgebraicSet| *2 *3 *4 *5)) (|ofCategory| *5 (|PolynomialCategory| *2 *4 *3)))) (|simplify| (*1 *1 *1) (AND (|ofCategory| *2 (|CharacteristicZero|)) (|ofCategory| *2 (|EuclideanDomain|)) (|ofCategory| *2 (|GcdDomain|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|isDomain| *1 (|QuasiAlgebraicSet| *2 *3 *4 *5)) (|ofCategory| *5 (|PolynomialCategory| *2 *4 *3))))) 
(|Join| (|SetCategory|) (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |empty| ($)) (SIGNATURE |quasiAlgebraicSet| ($ (|List| |#4|) |#4|)) (SIGNATURE |status| ((|Union| (|Boolean|) "failed") $)) (SIGNATURE |setStatus| ($ $ (|Union| (|Boolean|) "failed"))) (SIGNATURE |empty?| ((|Boolean|) $)) (SIGNATURE |definingEquations| ((|List| |#4|) $)) (SIGNATURE |definingInequation| (|#4| $)) (SIGNATURE |idealSimplify| ($ $)) (IF (|has| |#1| (|EuclideanDomain|)) (IF (|has| |#1| (|CharacteristicZero|)) (SIGNATURE |simplify| ($ $)) |noBranch|) |noBranch|))) 
((|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) 37)) (|subTriSet?| (((|Boolean|) |#5| |#5|) 51)) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) 73) (((|Boolean|) |#5| |#5|) 60)) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) 57)) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) 62)) (|stopTable!| (((|Void|)) 33)) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) 29)) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) 80)) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) 78)) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) 100)) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) 46)) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) 70)) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) 56)) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) 58)) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) 59)) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) 96)) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) 42))) 
(((|QuasiComponentPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |startTable!| ((|Void|) (|String|) (|String|) (|String|))) (SIGNATURE |stopTable!| ((|Void|))) (SIGNATURE |supDimElseRittWu?| ((|Boolean|) |#5| |#5|)) (SIGNATURE |algebraicSort| ((|List| |#5|) (|List| |#5|))) (SIGNATURE |moreAlgebraic?| ((|Boolean|) |#5| |#5|)) (SIGNATURE |subTriSet?| ((|Boolean|) |#5| |#5|)) (SIGNATURE |subPolSet?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |internalSubPolSet?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |internalInfRittWu?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |infRittWu?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |internalSubQuasiComponent?| ((|Union| (|Boolean|) "failed") |#5| |#5|)) (SIGNATURE |subQuasiComponent?| ((|Boolean|) |#5| |#5|)) (SIGNATURE |subQuasiComponent?| ((|Boolean|) |#5| (|List| |#5|))) (SIGNATURE |removeSuperfluousQuasiComponents| ((|List| |#5|) (|List| |#5|))) (SIGNATURE |subCase?| ((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) (SIGNATURE |removeSuperfluousCases| ((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) (SIGNATURE |prepareDecompose| ((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|))) (SIGNATURE |branchIfCan| ((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |QuasiComponentPackage|)) 
((|branchIfCan| (*1 *2 *3 *4 *3 *5 *5 *5 *5 *5) (|partial| AND (|isDomain| *5 (|Boolean|)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8)) (|isDomain| *2 (|Record| (|:| |eq| (|List| *9)) (|:| |tower| *4) (|:| |ineq| (|List| *9)))) (|isDomain| *1 (|QuasiComponentPackage| *6 *7 *8 *9 *4)) (|isDomain| *3 (|List| *9)) (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *9)))) (|prepareDecompose| (*1 *2 *3 *4 *5 *5) (AND (|isDomain| *4 (|List| *10)) (|isDomain| *5 (|Boolean|)) (|ofCategory| *10 (|RegularTriangularSetCategory| *6 *7 *8 *9)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8)) (|isDomain| *2 (|List| (|Record| (|:| |eq| (|List| *9)) (|:| |tower| *10) (|:| |ineq| (|List| *9))))) (|isDomain| *1 (|QuasiComponentPackage| *6 *7 *8 *9 *10)) (|isDomain| *3 (|List| *9)))) (|removeSuperfluousCases| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |val| (|List| *6)) (|:| |tower| *7)))) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|QuasiComponentPackage| *3 *4 *5 *6 *7)))) (|subCase?| (*1 *2 *3 *3) (AND (|isDomain| *3 (|Record| (|:| |val| (|List| *7)) (|:| |tower| *8))) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *8)))) (|removeSuperfluousQuasiComponents| (*1 *2 *2) (AND (|isDomain| *2 (|List| *7)) (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *1 (|QuasiComponentPackage| *3 *4 *5 *6 *7)))) (|subQuasiComponent?| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|QuasiComponentPackage| *5 *6 *7 *8 *3)))) (|subQuasiComponent?| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|internalSubQuasiComponent?| (*1 *2 *3 *3) (|partial| AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|infRittWu?| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|internalInfRittWu?| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|internalSubPolSet?| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|subPolSet?| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|subTriSet?| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|moreAlgebraic?| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|algebraicSort| (*1 *2 *2) (AND (|isDomain| *2 (|List| *7)) (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *1 (|QuasiComponentPackage| *3 *4 *5 *6 *7)))) (|supDimElseRittWu?| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|stopTable!| (*1 *2) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|QuasiComponentPackage| *3 *4 *5 *6 *7)) (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)))) (|startTable!| (*1 *2 *3 *3 *3) (AND (|isDomain| *3 (|String|)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))) 
(CATEGORY |package| (SIGNATURE |startTable!| ((|Void|) (|String|) (|String|) (|String|))) (SIGNATURE |stopTable!| ((|Void|))) (SIGNATURE |supDimElseRittWu?| ((|Boolean|) |#5| |#5|)) (SIGNATURE |algebraicSort| ((|List| |#5|) (|List| |#5|))) (SIGNATURE |moreAlgebraic?| ((|Boolean|) |#5| |#5|)) (SIGNATURE |subTriSet?| ((|Boolean|) |#5| |#5|)) (SIGNATURE |subPolSet?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |internalSubPolSet?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |internalInfRittWu?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |infRittWu?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |internalSubQuasiComponent?| ((|Union| (|Boolean|) "failed") |#5| |#5|)) (SIGNATURE |subQuasiComponent?| ((|Boolean|) |#5| |#5|)) (SIGNATURE |subQuasiComponent?| ((|Boolean|) |#5| (|List| |#5|))) (SIGNATURE |removeSuperfluousQuasiComponents| ((|List| |#5|) (|List| |#5|))) (SIGNATURE |subCase?| ((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) (SIGNATURE |removeSuperfluousCases| ((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) (SIGNATURE |prepareDecompose| ((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|))) (SIGNATURE |branchIfCan| ((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)))) 
((|variable| (((|Symbol|) $) 15)) (|value| (((|String|) $) 16)) (|equation| (($ (|Symbol|) (|String|)) 14)) (|coerce| (((|OutputForm|) $) 13))) 
(((|QueryEquation|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |equation| ($ (|Symbol|) (|String|))) (SIGNATURE |variable| ((|Symbol|) $)) (SIGNATURE |value| ((|String|) $))))) (T |QueryEquation|)) 
((|equation| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|String|)) (|isDomain| *1 (|QueryEquation|)))) (|variable| (*1 *2 *1) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|QueryEquation|)))) (|value| (*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|QueryEquation|))))) 
(|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |equation| ($ (|Symbol|) (|String|))) (SIGNATURE |variable| ((|Symbol|) $)) (SIGNATURE |value| ((|String|) $)))) 
((|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) 14))) 
(((|QuotientFieldCategoryFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#2| |#1|) |#3|))) (|IntegralDomain|) (|IntegralDomain|) (|QuotientFieldCategory| |#1|) (|QuotientFieldCategory| |#2|)) (T |QuotientFieldCategoryFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|IntegralDomain|)) (|ofCategory| *2 (|QuotientFieldCategory| *6)) (|isDomain| *1 (|QuotientFieldCategoryFunctions2| *5 *6 *4 *2)) (|ofCategory| *4 (|QuotientFieldCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#2| |#1|) |#3|))) 
((|retractIfCan| (((|Union| |#2| "failed") $) NIL) (((|Union| (|Symbol|) "failed") $) 65) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL) (((|Union| (|Integer|) "failed") $) 95)) (|retract| ((|#2| $) NIL) (((|Symbol|) $) 60) (((|Fraction| (|Integer|)) $) NIL) (((|Integer|) $) 92)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| $) (|Vector| $)) 112) (((|Matrix| |#2|) (|Matrix| $)) 28)) (|random| (($) 98)) (|patternMatch| (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) 74) (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) 83)) (|numerator| (($ $) 10)) (|nextItem| (((|Union| $ "failed") $) 20)) (|map| (($ (|Mapping| |#2| |#2|) $) 22)) (|init| (($) 16)) (|fractionPart| (($ $) 54)) (|differentiate| (($ $) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Symbol|)) NIL) (($ $ (|List| (|Symbol|))) NIL) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#2| |#2|)) 36)) (|denominator| (($ $) 12)) (|convert| (((|Pattern| (|Integer|)) $) 69) (((|Pattern| (|Float|)) $) 78) (((|InputForm|) $) 40) (((|Float|) $) 44) (((|DoubleFloat|) $) 47)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) 90) (($ |#2|) NIL) (($ (|Symbol|)) 57)) (|characteristic| (((|NonNegativeInteger|)) 31)) (< (((|Boolean|) $ $) 50))) 
(((|QuotientFieldCategory&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE |init| (|#1|)) (SIGNATURE |nextItem| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |convert| ((|DoubleFloat|) |#1|)) (SIGNATURE |convert| ((|Float|) |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |retract| ((|Symbol|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Symbol|) "failed") |#1|)) (SIGNATURE |coerce| (|#1| (|Symbol|))) (SIGNATURE |random| (|#1|)) (SIGNATURE |fractionPart| (|#1| |#1|)) (SIGNATURE |denominator| (|#1| |#1|)) (SIGNATURE |numerator| (|#1| |#1|)) (SIGNATURE |patternMatch| ((|PatternMatchResult| (|Float|) |#1|) |#1| (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) |#1|))) (SIGNATURE |patternMatch| ((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|))) (SIGNATURE |convert| ((|Pattern| (|Float|)) |#1|)) (SIGNATURE |convert| ((|Pattern| (|Integer|)) |#1|)) (SIGNATURE |reducedSystem| ((|Matrix| |#2|) (|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Matrix| (|Integer|)) (|Matrix| |#1|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |coerce| (|#1| |#1|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |characteristic| ((|NonNegativeInteger|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|QuotientFieldCategory| |#2|) (|IntegralDomain|)) (T |QuotientFieldCategory&|)) 
((|characteristic| (*1 *2) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|QuotientFieldCategory&| *3 *4)) (|ofCategory| *3 (|QuotientFieldCategory| *4))))) 
(CATEGORY |domain| (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE |init| (|#1|)) (SIGNATURE |nextItem| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |convert| ((|DoubleFloat|) |#1|)) (SIGNATURE |convert| ((|Float|) |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |retract| ((|Symbol|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Symbol|) "failed") |#1|)) (SIGNATURE |coerce| (|#1| (|Symbol|))) (SIGNATURE |random| (|#1|)) (SIGNATURE |fractionPart| (|#1| |#1|)) (SIGNATURE |denominator| (|#1| |#1|)) (SIGNATURE |numerator| (|#1| |#1|)) (SIGNATURE |patternMatch| ((|PatternMatchResult| (|Float|) |#1|) |#1| (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) |#1|))) (SIGNATURE |patternMatch| ((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|))) (SIGNATURE |convert| ((|Pattern| (|Float|)) |#1|)) (SIGNATURE |convert| ((|Pattern| (|Integer|)) |#1|)) (SIGNATURE |reducedSystem| ((|Matrix| |#2|) (|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Matrix| (|Integer|)) (|Matrix| |#1|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |coerce| (|#1| |#1|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |characteristic| ((|NonNegativeInteger|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|wholePart| ((|#1| $) 137 (|has| |#1| (|EuclideanDomain|)))) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 128 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) 73)) (|squareFree| (((|Factored| $) $) 72)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 131 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|sizeLess?| (((|Boolean|) $ $) 58)) (|sign| (((|Integer|) $) 118 (|has| |#1| (|OrderedIntegralDomain|)))) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 176) (((|Union| (|Symbol|) "failed") $) 126 (|has| |#1| (|RetractableTo| (|Symbol|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) 110 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Integer|) "failed") $) 108 (|has| |#1| (|RetractableTo| (|Integer|))))) (|retract| ((|#1| $) 175) (((|Symbol|) $) 125 (|has| |#1| (|RetractableTo| (|Symbol|)))) (((|Fraction| (|Integer|)) $) 109 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Integer|) $) 107 (|has| |#1| (|RetractableTo| (|Integer|))))) (|rem| (($ $ $) 54)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) 150 (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) 149 (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) 148) (((|Matrix| |#1|) (|Matrix| $)) 147)) (|recip| (((|Union| $ "failed") $) 33)) (|random| (($) 135 (|has| |#1| 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(((|QuotientFieldCategory| |#1|) (|Category|) (|IntegralDomain|)) (T |QuotientFieldCategory|)) 
((/ (*1 *1 *2 *2) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|numer| (*1 *2 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|denom| (*1 *2 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|numerator| (*1 *1 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|denominator| (*1 *1 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|wholePart| (*1 *2 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|EuclideanDomain|)))) (|fractionPart| (*1 *1 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|EuclideanDomain|)))) (|random| (*1 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegerNumberSystem|)) (|ofCategory| *2 (|IntegralDomain|)))) (|ceiling| (*1 *2 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|IntegerNumberSystem|)))) (|floor| (*1 *2 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|IntegerNumberSystem|))))) 
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(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) . T) ((|Algebra| |#1|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) . T) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|DoubleFloat|)) |has| |#1| (|RealConstant|)) ((|ConvertibleTo| (|Float|)) |has| |#1| (|RealConstant|)) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|ConvertibleTo| (|Pattern| (|Float|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) ((|ConvertibleTo| (|Pattern| (|Integer|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) |has| |#1| (|DifferentialRing|)) ((|DivisionRing|) . T) ((|Eltable| |#1| $) |has| |#1| (|Eltable| |#1| |#1|)) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Evalable| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Field|) . T) ((|FullyEvalableOver| |#1|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyPatternMatchable| |#1|) . T) ((|GcdDomain|) . T) ((|InnerEvalable| (|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|IntegralDomain|) . T) ((|LeftModule| (|Fraction| (|Integer|))) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|LinearlyExplicitRingOver| (|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| (|Fraction| (|Integer|))) . T) ((|Module| |#1|) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedAbelianMonoid|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedAbelianSemiGroup|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedCancellationAbelianMonoid|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedIntegralDomain|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedRing|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedSet|) OR (|has| |#1| (|OrderedSet|)) (|has| |#1| (|OrderedIntegralDomain|))) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PatternMatchable| (|Float|)) |has| |#1| (|PatternMatchable| (|Float|))) ((|PatternMatchable| (|Integer|)) |has| |#1| (|PatternMatchable| (|Integer|))) ((|Patternable| |#1|) . T) ((|PolynomialFactorizationExplicit|) |has| |#1| (|PolynomialFactorizationExplicit|)) ((|PrincipalIdealDomain|) . T) ((|RealConstant|) |has| |#1| (|RealConstant|)) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| (|Symbol|)) |has| |#1| (|RetractableTo| (|Symbol|))) ((|RetractableTo| |#1|) . T) ((|RightModule| (|Fraction| (|Integer|))) . T) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|StepThrough|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) 11)) (|matrix| (((|SquareMatrix| |#1| |#2|) $) 12)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) 16)) (|coerce| (((|OutputForm|) $) NIL)) (|Zero| (($) NIL T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL))) 
(((|QuadraticForm| |#1| |#2|) (|Join| (|AbelianGroup|) (CATEGORY |domain| (SIGNATURE |quadraticForm| ($ (|SquareMatrix| |#1| |#2|))) (SIGNATURE |matrix| ((|SquareMatrix| |#1| |#2|) $)) (SIGNATURE |elt| (|#2| $ (|DirectProduct| |#1| |#2|))))) (|PositiveInteger|) (|Field|)) (T |QuadraticForm|)) 
((|quadraticForm| (*1 *1 *2) (AND (|isDomain| *2 (|SquareMatrix| *3 *4)) (|ofType| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Field|)) (|isDomain| *1 (|QuadraticForm| *3 *4)))) (|matrix| (*1 *2 *1) (AND (|isDomain| *2 (|SquareMatrix| *3 *4)) (|isDomain| *1 (|QuadraticForm| *3 *4)) (|ofType| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Field|)))) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 (|DirectProduct| *4 *2)) (|ofType| *4 (|PositiveInteger|)) (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|QuadraticForm| *4 *2))))) 
(|Join| (|AbelianGroup|) (CATEGORY |domain| (SIGNATURE |quadraticForm| ($ (|SquareMatrix| |#1| |#2|))) (SIGNATURE |matrix| ((|SquareMatrix| |#1| |#2|) $)) (SIGNATURE |elt| (|#2| $ (|DirectProduct| |#1| |#2|))))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|sample| (($) 7 T CONST)) (|rotate!| (($ $) 43)) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|length| (((|NonNegativeInteger|) $) 42)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|inspect| ((|#1| $) 36)) (|insert!| (($ |#1| $) 37)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|front| ((|#1| $) 41)) (|extract!| ((|#1| $) 38)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|enqueue!| ((|#1| |#1| $) 45)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|dequeue!| ((|#1| $) 44)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|bag| (($ (|List| |#1|)) 39)) (|back| ((|#1| $) 40)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|QueueAggregate| |#1|) (|Category|) (|Type|)) (T |QueueAggregate|)) 
((|enqueue!| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|dequeue!| (*1 *2 *1) (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|rotate!| (*1 *1 *1) (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|length| (*1 *2 *1) (AND (|ofCategory| *1 (|QueueAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|front| (*1 *2 *1) (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|back| (*1 *2 *1) (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|BagAggregate| |t#1|) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (SIGNATURE |enqueue!| (|t#1| |t#1| $)) (SIGNATURE |dequeue!| (|t#1| $)) (SIGNATURE |rotate!| ($ $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |front| (|t#1| $)) (SIGNATURE |back| (|t#1| $)))) 
(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((|zero?| (((|Boolean|) $) 42)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL) (((|Union| |#2| "failed") $) 45)) (|retract| (((|Integer|) $) NIL) (((|Fraction| (|Integer|)) $) NIL) ((|#2| $) 43)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 78)) (|rational?| (((|Boolean|) $) 72)) (|rational| (((|Fraction| (|Integer|)) $) 76)) (|one?| (((|Boolean|) $) 41)) (|norm| ((|#2| $) 22)) (|map| (($ (|Mapping| |#2| |#2|) $) 19)) (|inv| (($ $) 61)) (|differentiate| (($ $) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Symbol|)) NIL) (($ $ (|List| (|Symbol|))) NIL) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#2| |#2|)) 34)) (|convert| (((|InputForm|) $) 67)) (|conjugate| (($ $) 17)) (|coerce| (((|OutputForm|) $) 56) (($ (|Integer|)) 38) (($ |#2|) 36) (($ (|Fraction| (|Integer|))) NIL)) (|characteristic| (((|NonNegativeInteger|)) 10)) (|abs| ((|#2| $) 71)) (= (((|Boolean|) $ $) 25)) (< (((|Boolean|) $ $) 69)) (- (($ $) 29) (($ $ $) 28)) (+ (($ $ $) 26)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 33) (($ $ $) NIL) (($ $ |#2|) NIL) (($ |#2| $) 30) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL))) 
(((|QuaternionCategory&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)) (SIGNATURE * (|#1| |#1| (|Fraction| (|Integer|)))) (SIGNATURE |inv| (|#1| |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |rational?| ((|Boolean|) |#1|)) (SIGNATURE |abs| (|#2| |#1|)) (SIGNATURE |norm| (|#2| |#1|)) (SIGNATURE |conjugate| (|#1| |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |characteristic| ((|NonNegativeInteger|))) (SIGNATURE |one?| ((|Boolean|) |#1|)) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE |zero?| ((|Boolean|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|)) (SIGNATURE + (|#1| |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|))) (|QuaternionCategory| |#2|) (|CommutativeRing|)) (T |QuaternionCategory&|)) 
((|characteristic| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|QuaternionCategory&| *3 *4)) (|ofCategory| *3 (|QuaternionCategory| *4))))) 
(CATEGORY |domain| (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)) (SIGNATURE * (|#1| |#1| (|Fraction| (|Integer|)))) (SIGNATURE |inv| (|#1| |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |rational?| ((|Boolean|) |#1|)) (SIGNATURE |abs| (|#2| |#1|)) (SIGNATURE |norm| (|#2| |#1|)) (SIGNATURE |conjugate| (|#1| |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |characteristic| ((|NonNegativeInteger|))) (SIGNATURE |one?| ((|Boolean|) |#1|)) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE |zero?| ((|Boolean|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|)) (SIGNATURE + (|#1| |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 117 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) 115 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) 114)) (|retract| (((|Integer|) $) 118 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) 116 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) 113)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) 88 (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) 87 (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) 86) (((|Matrix| |#1|) (|Matrix| $)) 85)) (|recip| (((|Union| $ "failed") $) 33)) (|real| ((|#1| $) 78)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 74 (|has| |#1| (|IntegerNumberSystem|)))) (|rational?| (((|Boolean|) $) 76 (|has| |#1| (|IntegerNumberSystem|)))) (|rational| (((|Fraction| (|Integer|)) $) 75 (|has| |#1| (|IntegerNumberSystem|)))) (|quatern| (($ |#1| |#1| |#1| |#1|) 79)) (|one?| (((|Boolean|) $) 30)) (|norm| ((|#1| $) 80)) (|min| (($ $ $) 66 (|has| |#1| (|OrderedSet|)))) (|max| (($ $ $) 65 (|has| |#1| (|OrderedSet|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 89)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 71 (|has| |#1| (|Field|)))) (|imagK| ((|#1| $) 81)) (|imagJ| ((|#1| $) 82)) (|imagI| ((|#1| $) 83)) (|hash| (((|SingleInteger|) $) 10)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) 95 (|has| |#1| (|Evalable| |#1|))) (($ $ |#1| |#1|) 94 (|has| |#1| (|Evalable| |#1|))) (($ $ (|Equation| |#1|)) 93 (|has| |#1| (|Evalable| |#1|))) (($ $ (|List| (|Equation| |#1|))) 92 (|has| |#1| (|Evalable| |#1|))) (($ $ (|List| (|Symbol|)) (|List| |#1|)) 91 (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|))) (($ $ (|Symbol|) |#1|) 90 (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|)))) (|elt| (($ $ |#1|) 96 (|has| |#1| (|Eltable| |#1| |#1|)))) (|differentiate| (($ $) 112 (|has| |#1| (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) 110 (|has| |#1| (|DifferentialRing|))) (($ $ (|Symbol|)) 108 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) 107 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 106 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 105 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) 98) (($ $ (|Mapping| |#1| |#1|)) 97)) (|convert| (((|InputForm|) $) 72 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|conjugate| (($ $) 84)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ |#1|) 36) (($ (|Fraction| (|Integer|))) 60 (OR (|has| |#1| (|Field|)) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))))) (|charthRoot| (((|Union| $ "failed") $) 73 (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|abs| ((|#1| $) 77 (|has| |#1| (|RealNumberSystem|)))) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 70 (|has| |#1| (|Field|)))) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $) 111 (|has| |#1| (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) 109 (|has| |#1| (|DifferentialRing|))) (($ $ (|Symbol|)) 104 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) 103 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 102 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 101 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) 100) (($ $ (|Mapping| |#1| |#1|)) 99)) (>= (((|Boolean|) $ $) 63 (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) 62 (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 64 (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) 61 (|has| |#1| (|OrderedSet|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 69 (|has| |#1| (|Field|)))) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 38) (($ |#1| $) 37) (($ $ (|Fraction| (|Integer|))) 68 (|has| |#1| (|Field|))) (($ (|Fraction| (|Integer|)) $) 67 (|has| |#1| (|Field|))))) 
(((|QuaternionCategory| |#1|) (|Category|) (|CommutativeRing|)) (T |QuaternionCategory|)) 
((|conjugate| (*1 *1 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagI| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagJ| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagK| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|norm| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|quatern| (*1 *1 *2 *2 *2 *2) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|real| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|abs| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|RealNumberSystem|)))) (|rational?| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|)))) (|rational| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|rationalIfCan| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|QuaternionCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Fraction| (|Integer|)))))) 
(|Join| (|Algebra| |t#1|) (|FullyRetractableTo| |t#1|) (|DifferentialExtension| |t#1|) (|FullyEvalableOver| |t#1|) (|FullyLinearlyExplicitRingOver| |t#1|) (CATEGORY |domain| (SIGNATURE |conjugate| ($ $)) (SIGNATURE |imagI| (|t#1| $)) (SIGNATURE |imagJ| (|t#1| $)) (SIGNATURE |imagK| (|t#1| $)) (SIGNATURE |norm| (|t#1| $)) (SIGNATURE |quatern| ($ |t#1| |t#1| |t#1| |t#1|)) (SIGNATURE |real| (|t#1| $)) (IF (|has| |t#1| (|EntireRing|)) (ATTRIBUTE (|EntireRing|)) |noBranch|) (IF (|has| |t#1| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |noBranch|) (IF (|has| |t#1| (|Field|)) (ATTRIBUTE (|DivisionRing|)) |noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |noBranch|) (IF (|has| |t#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |noBranch|) (IF (|has| |t#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |noBranch|) (IF (|has| |t#1| (|RealNumberSystem|)) (SIGNATURE |abs| (|t#1| $)) |noBranch|) (IF (|has| |t#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") $))) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) |has| |#1| (|Field|)) ((|Algebra| |#1|) . T) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) |has| |#1| (|Field|)) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|Field|)) (|has| |#1| (|EntireRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) |has| |#1| (|DifferentialRing|)) ((|DivisionRing|) |has| |#1| (|Field|)) ((|Eltable| |#1| $) |has| |#1| (|Eltable| |#1| |#1|)) ((|EntireRing|) OR (|has| |#1| (|Field|)) (|has| |#1| (|EntireRing|))) ((|Evalable| |#1|) |has| |#1| (|Evalable| |#1|)) ((|FullyEvalableOver| |#1|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|InnerEvalable| (|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|LeftModule| (|Fraction| (|Integer|))) |has| |#1| (|Field|)) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearlyExplicitRingOver| (|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| (|Fraction| (|Integer|))) |has| |#1| (|Field|)) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightModule| (|Fraction| (|Integer|))) |has| |#1| (|Field|)) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|Field|)) (|has| |#1| (|EntireRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) 16))) 
(((|QuaternionCategoryFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#3| (|Mapping| |#4| |#2|) |#1|))) (|QuaternionCategory| |#2|) (|CommutativeRing|) (|QuaternionCategory| |#4|) (|CommutativeRing|)) (T |QuaternionCategoryFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|CommutativeRing|)) (|ofCategory| *6 (|CommutativeRing|)) (|ofCategory| *2 (|QuaternionCategory| *6)) (|isDomain| *1 (|QuaternionCategoryFunctions2| *4 *5 *2 *6)) (|ofCategory| *4 (|QuaternionCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |map| (|#3| (|Mapping| |#4| |#2|) |#1|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) NIL)) (|retract| (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| |#1|) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|real| ((|#1| $) 12)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|IntegerNumberSystem|)))) (|rational?| (((|Boolean|) $) NIL (|has| |#1| (|IntegerNumberSystem|)))) (|rational| (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|IntegerNumberSystem|)))) (|quatern| (($ |#1| |#1| |#1| |#1|) 16)) (|one?| (((|Boolean|) $) NIL)) (|norm| ((|#1| $) NIL)) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL (|has| |#1| (|Field|)))) (|imagK| ((|#1| $) 15)) (|imagJ| ((|#1| $) 14)) (|imagI| ((|#1| $) 13)) (|hash| (((|SingleInteger|) $) NIL)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ |#1| |#1|) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ (|Equation| |#1|)) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ (|List| (|Equation| |#1|))) NIL (|has| |#1| (|Evalable| |#1|))) (($ $ (|List| (|Symbol|)) (|List| |#1|)) NIL (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|))) (($ $ (|Symbol|) |#1|) NIL (|has| |#1| (|InnerEvalable| (|Symbol|) |#1|)))) (|elt| (($ $ |#1|) NIL (|has| |#1| (|Eltable| |#1| |#1|)))) (|differentiate| (($ $) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#1| |#1|)) NIL)) (|convert| (((|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|conjugate| (($ $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ |#1|) NIL) (($ (|Fraction| (|Integer|))) NIL (OR (|has| |#1| (|Field|)) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))))) (|charthRoot| (((|Union| $ "failed") $) NIL (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|abs| ((|#1| $) NIL (|has| |#1| (|RealNumberSystem|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| |#1| (|Field|)))) (|Zero| (($) 8 T CONST)) (|One| (($) 10 T CONST)) (D (($ $) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#1| |#1|)) NIL)) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| |#1| (|Field|)))) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 20) (($ $ |#1|) NIL) (($ |#1| $) NIL) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Field|))) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Field|))))) 
(((|Quaternion| |#1|) (|QuaternionCategory| |#1|) (|CommutativeRing|)) (T |Quaternion|)) 
NIL 
(|QuaternionCategory| |#1|) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|sample| (($) NIL T CONST)) (|rotate!| (($ $) 20)) (|queue| (($ (|List| |#1|)) 29)) (|parts| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|length| (((|NonNegativeInteger|) $) 22)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|inspect| ((|#1| $) 24)) (|insert!| (($ |#1| $) 15)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|front| ((|#1| $) 23)) (|extract!| ((|#1| $) 19)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|enqueue!| ((|#1| |#1| $) 14)) (|empty?| (((|Boolean|) $) 17)) (|empty| (($) NIL)) (|dequeue!| ((|#1| $) 18)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| |#1| (|SetCategory|)))) (|bag| (($ (|List| |#1|)) NIL)) (|back| ((|#1| $) 26)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|Queue| |#1|) (|Join| (|QueueAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |queue| ($ (|List| |#1|))) (SIGNATURE |dequeue!| (|#1| $)) (SIGNATURE |extract!| (|#1| $)) (SIGNATURE |enqueue!| (|#1| |#1| $)) (SIGNATURE |insert!| ($ |#1| $)) (SIGNATURE |inspect| (|#1| $)) (SIGNATURE |front| (|#1| $)) (SIGNATURE |back| (|#1| $)) (SIGNATURE |rotate!| ($ $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |less?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |size?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |bag| ($ (|List| |#1|))) (SIGNATURE |empty?| ((|Boolean|) $)) (SIGNATURE |empty| ($)) (SIGNATURE |sample| ($)) (SIGNATURE |copy| ($ $)) (SIGNATURE |eq?| ((|Boolean|) $ $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (IF (|has| $ (ATTRIBUTE |shallowlyMutable|)) (SIGNATURE |map!| ($ (|Mapping| |#1| |#1|) $)) |noBranch|) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |latex| ((|String|) $)) (SIGNATURE |hash| ((|SingleInteger|) $)) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE = ((|Boolean|) $ $)) (SIGNATURE ~= ((|Boolean|) $ $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (PROGN (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |#| ((|NonNegativeInteger|) $)) (SIGNATURE |parts| ((|List| |#1|) $)) (SIGNATURE |members| ((|List| |#1|) $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |member?| ((|Boolean|) |#1| $)) (SIGNATURE |count| ((|NonNegativeInteger|) |#1| $))) |noBranch|) |noBranch|))) (|SetCategory|)) (T |Queue|)) 
((|eq?| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Queue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|copy| (*1 *1 *1) (AND (|isDomain| *1 (|Queue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|empty| (*1 *1) (AND (|isDomain| *1 (|Queue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|empty?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Queue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|less?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Queue| *4)) (|ofCategory| *4 (|SetCategory|)))) (|more?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Queue| *4)) (|ofCategory| *4 (|SetCategory|)))) (|size?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Queue| *4)) (|ofCategory| *4 (|SetCategory|)))) (|sample| (*1 *1) (AND (|isDomain| *1 (|Queue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|#| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Queue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Queue| *3)))) (|map!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Queue| *3)))) (|any?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Queue| *4)))) (|every?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Queue| *4)))) (|count| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Queue| *4)))) (|parts| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|Queue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|members| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|Queue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|count| (*1 *2 *3 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Queue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|member?| (*1 *2 *3 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Queue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|latex| (*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|Queue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|hash| (*1 *2 *1) (AND (|isDomain| *2 (|SingleInteger|)) (|isDomain| *1 (|Queue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|Queue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (= (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Queue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (~= (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Queue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|bag| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Queue| *3)))) (|extract!| (*1 *2 *1) (AND (|isDomain| *1 (|Queue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|insert!| (*1 *1 *2 *1) (AND (|isDomain| *1 (|Queue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|inspect| (*1 *2 *1) (AND (|isDomain| *1 (|Queue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|enqueue!| (*1 *2 *2 *1) (AND (|isDomain| *1 (|Queue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|dequeue!| (*1 *2 *1) (AND (|isDomain| *1 (|Queue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|rotate!| (*1 *1 *1) (AND (|isDomain| *1 (|Queue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|length| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Queue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|front| (*1 *2 *1) (AND (|isDomain| *1 (|Queue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|back| (*1 *2 *1) (AND (|isDomain| *1 (|Queue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|queue| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Queue| *3))))) 
(|Join| (|QueueAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |queue| ($ (|List| |#1|))) (SIGNATURE |dequeue!| (|#1| $)) (SIGNATURE |extract!| (|#1| $)) (SIGNATURE |enqueue!| (|#1| |#1| $)) (SIGNATURE |insert!| ($ |#1| $)) (SIGNATURE |inspect| (|#1| $)) (SIGNATURE |front| (|#1| $)) (SIGNATURE |back| (|#1| $)) (SIGNATURE |rotate!| ($ $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |less?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |size?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |bag| ($ (|List| |#1|))) (SIGNATURE |empty?| ((|Boolean|) $)) (SIGNATURE |empty| ($)) (SIGNATURE |sample| ($)) (SIGNATURE |copy| ($ $)) (SIGNATURE |eq?| ((|Boolean|) $ $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (IF (|has| $ (ATTRIBUTE |shallowlyMutable|)) (SIGNATURE |map!| ($ (|Mapping| |#1| |#1|) $)) |noBranch|) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |latex| ((|String|) $)) (SIGNATURE |hash| ((|SingleInteger|) $)) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE = ((|Boolean|) $ $)) (SIGNATURE ~= ((|Boolean|) $ $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (PROGN (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |#| ((|NonNegativeInteger|) $)) (SIGNATURE |parts| ((|List| |#1|) $)) (SIGNATURE |members| ((|List| |#1|) $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |member?| ((|Boolean|) |#1| $)) (SIGNATURE |count| ((|NonNegativeInteger|) |#1| $))) |noBranch|) |noBranch|))) 
((|sqrt| (($ $) 12)) (|nthRoot| (($ $ (|Integer|)) 13))) 
(((|RadicalCategory&| |#1|) (CATEGORY |domain| (SIGNATURE |sqrt| (|#1| |#1|)) (SIGNATURE |nthRoot| (|#1| |#1| (|Integer|)))) (|RadicalCategory|)) (T |RadicalCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |sqrt| (|#1| |#1|)) (SIGNATURE |nthRoot| (|#1| |#1| (|Integer|)))) 
((|sqrt| (($ $) 6)) (|nthRoot| (($ $ (|Integer|)) 7)) (** (($ $ (|Fraction| (|Integer|))) 8))) 
(((|RadicalCategory|) (|Category|)) (T |RadicalCategory|)) 
((** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RadicalCategory|)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|nthRoot| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RadicalCategory|)) (|isDomain| *2 (|Integer|)))) (|sqrt| (*1 *1 *1) (|ofCategory| *1 (|RadicalCategory|)))) 
(|Join| (CATEGORY |domain| (SIGNATURE |sqrt| ($ $)) (SIGNATURE |nthRoot| ($ $ (|Integer|))) (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|unitCanonical| (($ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|unit?| (((|Boolean|) $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|traceMatrix| (((|Matrix| (|Fraction| |#2|)) (|Vector| $)) NIL) (((|Matrix| (|Fraction| |#2|))) NIL)) (|trace| (((|Fraction| |#2|) $) NIL)) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|squareFree| (((|Factored| $) $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|sizeLess?| (((|Boolean|) $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|size| (((|NonNegativeInteger|)) NIL (|has| (|Fraction| |#2|) (|Finite|)))) (|singularAtInfinity?| (((|Boolean|)) NIL)) (|singular?| (((|Boolean|) |#1|) 147) (((|Boolean|) |#2|) 152)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (|has| (|Fraction| |#2|) (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| (|Fraction| |#2|) (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Fraction| |#2|) "failed") $) NIL)) (|retract| (((|Integer|) $) NIL (|has| (|Fraction| |#2|) (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) NIL (|has| (|Fraction| |#2|) (|RetractableTo| (|Fraction| (|Integer|))))) (((|Fraction| |#2|) $) NIL)) (|represents| (($ (|Vector| (|Fraction| |#2|)) (|Vector| $)) NIL) (($ (|Vector| (|Fraction| |#2|))) 70) (($ (|Vector| |#2|) |#2|) NIL)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|rem| (($ $ $) NIL 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(((|PositiveInteger|)) NIL)) (|random| (($) NIL (|has| (|Fraction| |#2|) (|Finite|)))) (|ramifiedAtInfinity?| (((|Boolean|)) NIL)) (|ramified?| (((|Boolean|) |#1|) 56) (((|Boolean|) |#2|) 149)) (|quo| (($ $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|primitivePart| (($ $) NIL)) (|primitiveElement| (($) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|primitive?| (((|Boolean|) $) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))) (($ $) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|prime?| (((|Boolean|) $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|order| (((|PositiveInteger|) $) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))) (((|OnePointCompletion| (|PositiveInteger|)) $) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|one?| (((|Boolean|) $) NIL)) (|numberOfComponents| (((|NonNegativeInteger|)) NIL)) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) NIL)) (|norm| (((|Fraction| |#2|) $) NIL)) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) NIL (|has| |#1| (|Field|)))) (|nextItem| (((|Union| $ "failed") $) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|minimalPolynomial| ((|#3| $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|lookup| (((|PositiveInteger|) $) NIL (|has| (|Fraction| |#2|) (|Finite|)))) (|lift| ((|#3| $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|lcm| (($ (|List| $)) NIL (|has| (|Fraction| |#2|) (|Field|))) (($ $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|latex| (((|String|) $) NIL)) (|inverseIntegralMatrixAtInfinity| (((|Matrix| 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(((|NonNegativeInteger|)) NIL)) (|generator| (($) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|gcd| (($ (|List| $)) NIL (|has| (|Fraction| |#2|) (|Field|))) (($ $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|factor| (((|Factored| $) $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL (|has| (|Fraction| |#2|) (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|exquo| (((|Union| $ "failed") $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| (|Fraction| |#2|) (|Field|)))) 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(|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|)) NIL (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|NonNegativeInteger|)) NIL (OR (AND (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|))) (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (($ $) NIL (OR (AND (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|))) (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))))) (|derivationCoordinates| (((|Matrix| (|Fraction| |#2|)) (|Vector| $) (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|))) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|definingPolynomial| ((|#3|) 53)) (|createPrimitiveElement| (($) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|coordinates| (((|Vector| (|Fraction| |#2|)) $ (|Vector| $)) NIL) (((|Matrix| (|Fraction| |#2|)) (|Vector| $) (|Vector| $)) NIL) (((|Vector| (|Fraction| |#2|)) $) 72) (((|Matrix| (|Fraction| |#2|)) (|Vector| $)) NIL)) (|convert| (((|Vector| (|Fraction| |#2|)) $) NIL) (($ (|Vector| (|Fraction| |#2|))) NIL) ((|#3| $) NIL) (($ |#3|) NIL)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (|complementaryBasis| (((|Vector| $) (|Vector| $)) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ (|Fraction| |#2|)) NIL) (($ (|Fraction| (|Integer|))) NIL (OR (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|RetractableTo| (|Fraction| (|Integer|)))))) (($ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|charthRoot| (($ $) NIL (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))) (((|Union| $ "failed") $) NIL (|has| (|Fraction| |#2|) (|CharacteristicNonZero|)))) (|characteristicPolynomial| ((|#3| $) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|branchPointAtInfinity?| (((|Boolean|)) 60)) (|branchPoint?| (((|Boolean|) |#1|) 153) (((|Boolean|) |#2|) 154)) (|basis| (((|Vector| $)) 124)) (|associates?| (((|Boolean|) $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) NIL)) (|absolutelyIrreducible?| (((|Boolean|)) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| (|Fraction| |#2|) (|Field|)))) (|Zero| (($) 94 T CONST)) (|One| (($) NIL T CONST)) (D (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|)) (|NonNegativeInteger|)) NIL (|has| (|Fraction| |#2|) (|Field|))) (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|))) NIL (|has| (|Fraction| |#2|) (|Field|))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|)) NIL (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|NonNegativeInteger|)) NIL (OR (AND (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|))) (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)))) (($ $) NIL (OR (AND (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|))) (|has| (|Fraction| |#2|) (|FiniteFieldCategory|))))) (= (((|Boolean|) $ $) NIL)) (/ (($ $ $) NIL (|has| (|Fraction| |#2|) (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| (|Fraction| |#2|) (|Field|)))) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| |#2|)) NIL) (($ (|Fraction| |#2|) $) NIL) (($ (|Fraction| (|Integer|)) $) NIL (|has| (|Fraction| |#2|) (|Field|))) (($ $ (|Fraction| (|Integer|))) NIL (|has| (|Fraction| |#2|) (|Field|))))) 
(((|RadicalFunctionField| |#1| |#2| |#3| |#4| |#5|) (|FunctionFieldCategory| |#1| |#2| |#3|) (|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) (T |RadicalFunctionField|)) 
NIL 
(|FunctionFieldCategory| |#1| |#2| |#3|) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|wholeRagits| (((|List| (|Integer|)) $) 54)) (|wholeRadix| (($ (|List| (|Integer|))) 62)) (|wholePart| (((|Integer|) $) 40 (|has| (|Integer|) (|EuclideanDomain|)))) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Integer|) (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Integer|) (|PolynomialFactorizationExplicit|)))) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sign| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedIntegralDomain|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 49) (((|Union| (|Symbol|) "failed") $) NIL (|has| (|Integer|) (|RetractableTo| (|Symbol|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) 47 (|has| (|Integer|) (|RetractableTo| (|Integer|)))) (((|Union| (|Integer|) "failed") $) 49 (|has| (|Integer|) (|RetractableTo| (|Integer|))))) (|retract| (((|Integer|) $) NIL) (((|Symbol|) $) NIL (|has| (|Integer|) (|RetractableTo| (|Symbol|)))) (((|Fraction| (|Integer|)) $) NIL (|has| (|Integer|) (|RetractableTo| (|Integer|)))) (((|Integer|) $) NIL (|has| (|Integer|) (|RetractableTo| (|Integer|))))) (|rem| (($ $ $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| (|Integer|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| (|Integer|) (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| (|Integer|)) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|random| (($) NIL (|has| (|Integer|) (|IntegerNumberSystem|)))) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|prefixRagits| (((|List| (|Integer|)) $) 60)) (|positive?| (((|Boolean|) $) NIL (|has| (|Integer|) (|OrderedIntegralDomain|)))) (|patternMatch| (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (|has| (|Integer|) (|PatternMatchable| (|Integer|)))) (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (|has| (|Integer|) (|PatternMatchable| (|Float|))))) (|one?| (((|Boolean|) $) NIL)) (|numerator| (($ $) NIL)) (|numer| (((|Integer|) $) 37)) (|nextItem| (((|Union| $ "failed") $) NIL (|has| (|Integer|) (|StepThrough|)))) (|negative?| (((|Boolean|) $) NIL (|has| (|Integer|) (|OrderedIntegralDomain|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|min| (($ $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|map| (($ (|Mapping| (|Integer|) (|Integer|)) $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL)) (|init| (($) NIL (|has| (|Integer|) (|StepThrough|)) CONST)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|fractionPart| (($ $) NIL (|has| (|Integer|) (|EuclideanDomain|))) (((|Fraction| (|Integer|)) $) 42)) (|fractRagits| (((|Stream| (|Integer|)) $) 59)) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) 63)) (|floor| (((|Integer|) $) 53 (|has| (|Integer|) (|IntegerNumberSystem|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Integer|) (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| (|Integer|) (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|eval| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) NIL (|has| (|Integer|) (|Evalable| (|Integer|)))) (($ $ (|Integer|) (|Integer|)) NIL (|has| (|Integer|) (|Evalable| (|Integer|)))) (($ $ (|Equation| (|Integer|))) NIL (|has| (|Integer|) (|Evalable| (|Integer|)))) (($ $ (|List| (|Equation| (|Integer|)))) NIL (|has| (|Integer|) (|Evalable| (|Integer|)))) (($ $ (|List| (|Symbol|)) (|List| (|Integer|))) NIL (|has| (|Integer|) (|InnerEvalable| (|Symbol|) (|Integer|)))) (($ $ (|Symbol|) (|Integer|)) NIL (|has| (|Integer|) (|InnerEvalable| (|Symbol|) (|Integer|))))) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|elt| (($ $ (|Integer|)) NIL (|has| (|Integer|) (|Eltable| (|Integer|) (|Integer|))))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|differentiate| (($ $) 11 (|has| (|Integer|) (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|Integer|) (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| 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(($ (|Symbol|)) NIL (|has| (|Integer|) (|RetractableTo| (|Symbol|)))) (((|Fraction| (|Integer|)) $) 17)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| (|Integer|) (|PolynomialFactorizationExplicit|))) (|has| (|Integer|) (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) 9)) (|ceiling| (((|Integer|) $) 51 (|has| (|Integer|) (|IntegerNumberSystem|)))) (|associates?| (((|Boolean|) $ $) NIL)) (|abs| (($ $) NIL (|has| (|Integer|) (|OrderedIntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) 10 T CONST)) (|One| (($) 12 T CONST)) (D (($ $) NIL (|has| (|Integer|) (|DifferentialRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| (|Integer|) (|DifferentialRing|))) (($ $ (|Symbol|)) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| (|Integer|) (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| (|Integer|) (|Integer|)) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| (|Integer|) (|Integer|))) NIL)) (>= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (= (((|Boolean|) $ $) 14)) (<= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (< (((|Boolean|) $ $) 33 (|has| (|Integer|) (|OrderedSet|)))) (/ (($ $ $) 29) (($ (|Integer|) (|Integer|)) 31)) (- (($ $) 15) (($ $ $) 22)) (+ (($ $ $) 20)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 25) (($ $ $) 27) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ (|Integer|) $) 25) (($ $ (|Integer|)) NIL))) 
(((|RadixExpansion| |#1|) (|Join| (|QuotientFieldCategory| (|Integer|)) (CATEGORY |domain| (SIGNATURE |coerce| ((|Fraction| (|Integer|)) $)) (SIGNATURE |fractionPart| ((|Fraction| (|Integer|)) $)) (SIGNATURE |wholeRagits| ((|List| (|Integer|)) $)) (SIGNATURE |fractRagits| ((|Stream| (|Integer|)) $)) (SIGNATURE |prefixRagits| ((|List| (|Integer|)) $)) (SIGNATURE |cycleRagits| ((|List| (|Integer|)) $)) (SIGNATURE |wholeRadix| ($ (|List| (|Integer|)))) (SIGNATURE |fractRadix| ($ (|List| (|Integer|)) (|List| (|Integer|)))))) (|Integer|)) (T |RadixExpansion|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|RadixExpansion| *3)) (|ofType| *3 (|Integer|)))) (|fractionPart| (*1 *2 *1) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|RadixExpansion| *3)) (|ofType| *3 (|Integer|)))) (|wholeRagits| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|RadixExpansion| *3)) (|ofType| *3 (|Integer|)))) (|fractRagits| (*1 *2 *1) (AND (|isDomain| *2 (|Stream| (|Integer|))) (|isDomain| *1 (|RadixExpansion| *3)) (|ofType| *3 (|Integer|)))) (|prefixRagits| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|RadixExpansion| *3)) (|ofType| *3 (|Integer|)))) (|cycleRagits| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|RadixExpansion| *3)) (|ofType| *3 (|Integer|)))) (|wholeRadix| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|RadixExpansion| *3)) (|ofType| *3 (|Integer|)))) (|fractRadix| (*1 *1 *2 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|RadixExpansion| *3)) (|ofType| *3 (|Integer|))))) 
(|Join| (|QuotientFieldCategory| (|Integer|)) (CATEGORY |domain| (SIGNATURE |coerce| ((|Fraction| (|Integer|)) $)) (SIGNATURE |fractionPart| ((|Fraction| (|Integer|)) $)) (SIGNATURE |wholeRagits| ((|List| (|Integer|)) $)) (SIGNATURE |fractRagits| ((|Stream| (|Integer|)) $)) (SIGNATURE |prefixRagits| ((|List| (|Integer|)) $)) (SIGNATURE |cycleRagits| ((|List| (|Integer|)) $)) (SIGNATURE |wholeRadix| ($ (|List| (|Integer|)))) (SIGNATURE |fractRadix| ($ (|List| (|Integer|)) (|List| (|Integer|)))))) 
((|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) 9))) 
(((|RadixUtilities|) (CATEGORY |package| (SIGNATURE |radix| ((|Any|) (|Fraction| (|Integer|)) (|Integer|))))) (T |RadixUtilities|)) 
((|radix| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|Integer|))) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|RadixUtilities|))))) 
(CATEGORY |package| (SIGNATURE |radix| ((|Any|) (|Fraction| (|Integer|)) (|Integer|)))) 
((|size| (((|Integer|)) 13)) (|seed| (((|Integer|)) 16)) (|reseed| (((|Void|) (|Integer|)) 15)) (|randnum| (((|Integer|) (|Integer|)) 17) (((|Integer|)) 12))) 
(((|RandomNumberSource|) (CATEGORY |package| (SIGNATURE |randnum| ((|Integer|))) (SIGNATURE |size| ((|Integer|))) (SIGNATURE |randnum| ((|Integer|) (|Integer|))) (SIGNATURE |reseed| ((|Void|) (|Integer|))) (SIGNATURE |seed| ((|Integer|))))) (T |RandomNumberSource|)) 
((|seed| (*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|RandomNumberSource|)))) (|reseed| (*1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|RandomNumberSource|)))) (|randnum| (*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|RandomNumberSource|)))) (|size| (*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|RandomNumberSource|)))) (|randnum| (*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|RandomNumberSource|))))) 
(CATEGORY |package| (SIGNATURE |randnum| ((|Integer|))) (SIGNATURE |size| ((|Integer|))) (SIGNATURE |randnum| ((|Integer|) (|Integer|))) (SIGNATURE |reseed| ((|Void|) (|Integer|))) (SIGNATURE |seed| ((|Integer|)))) 
((|factorSquareFree| (((|Factored| |#1|) |#1|) 40)) (|factor| (((|Factored| |#1|) |#1|) 39))) 
(((|RationalFactorize| |#1|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) (SIGNATURE |factorSquareFree| ((|Factored| |#1|) |#1|))) (|UnivariatePolynomialCategory| (|Fraction| (|Integer|)))) (T |RationalFactorize|)) 
((|factorSquareFree| (*1 *2 *3) (AND (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|RationalFactorize| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|)))))) (|factor| (*1 *2 *3) (AND (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|RationalFactorize| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|))))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) (SIGNATURE |factorSquareFree| ((|Factored| |#1|) |#1|))) 
((|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) 14)) (|rational?| (((|Boolean|) |#1|) 13)) (|rational| (((|Fraction| (|Integer|)) |#1|) 9))) 
(((|RationalRetractions| |#1|) (CATEGORY |package| (SIGNATURE |rational| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |rational?| ((|Boolean|) |#1|)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|))) (|RetractableTo| (|Fraction| (|Integer|)))) (T |RationalRetractions|)) 
((|rationalIfCan| (*1 *2 *3) (|partial| AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|RationalRetractions| *3)) (|ofCategory| *3 (|RetractableTo| *2)))) (|rational?| (*1 *2 *3) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|RationalRetractions| *3)) (|ofCategory| *3 (|RetractableTo| (|Fraction| (|Integer|)))))) (|rational| (*1 *2 *3) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|RationalRetractions| *3)) (|ofCategory| *3 (|RetractableTo| *2))))) 
(CATEGORY |package| (SIGNATURE |rational| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |rational?| ((|Boolean|) |#1|)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|))) 
((|setelt| ((|#2| $ "value" |#2|) 12)) (|elt| ((|#2| $ "value") 10)) (|child?| (((|Boolean|) $ $) 18))) 
(((|RecursiveAggregate&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |setelt| (|#2| |#1| "value" |#2|)) (SIGNATURE |child?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |elt| (|#2| |#1| "value"))) (|RecursiveAggregate| |#2|) (|Type|)) (T |RecursiveAggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |setelt| (|#2| |#1| "value" |#2|)) (SIGNATURE |child?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |elt| (|#2| |#1| "value"))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) 45)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setvalue!| ((|#1| $ |#1|) 36 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) 7 T CONST)) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) 47)) (|node?| (((|Boolean|) $ $) 39 (|has| |#1| (|SetCategory|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|leaves| (((|List| |#1|) $) 42)) (|leaf?| (((|Boolean|) $) 46)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| ((|#1| $ "value") 44)) (|distance| (((|Integer|) $ $) 41)) (|cyclic?| (((|Boolean|) $) 43)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|children| (((|List| $) $) 48)) (|child?| (((|Boolean|) $ $) 40 (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|RecursiveAggregate| |#1|) (|Category|) (|Type|)) (T |RecursiveAggregate|)) 
((|children| (*1 *2 *1) (AND (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RecursiveAggregate| *3)))) (|nodes| (*1 *2 *1) (AND (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RecursiveAggregate| *3)))) (|leaf?| (*1 *2 *1) (AND (|ofCategory| *1 (|RecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|value| (*1 *2 *1) (AND (|ofCategory| *1 (|RecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 "value") (|ofCategory| *1 (|RecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|cyclic?| (*1 *2 *1) (AND (|ofCategory| *1 (|RecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|leaves| (*1 *2 *1) (AND (|ofCategory| *1 (|RecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|List| *3)))) (|distance| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|Integer|)))) (|child?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|node?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|setchildren!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|RecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|setelt| (*1 *2 *1 *3 *2) (AND (|isDomain| *3 "value") (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|RecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setvalue!| (*1 *2 *1 *2) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|RecursiveAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|HomogeneousAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |children| ((|List| $) $)) (SIGNATURE |nodes| ((|List| $) $)) (SIGNATURE |leaf?| ((|Boolean|) $)) (SIGNATURE |value| (|t#1| $)) (SIGNATURE |elt| (|t#1| $ "value")) (SIGNATURE |cyclic?| ((|Boolean|) $)) (SIGNATURE |leaves| ((|List| |t#1|) $)) (SIGNATURE |distance| ((|Integer|) $ $)) (IF (|has| |t#1| (|SetCategory|)) (PROGN (SIGNATURE |child?| ((|Boolean|) $ $)) (SIGNATURE |node?| ((|Boolean|) $ $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |shallowlyMutable|)) (PROGN (SIGNATURE |setchildren!| ($ $ (|List| $))) (SIGNATURE |setelt| (|t#1| $ "value" |t#1|)) (SIGNATURE |setvalue!| (|t#1| $ |t#1|))) |noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((|sqrt| (($ $) 9) (($ $ (|NonNegativeInteger|)) 43) (($ (|Fraction| (|Integer|))) 12) (($ (|Integer|)) 15)) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) 23) (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) 28)) (|nthRoot| (($ $ (|Integer|)) 49)) (|characteristic| (((|NonNegativeInteger|)) 16)) (|allRootsOf| (((|List| $) (|SparseUnivariatePolynomial| $)) NIL) (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) 54) (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) 59) (((|List| $) (|Polynomial| $)) 63) (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) 67) (((|List| $) (|Polynomial| (|Integer|))) 71)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL) (($ $ (|Fraction| (|Integer|))) 47))) 
(((|RealClosedField&| |#1|) (CATEGORY |domain| (SIGNATURE |sqrt| (|#1| (|Integer|))) (SIGNATURE |sqrt| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |sqrt| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |allRootsOf| ((|List| |#1|) (|Polynomial| (|Integer|)))) (SIGNATURE |allRootsOf| ((|List| |#1|) (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |allRootsOf| ((|List| |#1|) (|Polynomial| |#1|))) (SIGNATURE |allRootsOf| ((|List| |#1|) (|SparseUnivariatePolynomial| (|Integer|)))) (SIGNATURE |allRootsOf| ((|List| |#1|) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|))))) (SIGNATURE |allRootsOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |rootOf| ((|Union| |#1| "failed") (|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|))) (SIGNATURE |rootOf| ((|Union| |#1| "failed") (|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|OutputForm|))) (SIGNATURE ** (|#1| |#1| (|Fraction| (|Integer|)))) (SIGNATURE |nthRoot| (|#1| |#1| (|Integer|))) (SIGNATURE |sqrt| (|#1| |#1|)) (SIGNATURE ** (|#1| |#1| (|Integer|))) (SIGNATURE |characteristic| ((|NonNegativeInteger|))) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|)))) (|RealClosedField|)) (T |RealClosedField&|)) 
((|characteristic| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|RealClosedField&| *3)) (|ofCategory| *3 (|RealClosedField|))))) 
(CATEGORY |domain| (SIGNATURE |sqrt| (|#1| (|Integer|))) (SIGNATURE |sqrt| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |sqrt| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |allRootsOf| ((|List| |#1|) (|Polynomial| (|Integer|)))) (SIGNATURE |allRootsOf| ((|List| |#1|) (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |allRootsOf| ((|List| |#1|) (|Polynomial| |#1|))) (SIGNATURE |allRootsOf| ((|List| |#1|) (|SparseUnivariatePolynomial| (|Integer|)))) (SIGNATURE |allRootsOf| ((|List| |#1|) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|))))) (SIGNATURE |allRootsOf| ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |rootOf| ((|Union| |#1| "failed") (|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|))) (SIGNATURE |rootOf| ((|Union| |#1| "failed") (|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|OutputForm|))) (SIGNATURE ** (|#1| |#1| (|Fraction| (|Integer|)))) (SIGNATURE |nthRoot| (|#1| |#1| (|Integer|))) (SIGNATURE |sqrt| (|#1| |#1|)) (SIGNATURE ** (|#1| |#1| (|Integer|))) (SIGNATURE |characteristic| ((|NonNegativeInteger|))) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 89)) (|unitCanonical| (($ $) 90)) (|unit?| (((|Boolean|) $) 92)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 110)) (|squareFree| (((|Factored| $) $) 111)) (|sqrt| (($ $) 73) (($ $ (|NonNegativeInteger|)) 59) (($ (|Fraction| (|Integer|))) 58) (($ (|Integer|)) 57)) (|sizeLess?| (((|Boolean|) $ $) 101)) (|sign| (((|Integer|) $) 128)) (|sample| (($) 16 T CONST)) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) 67) (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) 66)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 85 (|has| (|Fraction| (|Integer|)) (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) 83 (|has| (|Fraction| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Fraction| (|Integer|)) "failed") $) 81)) (|retract| (((|Integer|) $) 86 (|has| (|Fraction| (|Integer|)) (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) 84 (|has| (|Fraction| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (((|Fraction| (|Integer|)) $) 80)) (|rename!| (($ $ (|OutputForm|)) 56)) (|rename| (($ $ (|OutputForm|)) 55)) (|rem| (($ $ $) 105)) (|recip| (((|Union| $ "failed") $) 33)) (|quo| (($ $ $) 104)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 99)) (|prime?| (((|Boolean|) $) 112)) (|positive?| (((|Boolean|) $) 126)) (|one?| (((|Boolean|) $) 30)) (|nthRoot| (($ $ (|Integer|)) 72)) (|negative?| (((|Boolean|) $) 127)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 108)) (|min| (($ $ $) 125)) (|max| (($ $ $) 124)) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) 68)) (|mainForm| (((|Union| (|OutputForm|) "failed") $) 70)) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) 69)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 93)) (|lcm| (($ (|List| $)) 97) (($ $ $) 96)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 113)) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 98)) (|gcd| (($ (|List| $)) 95) (($ $ $) 94)) (|factor| (((|Factored| $) $) 109)) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 107) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 106)) (|exquo| (((|Union| $ "failed") $ $) 88)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 100)) (|euclideanSize| (((|NonNegativeInteger|) $) 102)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 103)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ (|Fraction| (|Integer|))) 118) (($ $) 87) (($ (|Fraction| (|Integer|))) 82) (($ (|Integer|)) 79) (($ (|Fraction| (|Integer|))) 76)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 91)) (|approximate| (((|Fraction| (|Integer|)) $ $) 54)) (|allRootsOf| (((|List| $) (|SparseUnivariatePolynomial| $)) 65) (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) 64) (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) 63) (((|List| $) (|Polynomial| $)) 62) (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) 61) (((|List| $) (|Polynomial| (|Integer|))) 60)) (|abs| (($ $) 129)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 114)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (>= (((|Boolean|) $ $) 122)) (> (((|Boolean|) $ $) 121)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 123)) (< (((|Boolean|) $ $) 120)) (/ (($ $ $) 119)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 115) (($ $ (|Fraction| (|Integer|))) 71)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ (|Fraction| (|Integer|)) $) 117) (($ $ (|Fraction| (|Integer|))) 116) (($ (|Integer|) $) 78) (($ $ (|Integer|)) 77) (($ (|Fraction| (|Integer|)) $) 75) (($ $ (|Fraction| (|Integer|))) 74))) 
(((|RealClosedField|) (|Category|)) (T |RealClosedField|)) 
((|sqrt| (*1 *1 *1) (|ofCategory| *1 (|RealClosedField|))) (|mainForm| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|OutputForm|)))) (|mainDefiningPolynomial| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|mainValue| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|rootOf| (*1 *1 *2 *3 *4) (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|OutputForm|)) (|ofCategory| *1 (|RealClosedField|)))) (|rootOf| (*1 *1 *2 *3) (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *1 (|RealClosedField|)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|List| *1)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| *1)) (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|List| *1)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| (|Fraction| (|Integer|)))) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| (|Integer|))) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|sqrt| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|sqrt| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|ofCategory| *1 (|RealClosedField|)))) (|sqrt| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|RealClosedField|)))) (|rename!| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|OutputForm|)))) (|rename| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|OutputForm|)))) (|approximate| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|Fraction| (|Integer|)))))) 
(|Join| (|CharacteristicZero|) (|OrderedRing|) (|CommutativeRing|) (|Field|) (|FullyRetractableTo| (|Fraction| (|Integer|))) (|Algebra| (|Integer|)) (|Algebra| (|Fraction| (|Integer|))) (|RadicalCategory|) (CATEGORY |domain| (SIGNATURE |mainForm| ((|Union| (|OutputForm|) "failed") $)) (SIGNATURE |mainDefiningPolynomial| ((|Union| (|SparseUnivariatePolynomial| $) "failed") $)) (SIGNATURE |mainValue| ((|Union| (|SparseUnivariatePolynomial| $) "failed") $)) (SIGNATURE |rootOf| ((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|))) (SIGNATURE |rootOf| ((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|))) (SIGNATURE |allRootsOf| ((|List| $) (|SparseUnivariatePolynomial| $))) (SIGNATURE |allRootsOf| ((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|))))) (SIGNATURE |allRootsOf| ((|List| $) (|SparseUnivariatePolynomial| (|Integer|)))) (SIGNATURE |allRootsOf| ((|List| $) (|Polynomial| $))) (SIGNATURE |allRootsOf| ((|List| $) (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |allRootsOf| ((|List| $) (|Polynomial| (|Integer|)))) (SIGNATURE |sqrt| ($ $ (|NonNegativeInteger|))) (SIGNATURE |sqrt| ($ $)) (SIGNATURE |sqrt| ($ (|Fraction| (|Integer|)))) (SIGNATURE |sqrt| ($ (|Integer|))) (SIGNATURE |rename!| ($ $ (|OutputForm|))) (SIGNATURE |rename| ($ $ (|OutputForm|))) (SIGNATURE |approximate| ((|Fraction| (|Integer|)) $ $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) . T) ((|Algebra| (|Integer|)) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) . T) ((|BiModule| (|Integer|) (|Integer|)) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|FullyRetractableTo| (|Fraction| (|Integer|))) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| (|Fraction| (|Integer|))) . T) ((|LeftModule| (|Integer|)) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| (|Fraction| (|Integer|))) . T) ((|Module| (|Integer|)) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T) ((|RetractableTo| (|Fraction| (|Integer|))) . T) ((|RetractableTo| (|Integer|)) |has| (|Fraction| (|Integer|)) (|RetractableTo| (|Integer|))) ((|RightModule| (|Fraction| (|Integer|))) . T) ((|RightModule| (|Integer|)) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|UniqueFactorizationDomain|) . T)) 
((|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) 61))) 
(((|ElementaryRischDE| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rischDE| ((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)))) (|Join| (|GcdDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|))) (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedField|) (|FunctionSpace| |#1|))) (T |ElementaryRischDE|)) 
((|rischDE| (*1 *2 *3 *4 *4 *5 *6 *7) (AND (|isDomain| *5 (|Symbol|)) (|isDomain| *6 (|Mapping| (|Union| (|Record| (|:| |mainpart| *4) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| *4) (|:| |logand| *4))))) "failed") *4 (|List| *4))) (|isDomain| *7 (|Mapping| (|Union| (|Record| (|:| |ratpart| *4) (|:| |coeff| *4)) "failed") *4 *4)) (|ofCategory| *4 (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedField|) (|FunctionSpace| *8))) (|ofCategory| *8 (|Join| (|GcdDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| *3) (|LinearlyExplicitRingOver| *3))) (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Record| (|:| |ans| *4) (|:| |right| *4) (|:| |sol?| (|Boolean|)))) (|isDomain| *1 (|ElementaryRischDE| *8 *4))))) 
(CATEGORY |package| (SIGNATURE |rischDE| ((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)))) 
((|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) 47))) 
(((|ElementaryRischDESystem| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rischDEsys| ((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)))) (|Join| (|GcdDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|))) (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedField|) (|FunctionSpace| |#1|))) (T |ElementaryRischDESystem|)) 
((|rischDEsys| (*1 *2 *3 *4 *4 *4 *5 *6 *7) (|partial| AND (|isDomain| *5 (|Symbol|)) (|isDomain| *6 (|Mapping| (|Union| (|Record| (|:| |mainpart| *4) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| *4) (|:| |logand| *4))))) "failed") *4 (|List| *4))) (|isDomain| *7 (|Mapping| (|Union| (|Record| (|:| |ratpart| *4) (|:| |coeff| *4)) "failed") *4 *4)) (|ofCategory| *4 (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedField|) (|FunctionSpace| *8))) (|ofCategory| *8 (|Join| (|GcdDomain|) (|OrderedSet|) (|CharacteristicZero|) (|RetractableTo| *3) (|LinearlyExplicitRingOver| *3))) (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|ElementaryRischDESystem| *8 *4))))) 
(CATEGORY |package| (SIGNATURE |rischDEsys| ((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)))) 
((|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) 30)) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) 56)) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) 61))) 
(((|TranscendentalRischDE| |#1| |#2|) (CATEGORY |package| (SIGNATURE |monomRDE| ((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|))) (SIGNATURE |baseRDE| ((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|))) (SIGNATURE |polyRDE| ((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|))) (|UnivariatePolynomialCategory| |#1|)) (T |TranscendentalRischDE|)) 
((|polyRDE| (*1 *2 *3 *3 *3 *4 *5) (AND (|isDomain| *5 (|Mapping| *3 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *6)) (|ofCategory| *6 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| *4))) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Union| (|:| |ans| (|Record| (|:| |ans| *3) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| *3) (|:| |c| *3) (|:| |m| *4) (|:| |alpha| *3) (|:| |beta| *3))))) (|isDomain| *1 (|TranscendentalRischDE| *6 *3)))) (|baseRDE| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Record| (|:| |ans| (|Fraction| *5)) (|:| |nosol| (|Boolean|)))) (|isDomain| *1 (|TranscendentalRischDE| *4 *5)) (|isDomain| *3 (|Fraction| *5)))) (|monomRDE| (*1 *2 *3 *3 *4) (|partial| AND (|isDomain| *4 (|Mapping| *6 *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |a| *6) (|:| |b| (|Fraction| *6)) (|:| |c| (|Fraction| *6)) (|:| |t| *6))) (|isDomain| *1 (|TranscendentalRischDE| *5 *6)) (|isDomain| *3 (|Fraction| *6))))) 
(CATEGORY |package| (SIGNATURE |monomRDE| ((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|))) (SIGNATURE |baseRDE| ((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|))) (SIGNATURE |polyRDE| ((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)))) 
((|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) 22)) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) 32))) 
(((|TranscendentalRischDESystem| |#1| |#2|) (CATEGORY |package| (SIGNATURE |monomRDEsys| ((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|))) (SIGNATURE |baseRDEsys| ((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|))) (|UnivariatePolynomialCategory| |#1|)) (T |TranscendentalRischDESystem|)) 
((|baseRDEsys| (*1 *2 *3 *3 *3) (|partial| AND (|ofCategory| *4 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|List| (|Fraction| *5))) (|isDomain| *1 (|TranscendentalRischDESystem| *4 *5)) (|isDomain| *3 (|Fraction| *5)))) (|monomRDEsys| (*1 *2 *3 *3 *3 *4) (|partial| AND (|isDomain| *4 (|Mapping| *6 *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |a| *6) (|:| |b| (|Fraction| *6)) (|:| |h| *6) (|:| |c1| (|Fraction| *6)) (|:| |c2| (|Fraction| *6)) (|:| |t| *6))) (|isDomain| *1 (|TranscendentalRischDESystem| *5 *6)) (|isDomain| *3 (|Fraction| *6))))) 
(CATEGORY |package| (SIGNATURE |monomRDEsys| ((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|))) (SIGNATURE |baseRDEsys| ((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)))) 
((|weighted| (((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|))))) 37)) (|uniform| (((|Mapping| |#1|) (|Set| |#1|)) 45)) (|rdHack1| (((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)) 34))) 
(((|RandomDistributions| |#1|) (CATEGORY |package| (SIGNATURE |uniform| ((|Mapping| |#1|) (|Set| |#1|))) (SIGNATURE |weighted| ((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|)))))) (SIGNATURE |rdHack1| ((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)))) (|SetCategory|)) (T |RandomDistributions|)) 
((|rdHack1| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Vector| *6)) (|isDomain| *4 (|Vector| (|Integer|))) (|isDomain| *5 (|Integer|)) (|ofCategory| *6 (|SetCategory|)) (|isDomain| *2 (|Mapping| *6)) (|isDomain| *1 (|RandomDistributions| *6)))) (|weighted| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Record| (|:| |value| *4) (|:| |weight| (|Integer|))))) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Mapping| *4)) (|isDomain| *1 (|RandomDistributions| *4)))) (|uniform| (*1 *2 *3) (AND (|isDomain| *3 (|Set| *4)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Mapping| *4)) (|isDomain| *1 (|RandomDistributions| *4))))) 
(CATEGORY |package| (SIGNATURE |uniform| ((|Mapping| |#1|) (|Set| |#1|))) (SIGNATURE |weighted| ((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|)))))) (SIGNATURE |rdHack1| ((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)))) 
((|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) 23))) 
(((|ReducedDivisor| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |order| ((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)))) (|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|) (|Join| (|Finite|) (|Field|))) (T |ReducedDivisor|)) 
((|order| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|FiniteDivisor| *6 *7 *4 *8)) (|isDomain| *5 (|Mapping| *9 *6)) (|ofCategory| *6 (|Field|)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *7))) (|ofCategory| *8 (|FunctionFieldCategory| *6 *7 *4)) (|ofCategory| *9 (|Join| (|Finite|) (|Field|))) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ReducedDivisor| *6 *7 *4 *8 *9))))) 
(CATEGORY |package| (SIGNATURE |order| ((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)))) 
((|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) 31) (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) 28)) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) 33) (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) 29) (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) 32) (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) 27)) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) 19)) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) 16))) 
(((|RealZeroPackage| |#1|) (CATEGORY |package| (SIGNATURE |realZeros| ((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|)) (SIGNATURE |realZeros| ((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) (SIGNATURE |realZeros| ((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|)))) (SIGNATURE |realZeros| ((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|)))) (SIGNATURE |refine| ((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|)))) (SIGNATURE |refine| ((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) (SIGNATURE |midpoint| ((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) (SIGNATURE |midpoints| ((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))))) (|UnivariatePolynomialCategory| (|Integer|))) (T |RealZeroPackage|)) 
((|midpoints| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) (|isDomain| *2 (|List| (|Fraction| (|Integer|)))) (|isDomain| *1 (|RealZeroPackage| *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Integer|))))) (|midpoint| (*1 *2 *3) (AND (|isDomain| *3 (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|RealZeroPackage| *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Integer|))))) (|refine| (*1 *2 *3 *2 *2) (|partial| AND (|isDomain| *2 (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) (|isDomain| *1 (|RealZeroPackage| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|refine| (*1 *2 *3 *2 *4) (AND (|isDomain| *2 (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) (|isDomain| *4 (|Fraction| (|Integer|))) (|isDomain| *1 (|RealZeroPackage| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|realZeros| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|Fraction| (|Integer|))) (|isDomain| *2 (|List| (|Record| (|:| |left| *5) (|:| |right| *5)))) (|isDomain| *1 (|RealZeroPackage| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))) (|isDomain| *4 (|Record| (|:| |left| *5) (|:| |right| *5))))) (|realZeros| (*1 *2 *3 *4) (AND (|isDomain| *2 (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) (|isDomain| *1 (|RealZeroPackage| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))) (|isDomain| *4 (|Fraction| (|Integer|))))) (|realZeros| (*1 *2 *3 *4) (AND (|isDomain| *2 (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) (|isDomain| *1 (|RealZeroPackage| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))) (|isDomain| *4 (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))))) (|realZeros| (*1 *2 *3) (AND (|isDomain| *2 (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) (|isDomain| *1 (|RealZeroPackage| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(CATEGORY |package| (SIGNATURE |realZeros| ((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|)) (SIGNATURE |realZeros| ((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) (SIGNATURE |realZeros| ((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|)))) (SIGNATURE |realZeros| ((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|)))) (SIGNATURE |refine| ((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|)))) (SIGNATURE |refine| ((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) (SIGNATURE |midpoint| ((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) (SIGNATURE |midpoints| ((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))))) 
((|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) 35) (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) 32)) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) 30) (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) 26) (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) 28) (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) 24))) 
(((|RealZeroPackageQ| |#1|) (CATEGORY |package| (SIGNATURE |realZeros| ((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|)) (SIGNATURE |realZeros| ((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) (SIGNATURE |realZeros| ((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|)))) (SIGNATURE |realZeros| ((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|)))) (SIGNATURE |refine| ((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|)))) (SIGNATURE |refine| ((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))))) (|UnivariatePolynomialCategory| (|Fraction| (|Integer|)))) (T |RealZeroPackageQ|)) 
((|refine| (*1 *2 *3 *2 *2) (|partial| AND (|isDomain| *2 (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) (|isDomain| *1 (|RealZeroPackageQ| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|)))))) (|refine| (*1 *2 *3 *2 *4) (AND (|isDomain| *2 (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) (|isDomain| *4 (|Fraction| (|Integer|))) (|isDomain| *1 (|RealZeroPackageQ| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|realZeros| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|Fraction| (|Integer|))) (|isDomain| *2 (|List| (|Record| (|:| |left| *5) (|:| |right| *5)))) (|isDomain| *1 (|RealZeroPackageQ| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|isDomain| *4 (|Record| (|:| |left| *5) (|:| |right| *5))))) (|realZeros| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Fraction| (|Integer|))) (|isDomain| *2 (|List| (|Record| (|:| |left| *4) (|:| |right| *4)))) (|isDomain| *1 (|RealZeroPackageQ| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|realZeros| (*1 *2 *3 *4) (AND (|isDomain| *2 (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) (|isDomain| *1 (|RealZeroPackageQ| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|)))) (|isDomain| *4 (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))))) (|realZeros| (*1 *2 *3) (AND (|isDomain| *2 (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) (|isDomain| *1 (|RealZeroPackageQ| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|))))))) 
(CATEGORY |package| (SIGNATURE |realZeros| ((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|)) (SIGNATURE |realZeros| ((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) (SIGNATURE |realZeros| ((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|)))) (SIGNATURE |realZeros| ((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|)))) (SIGNATURE |refine| ((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|)))) (SIGNATURE |refine| ((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))))) 
((|convert| (((|DoubleFloat|) $) 6) (((|Float|) $) 8))) 
(((|RealConstant|) (|Category|)) (T |RealConstant|)) 
NIL 
(|Join| (|ConvertibleTo| (|DoubleFloat|)) (|ConvertibleTo| (|Float|))) 
(((|ConvertibleTo| (|DoubleFloat|)) . T) ((|ConvertibleTo| (|Float|)) . T)) 
((|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) 27) (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) 26)) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) 36))) 
(((|RealSolvePackage|) (CATEGORY |package| (SIGNATURE |solve| ((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|))) (SIGNATURE |solve| ((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|))) (SIGNATURE |realSolve| ((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|))))) (T |RealSolvePackage|)) 
((|realSolve| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| (|Polynomial| (|Integer|)))) (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|List| (|Float|)))) (|isDomain| *1 (|RealSolvePackage|)) (|isDomain| *5 (|Float|)))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Polynomial| (|Integer|))) (|isDomain| *2 (|List| (|Float|))) (|isDomain| *1 (|RealSolvePackage|)) (|isDomain| *4 (|Float|)))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Polynomial| (|Fraction| (|Integer|)))) (|isDomain| *2 (|List| (|Float|))) (|isDomain| *1 (|RealSolvePackage|)) (|isDomain| *4 (|Float|))))) 
(CATEGORY |package| (SIGNATURE |solve| ((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|))) (SIGNATURE |solve| ((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|))) (SIGNATURE |realSolve| ((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 70)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sqrt| (($ $) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ (|Integer|)) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sign| (((|Integer|) $) 65)) (|sample| (($) NIL T CONST)) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) NIL) (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) 49)) (|retractIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| (|Fraction| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL) (((|Union| |#1| "failed") $) 108) (((|Union| (|Integer|) "failed") $) NIL (OR (|has| (|Fraction| (|Integer|)) (|RetractableTo| (|Integer|))) (|has| |#1| (|RetractableTo| (|Integer|)))))) (|retract| (((|Fraction| (|Integer|)) $) 14 (|has| (|Fraction| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))))) (((|Fraction| (|Integer|)) $) 14) ((|#1| $) 109) (((|Integer|) $) NIL (OR (|has| (|Fraction| (|Integer|)) (|RetractableTo| (|Integer|))) (|has| |#1| (|RetractableTo| (|Integer|)))))) (|rename!| (($ $ (|OutputForm|)) 40)) (|rename| (($ $ (|OutputForm|)) 41)) (|rem| (($ $ $) NIL)) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) 18)) (|recip| (((|Union| $ "failed") $) 83)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|positive?| (((|Boolean|) $) 60)) (|one?| (((|Boolean|) $) NIL)) (|nthRoot| (($ $ (|Integer|)) NIL)) (|negative?| (((|Boolean|) $) 63)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) 78)) (|mainForm| (((|Union| (|OutputForm|) "failed") $) 77)) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) 75)) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) 73)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ (|List| $)) NIL) (($ $ $) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 84)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ (|List| $)) NIL) (($ $ $) NIL)) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|coerce| (((|OutputForm|) $) 82) (($ (|Integer|)) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ $) 57) (($ (|Fraction| (|Integer|))) NIL) (($ (|Integer|)) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ |#1|) 111)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|associates?| (((|Boolean|) $ $) NIL)) (|approximate| (((|Fraction| (|Integer|)) $ $) 24)) (|allRootsOf| (((|List| $) (|SparseUnivariatePolynomial| $)) 55) (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) NIL) (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) NIL) (((|List| $) (|Polynomial| $)) NIL) (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) NIL) (((|List| $) (|Polynomial| (|Integer|))) NIL)) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) 39)) (|abs| (($ $) 19)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL)) (|Zero| (($) 28 T CONST)) (|One| (($) 34 T CONST)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 71)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 21)) (/ (($ $ $) 32)) (- (($ $) 33) (($ $ $) 69)) (+ (($ $ $) 104)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL) (($ $ (|Fraction| (|Integer|))) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 92) (($ $ $) 97) (($ (|Fraction| (|Integer|)) $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ (|Integer|) $) 92) (($ $ (|Integer|)) NIL) (($ (|Fraction| (|Integer|)) $) NIL) (($ $ (|Fraction| (|Integer|))) NIL) (($ |#1| $) 96) (($ $ |#1|) NIL))) 
(((|RealClosure| |#1|) (|Join| (|RealClosedField|) (|FullyRetractableTo| |#1|) (|Algebra| |#1|) (CATEGORY |domain| (SIGNATURE |algebraicOf| ($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|))) (SIGNATURE |mainCharacterization| ((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $)) (SIGNATURE |relativeApprox| ((|Fraction| (|Integer|)) $ $)))) (|Join| (|OrderedRing|) (|Field|) (|RealConstant|))) (T |RealClosure|)) 
((|algebraicOf| (*1 *1 *2 *3) (AND (|isDomain| *2 (|RightOpenIntervalRootCharacterization| (|RealClosure| *4) (|SparseUnivariatePolynomial| (|RealClosure| *4)))) (|isDomain| *3 (|OutputForm|)) (|isDomain| *1 (|RealClosure| *4)) (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|) (|RealConstant|))))) (|mainCharacterization| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|RightOpenIntervalRootCharacterization| (|RealClosure| *3) (|SparseUnivariatePolynomial| (|RealClosure| *3)))) (|isDomain| *1 (|RealClosure| *3)) (|ofCategory| *3 (|Join| (|OrderedRing|) (|Field|) (|RealConstant|))))) (|relativeApprox| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|RealClosure| *3)) (|ofCategory| *3 (|Join| (|OrderedRing|) (|Field|) (|RealConstant|)))))) 
(|Join| (|RealClosedField|) (|FullyRetractableTo| |#1|) (|Algebra| |#1|) (CATEGORY |domain| (SIGNATURE |algebraicOf| ($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|))) (SIGNATURE |mainCharacterization| ((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $)) (SIGNATURE |relativeApprox| ((|Fraction| (|Integer|)) $ $)))) 
((|shiftInfoRec| (((|Record| (|:| |max| (|Union| (|Integer|) "failed")) (|:| |ord| (|Union| (|Integer|) "failed")) (|:| |ker| (|Kernel| |#2|))) (|BasicOperator|) (|Symbol|) |#2|) 59 (|has| |#1| (|Ring|)))) (|numberOfValuesNeeded| (((|Integer|) (|Integer|) (|BasicOperator|) (|Symbol|) |#2|) 76)) (|getShiftRec| (((|Union| (|Integer|) "failed") (|BasicOperator|) (|Kernel| |#2|) (|Symbol|)) 56 (|has| |#1| (|Ring|)))) (|getOp| (((|BasicOperator|) |#2|) 103)) (|getEq| ((|#2| |#2|) 102)) (|evalRec| ((|#2| (|BasicOperator|) (|Symbol|) |#2| |#2| |#2| (|List| |#2|)) 72)) (|evalADE| ((|#2| (|BasicOperator|) (|Symbol|) |#2| |#2| |#2| (|List| |#2|)) 100))) 
(((|RecurrenceOperator| |#1| |#2|) (CATEGORY |package| (SIGNATURE |evalRec| (|#2| (|BasicOperator|) (|Symbol|) |#2| |#2| |#2| (|List| |#2|))) (SIGNATURE |evalADE| (|#2| (|BasicOperator|) (|Symbol|) |#2| |#2| |#2| (|List| |#2|))) (SIGNATURE |getEq| (|#2| |#2|)) (SIGNATURE |getOp| ((|BasicOperator|) |#2|)) (SIGNATURE |numberOfValuesNeeded| ((|Integer|) (|Integer|) (|BasicOperator|) (|Symbol|) |#2|)) (IF (|has| |#1| (|Ring|)) (PROGN (SIGNATURE |getShiftRec| ((|Union| (|Integer|) "failed") (|BasicOperator|) (|Kernel| |#2|) (|Symbol|))) (SIGNATURE |shiftInfoRec| ((|Record| (|:| |max| (|Union| (|Integer|) "failed")) (|:| |ord| (|Union| (|Integer|) "failed")) (|:| |ker| (|Kernel| |#2|))) (|BasicOperator|) (|Symbol|) |#2|))) |noBranch|)) (|Join| (|OrderedSet|) (|IntegralDomain|) (|ConvertibleTo| (|InputForm|))) (|Join| (|FunctionSpace| |#1|) (|AbelianMonoid|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Symbol|)) (|PartialDifferentialRing| (|Symbol|)) (|CombinatorialOpsCategory|))) (T |RecurrenceOperator|)) 
((|shiftInfoRec| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *6 (|Join| (|OrderedSet|) (|IntegralDomain|) (|ConvertibleTo| (|InputForm|)))) (|isDomain| *2 (|Record| (|:| |max| (|Union| (|Integer|) "failed")) (|:| |ord| (|Union| (|Integer|) "failed")) (|:| |ker| (|Kernel| *5)))) (|isDomain| *1 (|RecurrenceOperator| *6 *5)) (|ofCategory| *5 (|Join| (|FunctionSpace| *6) (|AbelianMonoid|) (|RetractableTo| (|Integer|)) (|RetractableTo| *4) (|PartialDifferentialRing| *4) (|CombinatorialOpsCategory|))))) (|getShiftRec| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *4 (|Kernel| *7)) (|ofCategory| *7 (|Join| (|FunctionSpace| *6) (|AbelianMonoid|) (|RetractableTo| *2) (|RetractableTo| *5) (|PartialDifferentialRing| *5) (|CombinatorialOpsCategory|))) (|isDomain| *5 (|Symbol|)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *6 (|Join| (|OrderedSet|) (|IntegralDomain|) (|ConvertibleTo| (|InputForm|)))) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|RecurrenceOperator| *6 *7)))) (|numberOfValuesNeeded| (*1 *2 *2 *3 *4 *5) (AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *2 (|Integer|)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *6 (|Join| (|OrderedSet|) (|IntegralDomain|) (|ConvertibleTo| (|InputForm|)))) (|isDomain| *1 (|RecurrenceOperator| *6 *5)) (|ofCategory| *5 (|Join| (|FunctionSpace| *6) (|AbelianMonoid|) (|RetractableTo| *2) (|RetractableTo| *4) (|PartialDifferentialRing| *4) (|CombinatorialOpsCategory|))))) (|getOp| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|) (|ConvertibleTo| (|InputForm|)))) (|isDomain| *2 (|BasicOperator|)) (|isDomain| *1 (|RecurrenceOperator| *4 *3)) (|ofCategory| *3 (|Join| (|FunctionSpace| *4) (|AbelianMonoid|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Symbol|)) (|PartialDifferentialRing| (|Symbol|)) (|CombinatorialOpsCategory|))))) (|getEq| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|) (|ConvertibleTo| (|InputForm|)))) (|isDomain| *1 (|RecurrenceOperator| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|AbelianMonoid|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Symbol|)) (|PartialDifferentialRing| (|Symbol|)) (|CombinatorialOpsCategory|))))) (|evalADE| (*1 *2 *3 *4 *2 *2 *2 *5) (AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *5 (|List| *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *6) (|AbelianMonoid|) (|RetractableTo| (|Integer|)) (|RetractableTo| *4) (|PartialDifferentialRing| *4) (|CombinatorialOpsCategory|))) (|isDomain| *4 (|Symbol|)) (|ofCategory| *6 (|Join| (|OrderedSet|) (|IntegralDomain|) (|ConvertibleTo| (|InputForm|)))) (|isDomain| *1 (|RecurrenceOperator| *6 *2)))) (|evalRec| (*1 *2 *3 *4 *2 *2 *2 *5) (AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *5 (|List| *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *6) (|AbelianMonoid|) (|RetractableTo| (|Integer|)) (|RetractableTo| *4) (|PartialDifferentialRing| *4) (|CombinatorialOpsCategory|))) (|isDomain| *4 (|Symbol|)) (|ofCategory| *6 (|Join| (|OrderedSet|) (|IntegralDomain|) (|ConvertibleTo| (|InputForm|)))) (|isDomain| *1 (|RecurrenceOperator| *6 *2))))) 
(CATEGORY |package| (SIGNATURE |evalRec| (|#2| (|BasicOperator|) (|Symbol|) |#2| |#2| |#2| (|List| |#2|))) (SIGNATURE |evalADE| (|#2| (|BasicOperator|) (|Symbol|) |#2| |#2| |#2| (|List| |#2|))) (SIGNATURE |getEq| (|#2| |#2|)) (SIGNATURE |getOp| ((|BasicOperator|) |#2|)) (SIGNATURE |numberOfValuesNeeded| ((|Integer|) (|Integer|) (|BasicOperator|) (|Symbol|) |#2|)) (IF (|has| |#1| (|Ring|)) (PROGN (SIGNATURE |getShiftRec| ((|Union| (|Integer|) "failed") (|BasicOperator|) (|Kernel| |#2|) (|Symbol|))) (SIGNATURE |shiftInfoRec| ((|Record| (|:| |max| (|Union| (|Integer|) "failed")) (|:| |ord| (|Union| (|Integer|) "failed")) (|:| |ker| (|Kernel| |#2|))) (|BasicOperator|) (|Symbol|) |#2|))) |noBranch|)) 
((|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) 20) ((|#2| |#2| |#1|) 15))) 
(((|ReductionOfOrder| |#1| |#2|) (CATEGORY |package| (SIGNATURE |ReduceOrder| (|#2| |#2| |#1|)) (SIGNATURE |ReduceOrder| ((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)))) (|Field|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|)) (T |ReductionOfOrder|)) 
((|ReduceOrder| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Record| (|:| |eq| *3) (|:| |op| (|List| *5)))) (|isDomain| *1 (|ReductionOfOrder| *5 *3)) (|isDomain| *4 (|List| *5)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *5)))) (|ReduceOrder| (*1 *2 *2 *3) (AND (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|ReductionOfOrder| *3 *2)) (|ofCategory| *2 (|LinearOrdinaryDifferentialOperatorCategory| *3))))) 
(CATEGORY |package| (SIGNATURE |ReduceOrder| (|#2| |#2| |#1|)) (SIGNATURE |ReduceOrder| ((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)))) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|setref| ((|#1| $ |#1|) 14)) (|setelt| ((|#1| $ |#1|) 12)) (|ref| (($ |#1|) 10)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|elt| ((|#1| $) 11)) (|deref| ((|#1| $) 13)) (|coerce| (((|OutputForm|) $) 21 (|has| |#1| (|SetCategory|)))) (= (((|Boolean|) $ $) 9))) 
(((|Reference| |#1|) (|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |ref| ($ |#1|)) (SIGNATURE |elt| (|#1| $)) (SIGNATURE |setelt| (|#1| $ |#1|)) (SIGNATURE |deref| (|#1| $)) (SIGNATURE |setref| (|#1| $ |#1|)) (SIGNATURE = ((|Boolean|) $ $)) (IF (|has| |#1| (|SetCategory|)) (ATTRIBUTE (|SetCategory|)) |noBranch|))) (|Type|)) (T |Reference|)) 
((|ref| (*1 *1 *2) (AND (|isDomain| *1 (|Reference| *2)) (|ofCategory| *2 (|Type|)))) (|elt| (*1 *2 *1) (AND (|isDomain| *1 (|Reference| *2)) (|ofCategory| *2 (|Type|)))) (|setelt| (*1 *2 *1 *2) (AND (|isDomain| *1 (|Reference| *2)) (|ofCategory| *2 (|Type|)))) (|deref| (*1 *2 *1) (AND (|isDomain| *1 (|Reference| *2)) (|ofCategory| *2 (|Type|)))) (|setref| (*1 *2 *1 *2) (AND (|isDomain| *1 (|Reference| *2)) (|ofCategory| *2 (|Type|)))) (= (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Reference| *3)) (|ofCategory| *3 (|Type|))))) 
(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |ref| ($ |#1|)) (SIGNATURE |elt| (|#1| $)) (SIGNATURE |setelt| (|#1| $ |#1|)) (SIGNATURE |deref| (|#1| $)) (SIGNATURE |setref| (|#1| $ |#1|)) (SIGNATURE = ((|Boolean|) $ $)) (IF (|has| |#1| (|SetCategory|)) (ATTRIBUTE (|SetCategory|)) |noBranch|))) 
((~= (((|Boolean|) $ $) NIL)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) NIL)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 104) (((|List| $) (|List| |#4|) (|Boolean|)) 105) (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) 103) (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) 106)) (|variables| (((|List| |#3|) $) NIL)) (|trivialIdeal?| (((|Boolean|) $) NIL)) (|triangular?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|stronglyReduced?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|stronglyReduce| ((|#4| |#4| $) NIL)) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) 98)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|select| (($ (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| |#4| "failed") $ |#3|) 53)) (|sample| (($) NIL T CONST)) (|roughUnitIdeal?| (((|Boolean|) $) 26 (|has| |#1| (|IntegralDomain|)))) (|roughSubIdeal?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|roughEqualIdeals?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|roughBase?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) NIL)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) NIL)) (|retract| (($ (|List| |#4|)) NIL)) (|rest| (((|Union| $ "failed") $) 39)) (|removeZero| ((|#4| |#4| $) 56)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|))))) (|remove| (($ |#4| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|)))) (($ (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 72 (|has| |#1| (|IntegralDomain|)))) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) NIL)) (|reduceByQuasiMonic| ((|#4| |#4| $) NIL)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|)))) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| (|Mapping| |#4| |#4| |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) NIL)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) NIL)) (|purelyTranscendental?| (((|Boolean|) |#4| $) NIL)) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) NIL)) (|purelyAlgebraic?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) 118)) (|parts| (((|List| |#4|) $) 16 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|normalized?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|mvar| ((|#3| $) 33)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#4|) $) 17 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#4| $) 25 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|))))) (|map!| (($ (|Mapping| |#4| |#4|) $) 23 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#4| |#4|) $) 21)) (|mainVariables| (((|List| |#3|) $) NIL)) (|mainVariable?| (((|Boolean|) |#3| $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL)) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) NIL)) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) 96)) (|last| (((|Union| |#4| "failed") $) 37)) (|invertibleSet| (((|List| $) |#4| $) 79)) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) NIL)) (|invertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) 89) (((|Boolean|) |#4| $) 51)) (|intersect| (((|List| $) |#4| $) 101) (((|List| $) (|List| |#4|) $) NIL) (((|List| $) (|List| |#4|) (|List| $)) 102) (((|List| $) |#4| (|List| $)) NIL)) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) 113)) (|internalAugment| (($ |#4| $) 69) (($ (|List| |#4|) $) 70) (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) 66)) (|initials| (((|List| |#4|) $) NIL)) (|initiallyReduced?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|initiallyReduce| ((|#4| |#4| $) NIL)) (|infRittWu?| (((|Boolean|) $ $) NIL)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) NIL (|has| |#1| (|IntegralDomain|)))) (|headReduced?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|headReduce| ((|#4| |#4| $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|first| (((|Union| |#4| "failed") $) 35)) (|find| (((|Union| |#4| "failed") (|Mapping| (|Boolean|) |#4|) $) NIL)) (|extendIfCan| (((|Union| $ "failed") $ |#4|) 47)) (|extend| (($ $ |#4|) NIL) (((|List| $) |#4| $) 81) (((|List| $) |#4| (|List| $)) NIL) (((|List| $) (|List| |#4|) $) NIL) (((|List| $) (|List| |#4|) (|List| $)) 76)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ |#4| |#4|) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|Equation| |#4|)) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|List| (|Equation| |#4|))) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) 15)) (|empty| (($) 13)) (|degree| (((|NonNegativeInteger|) $) NIL)) (|count| (((|NonNegativeInteger|) |#4| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) 12)) (|convert| (((|InputForm|) $) NIL (|has| |#4| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#4|)) 20)) (|collectUpper| (($ $ |#3|) 42)) (|collectUnder| (($ $ |#3|) 43)) (|collectQuasiMonic| (($ $) NIL)) (|collect| (($ $ |#3|) NIL)) (|coerce| (((|OutputForm|) $) 31) (((|List| |#4|) $) 40)) (|coHeight| (((|NonNegativeInteger|) $) NIL (|has| |#3| (|Finite|)))) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) NIL) (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) NIL)) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) NIL)) (|augment| (((|List| $) |#4| $) 78) (((|List| $) |#4| (|List| $)) NIL) (((|List| $) (|List| |#4|) $) NIL) (((|List| $) (|List| |#4|) (|List| $)) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|algebraicVariables| (((|List| |#3|) $) NIL)) (|algebraicCoefficients?| (((|Boolean|) |#4| $) NIL)) (|algebraic?| (((|Boolean|) |#3| $) 52)) (= (((|Boolean|) $ $) NIL)) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|RegularTriangularSet| |#1| |#2| |#3| |#4|) (|Join| (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |internalAugment| ((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |zeroSetSplit| ((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|))) (SIGNATURE |zeroSetSplit| ((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |internalZeroSetSplit| ((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |preprocess| ((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|))))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|)) (T |RegularTriangularSet|)) 
((|internalAugment| (*1 *2 *3 *1 *4 *4 *4 *4 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|List| (|RegularTriangularSet| *5 *6 *7 *3))) (|isDomain| *1 (|RegularTriangularSet| *5 *6 *7 *3)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)))) (|zeroSetSplit| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|List| (|RegularTriangularSet| *5 *6 *7 *8))) (|isDomain| *1 (|RegularTriangularSet| *5 *6 *7 *8)))) (|zeroSetSplit| (*1 *2 *3 *4 *4 *4 *4) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|List| (|RegularTriangularSet| *5 *6 *7 *8))) (|isDomain| *1 (|RegularTriangularSet| *5 *6 *7 *8)))) (|internalZeroSetSplit| (*1 *2 *3 *4 *4 *4) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|List| (|RegularTriangularSet| *5 *6 *7 *8))) (|isDomain| *1 (|RegularTriangularSet| *5 *6 *7 *8)))) (|preprocess| (*1 *2 *3 *4 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Record| (|:| |val| (|List| *8)) (|:| |towers| (|List| (|RegularTriangularSet| *5 *6 *7 *8))))) (|isDomain| *1 (|RegularTriangularSet| *5 *6 *7 *8)) (|isDomain| *3 (|List| *8))))) 
(|Join| (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |internalAugment| ((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |zeroSetSplit| ((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|))) (SIGNATURE |zeroSetSplit| ((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |internalZeroSetSplit| ((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |preprocess| ((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|))))) 
((|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) 56) (((|Matrix| |#1|) (|Matrix| |#1|)) 55) (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) 54) (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) 51)) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) 50) (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) 49)) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) 66) (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) 65) (((|Matrix| (|Integer|)) (|List| (|Integer|))) 62) (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) 61)) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) 79)) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) 36 (|has| |#1| (ATTRIBUTE (|commutative| "*")))) (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) 34 (|has| |#1| (ATTRIBUTE (|commutative| "*")))))) 
(((|RepresentationPackage1| |#1|) (CATEGORY |package| (IF (|has| |#1| (ATTRIBUTE (|commutative| "*"))) (SIGNATURE |antisymmetricTensors| ((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|))) |noBranch|) (IF (|has| |#1| (ATTRIBUTE (|commutative| "*"))) (SIGNATURE |antisymmetricTensors| ((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|))) |noBranch|) (SIGNATURE |createGenericMatrix| ((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|))) (SIGNATURE |symmetricTensors| ((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|))) (SIGNATURE |symmetricTensors| ((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|))) (SIGNATURE |tensorProduct| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |tensorProduct| ((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)))) (SIGNATURE |tensorProduct| ((|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |tensorProduct| ((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)))) (SIGNATURE |permutationRepresentation| ((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|))) (SIGNATURE |permutationRepresentation| ((|Matrix| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |permutationRepresentation| ((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|))) (SIGNATURE |permutationRepresentation| ((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))))) (|Ring|)) (T |RepresentationPackage1|)) 
((|permutationRepresentation| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|List| (|Integer|)))) (|isDomain| *2 (|List| (|Matrix| (|Integer|)))) (|isDomain| *1 (|RepresentationPackage1| *4)) (|ofCategory| *4 (|Ring|)))) (|permutationRepresentation| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Permutation| (|Integer|)))) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|List| (|Matrix| *4))) (|isDomain| *1 (|RepresentationPackage1| *5)) (|ofCategory| *5 (|Ring|)))) (|permutationRepresentation| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|Matrix| (|Integer|))) (|isDomain| *1 (|RepresentationPackage1| *4)) (|ofCategory| *4 (|Ring|)))) (|permutationRepresentation| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Permutation| (|Integer|))) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|RepresentationPackage1| *5)) (|ofCategory| *5 (|Ring|)))) (|tensorProduct| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|Matrix| *3))) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|RepresentationPackage1| *3)))) (|tensorProduct| (*1 *2 *2) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|RepresentationPackage1| *3)))) (|tensorProduct| (*1 *2 *2 *2) (AND (|isDomain| *2 (|List| (|Matrix| *3))) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|RepresentationPackage1| *3)))) (|tensorProduct| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|RepresentationPackage1| *3)))) (|symmetricTensors| (*1 *2 *2 *3) (AND (|isDomain| *2 (|List| (|Matrix| *4))) (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|RepresentationPackage1| *4)))) (|symmetricTensors| (*1 *2 *2 *3) (AND (|isDomain| *2 (|Matrix| *4)) (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|RepresentationPackage1| *4)))) (|createGenericMatrix| (*1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Matrix| (|Polynomial| *4))) (|isDomain| *1 (|RepresentationPackage1| *4)) (|ofCategory| *4 (|Ring|)))) (|antisymmetricTensors| (*1 *2 *2 *3) (AND (|isDomain| *2 (|List| (|Matrix| *4))) (|isDomain| *3 (|PositiveInteger|)) (|has| *4 (ATTRIBUTE (|commutative| "*"))) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|RepresentationPackage1| *4)))) (|antisymmetricTensors| (*1 *2 *2 *3) (AND (|isDomain| *2 (|Matrix| *4)) (|isDomain| *3 (|PositiveInteger|)) (|has| *4 (ATTRIBUTE (|commutative| "*"))) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|RepresentationPackage1| *4))))) 
(CATEGORY |package| (IF (|has| |#1| (ATTRIBUTE (|commutative| "*"))) (SIGNATURE |antisymmetricTensors| ((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|))) |noBranch|) (IF (|has| |#1| (ATTRIBUTE (|commutative| "*"))) (SIGNATURE |antisymmetricTensors| ((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|))) |noBranch|) (SIGNATURE |createGenericMatrix| ((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|))) (SIGNATURE |symmetricTensors| ((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|))) (SIGNATURE |symmetricTensors| ((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|))) (SIGNATURE |tensorProduct| ((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |tensorProduct| ((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)))) (SIGNATURE |tensorProduct| ((|Matrix| |#1|) (|Matrix| |#1|))) (SIGNATURE |tensorProduct| ((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)))) (SIGNATURE |permutationRepresentation| ((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|))) (SIGNATURE |permutationRepresentation| ((|Matrix| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |permutationRepresentation| ((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|))) (SIGNATURE |permutationRepresentation| ((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))))) 
((|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) 48 (|has| |#1| (|EuclideanDomain|)))) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) 71 (|has| |#1| (|Field|))) (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) 69 (|has| |#1| (|Field|)))) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) 73 (AND (|has| |#1| (|Field|)) (|has| |#1| (|Finite|))))) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) 78 (AND (|has| |#1| (|Field|)) (|has| |#1| (|Finite|)))) (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) 76 (AND (|has| |#1| (|Field|)) (|has| |#1| (|Finite|)))) (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) 75 (AND (|has| |#1| (|Field|)) (|has| |#1| (|Finite|)))) (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) 74 (AND (|has| |#1| (|Field|)) (|has| |#1| (|Finite|))))) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) 67 (|has| |#1| (|Field|))) (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) 66 (|has| |#1| (|Field|)))) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) 46 (|has| |#1| (|EuclideanDomain|)))) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) 32)) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) 29)) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) 62 (|has| |#1| (|Field|))) (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) 61 (|has| |#1| (|Field|))) (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) 60 (|has| |#1| (|Field|))))) 
(((|RepresentationPackage2| |#1|) (CATEGORY |package| (SIGNATURE |completeEchelonBasis| ((|Matrix| |#1|) (|Vector| (|Vector| |#1|)))) (SIGNATURE |createRandomElement| ((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|))) (IF (|has| |#1| (|EuclideanDomain|)) (PROGN (SIGNATURE |cyclicSubmodule| ((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|))) (SIGNATURE |standardBasisOfCyclicSubmodule| ((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)))) |noBranch|) (IF (|has| |#1| (|Field|)) (PROGN (SIGNATURE |areEquivalent?| ((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|))) (SIGNATURE |areEquivalent?| ((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)))) (SIGNATURE |areEquivalent?| ((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|))) (SIGNATURE |isAbsolutelyIrreducible?| ((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|))) (SIGNATURE |isAbsolutelyIrreducible?| ((|Boolean|) (|List| (|Matrix| |#1|)))) (SIGNATURE |split| ((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|))) (SIGNATURE |split| ((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))))) |noBranch|) (IF (|has| |#1| (|Finite|)) (IF (|has| |#1| (|Field|)) (PROGN (SIGNATURE |meatAxe| ((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|))) (SIGNATURE |meatAxe| ((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)))) (SIGNATURE |meatAxe| ((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|))) (SIGNATURE |meatAxe| ((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|))) (SIGNATURE |scanOneDimSubspaces| ((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)))) |noBranch|) |noBranch|)) (|Ring|)) (T |RepresentationPackage2|)) 
((|scanOneDimSubspaces| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Vector| *5))) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Vector| *5)) (|isDomain| *1 (|RepresentationPackage2| *5)) (|ofCategory| *5 (|Field|)) (|ofCategory| *5 (|Finite|)) (|ofCategory| *5 (|Ring|)))) (|meatAxe| (*1 *2 *3 *4) (AND (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|Field|)) (|ofCategory| *5 (|Finite|)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|List| (|List| (|Matrix| *5)))) (|isDomain| *1 (|RepresentationPackage2| *5)) (|isDomain| *3 (|List| (|Matrix| *5))))) (|meatAxe| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Field|)) (|ofCategory| *5 (|Finite|)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|List| (|List| (|Matrix| *5)))) (|isDomain| *1 (|RepresentationPackage2| *5)) (|isDomain| *3 (|List| (|Matrix| *5))))) (|meatAxe| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofCategory| *4 (|Finite|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|List| (|List| (|Matrix| *4)))) (|isDomain| *1 (|RepresentationPackage2| *4)) (|isDomain| *3 (|List| (|Matrix| *4))))) (|meatAxe| (*1 *2 *3 *4 *5 *5) (AND (|isDomain| *4 (|Boolean|)) (|isDomain| *5 (|Integer|)) (|ofCategory| *6 (|Field|)) (|ofCategory| *6 (|Finite|)) (|ofCategory| *6 (|Ring|)) (|isDomain| *2 (|List| (|List| (|Matrix| *6)))) (|isDomain| *1 (|RepresentationPackage2| *6)) (|isDomain| *3 (|List| (|Matrix| *6))))) (|split| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Vector| (|Vector| *5))) (|ofCategory| *5 (|Field|)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|List| (|List| (|Matrix| *5)))) (|isDomain| *1 (|RepresentationPackage2| *5)) (|isDomain| *3 (|List| (|Matrix| *5))))) (|split| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Vector| *5)) (|ofCategory| *5 (|Field|)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|List| (|List| (|Matrix| *5)))) (|isDomain| *1 (|RepresentationPackage2| *5)) (|isDomain| *3 (|List| (|Matrix| *5))))) (|isAbsolutelyIrreducible?| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Matrix| *4))) (|ofCategory| *4 (|Field|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|RepresentationPackage2| *4)))) (|isAbsolutelyIrreducible?| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Matrix| *5))) (|isDomain| *4 (|Integer|)) (|ofCategory| *5 (|Field|)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|RepresentationPackage2| *5)))) (|areEquivalent?| (*1 *2 *3 *3 *4) (AND (|isDomain| *3 (|List| (|Matrix| *5))) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Matrix| *5)) (|isDomain| *1 (|RepresentationPackage2| *5)) (|ofCategory| *5 (|Field|)) (|ofCategory| *5 (|Ring|)))) (|areEquivalent?| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| (|Matrix| *4))) (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|RepresentationPackage2| *4)) (|ofCategory| *4 (|Field|)) (|ofCategory| *4 (|Ring|)))) (|areEquivalent?| (*1 *2 *3 *3 *4 *5) (AND (|isDomain| *3 (|List| (|Matrix| *6))) (|isDomain| *4 (|Boolean|)) (|isDomain| *5 (|Integer|)) (|isDomain| *2 (|Matrix| *6)) (|isDomain| *1 (|RepresentationPackage2| *6)) (|ofCategory| *6 (|Field|)) (|ofCategory| *6 (|Ring|)))) (|standardBasisOfCyclicSubmodule| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Matrix| *5))) (|isDomain| *4 (|Vector| *5)) (|ofCategory| *5 (|EuclideanDomain|)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Matrix| *5)) (|isDomain| *1 (|RepresentationPackage2| *5)))) (|cyclicSubmodule| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Matrix| *5))) (|ofCategory| *5 (|EuclideanDomain|)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Vector| (|Vector| *5))) (|isDomain| *1 (|RepresentationPackage2| *5)) (|isDomain| *4 (|Vector| *5)))) (|createRandomElement| (*1 *2 *3 *2) (AND (|isDomain| *3 (|List| (|Matrix| *4))) (|isDomain| *2 (|Matrix| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|RepresentationPackage2| *4)))) (|completeEchelonBasis| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| (|Vector| *4))) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|RepresentationPackage2| *4))))) 
(CATEGORY |package| (SIGNATURE |completeEchelonBasis| ((|Matrix| |#1|) (|Vector| (|Vector| |#1|)))) (SIGNATURE |createRandomElement| ((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|))) (IF (|has| |#1| (|EuclideanDomain|)) (PROGN (SIGNATURE |cyclicSubmodule| ((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|))) (SIGNATURE |standardBasisOfCyclicSubmodule| ((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)))) |noBranch|) (IF (|has| |#1| (|Field|)) (PROGN (SIGNATURE |areEquivalent?| ((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|))) (SIGNATURE |areEquivalent?| ((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)))) (SIGNATURE |areEquivalent?| ((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|))) (SIGNATURE |isAbsolutelyIrreducible?| ((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|))) (SIGNATURE |isAbsolutelyIrreducible?| ((|Boolean|) (|List| (|Matrix| |#1|)))) (SIGNATURE |split| ((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|))) (SIGNATURE |split| ((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))))) |noBranch|) (IF (|has| |#1| (|Finite|)) (IF (|has| |#1| (|Field|)) (PROGN (SIGNATURE |meatAxe| ((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|))) (SIGNATURE |meatAxe| ((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)))) (SIGNATURE |meatAxe| ((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|))) (SIGNATURE |meatAxe| ((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|))) (SIGNATURE |scanOneDimSubspaces| ((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)))) |noBranch|) |noBranch|)) 
((|double| ((|#1| (|PositiveInteger|) |#1|) 9))) 
(((|RepeatedDoubling| |#1|) (CATEGORY |package| (SIGNATURE |double| (|#1| (|PositiveInteger|) |#1|))) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE + ($ $ $))))) (T |RepeatedDoubling|)) 
((|double| (*1 *2 *3 *2) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *1 (|RepeatedDoubling| *2)) (|ofCategory| *2 (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE + ($ $ $)))))))) 
(CATEGORY |package| (SIGNATURE |double| (|#1| (|PositiveInteger|) |#1|))) 
((|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) 58)) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) 48)) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) 41)) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) 67)) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) 33)) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) 61)) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) 65))) 
(((|RadicalEigenPackage|) (CATEGORY |package| (SIGNATURE |radicalEigenvectors| ((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|)))))) (SIGNATURE |radicalEigenvector| ((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|)))))) (SIGNATURE |radicalEigenvalues| ((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|)))))) (SIGNATURE |eigenMatrix| ((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|)))))) (SIGNATURE |normalise| ((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|))))) (SIGNATURE |gramschmidt| ((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|)))))) (SIGNATURE |orthonormalBasis| ((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|)))))))) (T |RadicalEigenPackage|)) 
((|orthonormalBasis| (*1 *2 *3) (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|Matrix| (|Expression| (|Integer|))))) (|isDomain| *1 (|RadicalEigenPackage|)))) (|gramschmidt| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|Matrix| (|Expression| (|Integer|))))) (|isDomain| *1 (|RadicalEigenPackage|)))) (|normalise| (*1 *2 *2) (AND (|isDomain| *2 (|Matrix| (|Expression| (|Integer|)))) (|isDomain| *1 (|RadicalEigenPackage|)))) (|eigenMatrix| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|Matrix| (|Expression| (|Integer|)))) (|isDomain| *1 (|RadicalEigenPackage|)))) (|radicalEigenvalues| (*1 *2 *3) (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|Expression| (|Integer|)))) (|isDomain| *1 (|RadicalEigenPackage|)))) (|radicalEigenvector| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|Matrix| (|Expression| (|Integer|))))) (|isDomain| *1 (|RadicalEigenPackage|)) (|isDomain| *3 (|Expression| (|Integer|))))) (|radicalEigenvectors| (*1 *2 *3) (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|)))))))) (|isDomain| *1 (|RadicalEigenPackage|))))) 
(CATEGORY |package| (SIGNATURE |radicalEigenvectors| ((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|)))))) (SIGNATURE |radicalEigenvector| ((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|)))))) (SIGNATURE |radicalEigenvalues| ((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|)))))) (SIGNATURE |eigenMatrix| ((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|)))))) (SIGNATURE |normalise| ((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|))))) (SIGNATURE |gramschmidt| ((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|)))))) (SIGNATURE |orthonormalBasis| ((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))))) 
((|expt| ((|#1| |#1| (|PositiveInteger|)) 9))) 
(((|RepeatedSquaring| |#1|) (CATEGORY |package| (SIGNATURE |expt| (|#1| |#1| (|PositiveInteger|)))) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE * ($ $ $))))) (T |RepeatedSquaring|)) 
((|expt| (*1 *2 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *1 (|RepeatedSquaring| *2)) (|ofCategory| *2 (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE * ($ $ $)))))))) 
(CATEGORY |package| (SIGNATURE |expt| (|#1| |#1| (|PositiveInteger|)))) 
((|coerce| ((|#1| (|Exit|)) 11) (((|Void|) |#1|) 9))) 
(((|ResolveLatticeCompletion| |#1|) (CATEGORY |package| (SIGNATURE |coerce| ((|Void|) |#1|)) (SIGNATURE |coerce| (|#1| (|Exit|)))) (|Type|)) (T |ResolveLatticeCompletion|)) 
((|coerce| (*1 *2 *3) (AND (|isDomain| *3 (|Exit|)) (|isDomain| *1 (|ResolveLatticeCompletion| *2)) (|ofCategory| *2 (|Type|)))) (|coerce| (*1 *2 *3) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ResolveLatticeCompletion| *3)) (|ofCategory| *3 (|Type|))))) 
(CATEGORY |package| (SIGNATURE |coerce| ((|Void|) |#1|)) (SIGNATURE |coerce| (|#1| (|Exit|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|reduce| (($ |#4|) 25)) (|recip| (((|Union| $ "failed") $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|lift| ((|#4| $) 27)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 46) (($ (|Integer|)) NIL) (($ |#1|) NIL) (($ |#4|) 26)) (|characteristic| (((|NonNegativeInteger|)) 43)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 21 T CONST)) (|One| (($) 23 T CONST)) (= (((|Boolean|) $ $) 40)) (- (($ $) 31) (($ $ $) NIL)) (+ (($ $ $) 29)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 36) (($ $ $) 33) (($ |#1| $) 38) (($ $ |#1|) NIL))) 
(((|ResidueRing| |#1| |#2| |#3| |#4| |#5|) (|Join| (|CommutativeRing|) (|Algebra| |#1|) (CATEGORY |domain| (SIGNATURE |reduce| ($ |#4|)) (SIGNATURE |coerce| ($ |#4|)) (SIGNATURE |lift| (|#4| $)))) (|Field|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|) (|List| |#4|)) (T |ResidueRing|)) 
((|reduce| (*1 *1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|ResidueRing| *3 *4 *5 *2 *6)) (|ofCategory| *2 (|PolynomialCategory| *3 *4 *5)) (|ofType| *6 (|List| *2)))) (|coerce| (*1 *1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|ResidueRing| *3 *4 *5 *2 *6)) (|ofCategory| *2 (|PolynomialCategory| *3 *4 *5)) (|ofType| *6 (|List| *2)))) (|lift| (*1 *2 *1) (AND (|ofCategory| *2 (|PolynomialCategory| *3 *4 *5)) (|isDomain| *1 (|ResidueRing| *3 *4 *5 *2 *6)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofType| *6 (|List| *2))))) 
(|Join| (|CommutativeRing|) (|Algebra| |#1|) (CATEGORY |domain| (SIGNATURE |reduce| ($ |#4|)) (SIGNATURE |coerce| ($ |#4|)) (SIGNATURE |lift| (|#4| $)))) 
((~= (((|Boolean|) $ $) NIL (OR (|has| (|Any|) (|SetCategory|)) (|has| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|SetCategory|))))) (|table| (($) NIL) (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))))) NIL)) (|swap!| (((|Void|) $ (|Symbol|) (|Symbol|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|showScalarValues| (((|Boolean|) (|Boolean|)) 39)) (|showArrayValues| (((|Boolean|) (|Boolean|)) 38)) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) NIL)) (|select!| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|)))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|select| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|)))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|search| (((|Union| (|Any|) "failed") (|Symbol|) $) NIL)) (|sample| (($) NIL T CONST)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|SetCategory|))))) (|remove!| (($ (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|)))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| (|Any|) "failed") (|Symbol|) $) NIL)) (|remove| (($ (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|SetCategory|)))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|)))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| (((|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|Mapping| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|)))) $ (|Record| (|:| |key| (|Symbol|)) (|:| 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((|factor| (((|Factored| |#1|) |#1|) 31))) 
(((|RationalFunctionFactor| |#1|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#1|) |#1|))) (|UnivariatePolynomialCategory| (|Fraction| (|Polynomial| (|Integer|))))) (T |RationalFunctionFactor|)) 
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(CATEGORY |package| (SIGNATURE |factorFraction| ((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))))) 
((|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) 15)) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) 22)) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) 24)) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) 18)) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) 29) (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) 31) (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) 26) (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) 27)) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) 11))) 
(((|RationalFunction| |#1|) (CATEGORY |package| (SIGNATURE |variables| ((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|)))) (SIGNATURE |mainVariable| ((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|)))) (SIGNATURE |univariate| ((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |multivariate| ((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|))) (SIGNATURE |eval| ((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)))) (SIGNATURE |eval| ((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |eval| ((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |eval| ((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))))) (SIGNATURE |coerce| ((|Fraction| (|Polynomial| |#1|)) |#1|))) (|IntegralDomain|)) (T |RationalFunction|)) 
((|coerce| (*1 *2 *3) (AND (|isDomain| *2 (|Fraction| (|Polynomial| *3))) (|isDomain| *1 (|RationalFunction| *3)) (|ofCategory| *3 (|IntegralDomain|)))) (|eval| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| (|Equation| (|Fraction| (|Polynomial| *4))))) (|isDomain| *2 (|Fraction| (|Polynomial| *4))) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *1 (|RationalFunction| *4)))) (|eval| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Equation| (|Fraction| (|Polynomial| *4)))) (|isDomain| *2 (|Fraction| (|Polynomial| *4))) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *1 (|RationalFunction| *4)))) (|eval| (*1 *2 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Symbol|))) (|isDomain| *4 (|List| (|Fraction| (|Polynomial| *5)))) (|isDomain| *2 (|Fraction| (|Polynomial| *5))) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *1 (|RationalFunction| *5)))) (|eval| (*1 *2 *2 *3 *2) (AND (|isDomain| *2 (|Fraction| (|Polynomial| *4))) (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *1 (|RationalFunction| *4)))) (|multivariate| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| *5))))) (|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Fraction| (|Polynomial| *5))) (|isDomain| *1 (|RationalFunction| *5)) (|ofCategory| *5 (|IntegralDomain|)))) (|univariate| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| *5))))) (|isDomain| *1 (|RationalFunction| *5)) (|isDomain| *3 (|Fraction| (|Polynomial| *5))))) (|mainVariable| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|Fraction| (|Polynomial| *4))) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|RationalFunction| *4)))) (|variables| (*1 *2 *3) (AND (|isDomain| *3 (|Fraction| (|Polynomial| *4))) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *1 (|RationalFunction| *4))))) 
(CATEGORY |package| (SIGNATURE |variables| ((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|)))) (SIGNATURE |mainVariable| ((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|)))) (SIGNATURE |univariate| ((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |multivariate| ((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|))) (SIGNATURE |eval| ((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)))) (SIGNATURE |eval| ((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |eval| ((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |eval| ((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))))) (SIGNATURE |coerce| ((|Fraction| (|Polynomial| |#1|)) |#1|))) 
((|setFoundZeroes| (((|List| |#1|) (|List| |#1|)) 45)) (|foundZeroes| (((|List| |#1|)) 9)) (|distinguishedRootsOf| (((|Record| (|:| |zeros| (|List| |#1|)) (|:| |extDegree| (|Integer|))) (|SparseUnivariatePolynomial| |#1|) |#1|) 19)) (|distinguishedCommonRootsOf| (((|Record| (|:| |zeros| (|List| |#1|)) (|:| |extDegree| (|Integer|))) (|List| (|SparseUnivariatePolynomial| |#1|)) |#1|) 37))) 
(((|RootsFindingPackage| |#1|) (CATEGORY |package| (SIGNATURE |distinguishedRootsOf| ((|Record| (|:| |zeros| (|List| |#1|)) (|:| |extDegree| (|Integer|))) (|SparseUnivariatePolynomial| |#1|) |#1|)) (SIGNATURE |distinguishedCommonRootsOf| ((|Record| (|:| |zeros| (|List| |#1|)) (|:| |extDegree| (|Integer|))) (|List| (|SparseUnivariatePolynomial| |#1|)) |#1|)) (SIGNATURE |foundZeroes| ((|List| |#1|))) (SIGNATURE |setFoundZeroes| ((|List| |#1|) (|List| |#1|)))) (|Field|)) (T |RootsFindingPackage|)) 
((|setFoundZeroes| (*1 *2 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|RootsFindingPackage| *3)))) (|foundZeroes| (*1 *2) (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|RootsFindingPackage| *3)) (|ofCategory| *3 (|Field|)))) (|distinguishedCommonRootsOf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|SparseUnivariatePolynomial| *4))) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|Record| (|:| |zeros| (|List| *4)) (|:| |extDegree| (|Integer|)))) (|isDomain| *1 (|RootsFindingPackage| *4)))) (|distinguishedRootsOf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|Record| (|:| |zeros| (|List| *4)) (|:| |extDegree| (|Integer|)))) (|isDomain| *1 (|RootsFindingPackage| *4))))) 
(CATEGORY |package| (SIGNATURE |distinguishedRootsOf| ((|Record| (|:| |zeros| (|List| |#1|)) (|:| |extDegree| (|Integer|))) (|SparseUnivariatePolynomial| |#1|) |#1|)) (SIGNATURE |distinguishedCommonRootsOf| ((|Record| (|:| |zeros| (|List| |#1|)) (|:| |extDegree| (|Integer|))) (|List| (|SparseUnivariatePolynomial| |#1|)) |#1|)) (SIGNATURE |foundZeroes| ((|List| |#1|))) (SIGNATURE |setFoundZeroes| ((|List| |#1|) (|List| |#1|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) NIL)) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) NIL) (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) NIL) (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) NIL)) (|variables| (((|List| (|OrderedVariableList| |#2|)) $) NIL)) (|trivialIdeal?| (((|Boolean|) $) NIL)) (|triangular?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|stronglyReduced?| (((|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL) (((|Boolean|) $) NIL)) (|stronglyReduce| (((|NewSparseMultivariatePolynomial| |#1| 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(|has| |#1| (|IntegralDomain|)))) (|roughBase?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|rewriteSetWithReduction| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $ (|Mapping| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Mapping| (|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) NIL)) (|rewriteIdealWithRemainder| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL (|has| |#1| (|IntegralDomain|)))) (|rewriteIdealWithHeadRemainder| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL (|has| |#1| (|IntegralDomain|)))) (|retractIfCan| (((|Union| $ "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) NIL)) (|retract| (($ (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) NIL)) (|rest| (((|Union| $ "failed") $) NIL)) (|removeZero| (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|SetCategory|))))) (|remove| (($ (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|SetCategory|)))) (($ (|Mapping| (|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|:| |den| |#1|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|reduced?| (((|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $ (|Mapping| (|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) NIL)) (|reduceByQuasiMonic| (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL)) (|reduce| (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|Mapping| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $ (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|SetCategory|)))) (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|Mapping| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $ (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|Mapping| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $ (|Mapping| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Mapping| (|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) NIL)) (|quasiComponent| (((|Record| (|:| |close| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|:| |open| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))))) $) NIL)) (|purelyTranscendental?| (((|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL)) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL)) (|purelyAlgebraic?| (((|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL) (((|Boolean|) $) NIL)) (|parts| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|normalized?| (((|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL) (((|Boolean|) $) NIL)) (|mvar| (((|OrderedVariableList| |#2|) $) NIL)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|SetCategory|))))) (|map!| (($ (|Mapping| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL)) (|mainVariables| (((|List| (|OrderedVariableList| |#2|)) $) NIL)) (|mainVariable?| (((|Boolean|) (|OrderedVariableList| |#2|) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL)) (|lastSubResultantElseSplit| (((|Union| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|List| $)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL)) (|lastSubResultant| (((|List| (|Record| (|:| |val| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|:| |tower| $))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL)) (|last| (((|Union| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) "failed") $) NIL)) (|invertibleSet| (((|List| $) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL)) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL)) (|invertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL) (((|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL)) (|intersect| (((|List| $) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL) (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL) (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| $)) NIL) (((|List| $) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|List| $)) NIL)) (|internalAugment| (($ (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL) (($ (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL)) (|initials| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL)) (|initiallyReduced?| (((|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL) (((|Boolean|) $) NIL)) (|initiallyReduce| (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL)) (|infRittWu?| (((|Boolean|) $ $) NIL)) (|headRemainder| (((|Record| (|:| |num| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|:| |den| |#1|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|headReduced?| (((|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL) (((|Boolean|) $) NIL)) (|headReduce| (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|first| (((|Union| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) "failed") $) NIL)) (|find| (((|Union| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) "failed") (|Mapping| (|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL)) (|extendIfCan| (((|Union| $ "failed") $ (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) NIL)) (|extend| (($ $ (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) NIL) (((|List| $) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL) (((|List| $) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|List| $)) NIL) (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL) (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| $)) NIL)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) NIL (AND (|has| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|Evalable| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|has| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|SetCategory|)))) (($ $ (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) NIL (AND (|has| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|Evalable| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|has| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|SetCategory|)))) (($ $ (|Equation| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) NIL (AND (|has| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|Evalable| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|has| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|SetCategory|)))) (($ $ (|List| (|Equation| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))))) NIL (AND (|has| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|Evalable| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|has| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|degree| (((|NonNegativeInteger|) $) NIL)) (|count| (((|NonNegativeInteger|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|SetCategory|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) NIL (|has| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) NIL)) (|collectUpper| (($ $ (|OrderedVariableList| |#2|)) NIL)) (|collectUnder| (($ $ (|OrderedVariableList| |#2|)) NIL)) (|collectQuasiMonic| (($ $) NIL)) (|collect| (($ $ (|OrderedVariableList| |#2|)) NIL)) (|coerce| (((|OutputForm|) $) NIL) (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL)) (|coHeight| (((|NonNegativeInteger|) $) NIL (|has| (|OrderedVariableList| |#2|) (|Finite|)))) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Mapping| (|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) NIL) (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Mapping| (|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Mapping| (|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) NIL)) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))))) NIL)) (|augment| (((|List| $) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL) (((|List| $) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) (|List| $)) NIL) (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL) (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| $)) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|algebraicVariables| (((|List| (|OrderedVariableList| |#2|)) $) NIL)) (|algebraicCoefficients?| (((|Boolean|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)) $) NIL)) (|algebraic?| (((|Boolean|) (|OrderedVariableList| |#2|) $) NIL)) (= (((|Boolean|) $ $) NIL)) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|RegularChain| |#1| |#2|) (|Join| (|RegularTriangularSetCategory| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (CATEGORY |domain| (SIGNATURE |zeroSetSplit| ((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|))))) (|GcdDomain|) (|List| (|Symbol|))) (T |RegularChain|)) 
((|zeroSetSplit| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|List| (|NewSparseMultivariatePolynomial| *5 (|OrderedVariableList| *6)))) (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|)) (|ofType| *6 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|RegularChain| *5 *6))) (|isDomain| *1 (|RegularChain| *5 *6))))) 
(|Join| (|RegularTriangularSetCategory| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (CATEGORY |domain| (SIGNATURE |zeroSetSplit| ((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|))))) 
((|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) 33)) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) 30)) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) NIL)) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) NIL)) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) NIL))) 
(((|RandomIntegerDistributions|) (CATEGORY |package| (SIGNATURE |uniform| ((|Mapping| (|Integer|)) (|Segment| (|Integer|)))) (SIGNATURE |binomial| ((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|)) (SIGNATURE |poisson| ((|Mapping| (|Integer|)) |RationalNumber|)) (SIGNATURE |geometric| ((|Mapping| (|Integer|)) |RationalNumber|)) (SIGNATURE |ridHack1| ((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|))))) (T |RandomIntegerDistributions|)) 
((|ridHack1| (*1 *2 *2 *2 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|RandomIntegerDistributions|)))) (|geometric| (*1 *2 *3) (AND (|isDomain| *3 |RationalNumber|) (|isDomain| *2 (|Mapping| (|Integer|))) (|isDomain| *1 (|RandomIntegerDistributions|)))) (|poisson| (*1 *2 *3) (AND (|isDomain| *3 |RationalNumber|) (|isDomain| *2 (|Mapping| (|Integer|))) (|isDomain| *1 (|RandomIntegerDistributions|)))) (|binomial| (*1 *2 *3 *4) (AND (|isDomain| *4 |RationalNumber|) (|isDomain| *2 (|Mapping| (|Integer|))) (|isDomain| *1 (|RandomIntegerDistributions|)) (|isDomain| *3 (|Integer|)))) (|uniform| (*1 *2 *3) (AND (|isDomain| *3 (|Segment| (|Integer|))) (|isDomain| *2 (|Mapping| (|Integer|))) (|isDomain| *1 (|RandomIntegerDistributions|))))) 
(CATEGORY |package| (SIGNATURE |uniform| ((|Mapping| (|Integer|)) (|Segment| (|Integer|)))) (SIGNATURE |binomial| ((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|)) (SIGNATURE |poisson| ((|Mapping| (|Integer|)) |RationalNumber|)) (SIGNATURE |geometric| ((|Mapping| (|Integer|)) |RationalNumber|)) (SIGNATURE |ridHack1| ((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)))) 
((|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) 10))) 
(((|Ring&| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|Ring|)) (T |Ring&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|Ring|) (|Category|)) (T |Ring|)) 
((|characteristic| (*1 *2) (AND (|ofCategory| *1 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|Ring|))))) 
(|Join| (|Rng|) (|Monoid|) (|LeftModule| $) (CATEGORY |domain| (SIGNATURE |characteristic| ((|NonNegativeInteger|))) (SIGNATURE |coerce| ($ (|Integer|))) (ATTRIBUTE |unitsKnown|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|interpolate| (((|Fraction| (|Polynomial| |#2|)) (|List| |#2|) (|List| |#2|) (|NonNegativeInteger|) (|NonNegativeInteger|)) 45))) 
(((|RationalInterpolation| |#1| |#2|) (CATEGORY |package| (SIGNATURE |interpolate| ((|Fraction| (|Polynomial| |#2|)) (|List| |#2|) (|List| |#2|) (|NonNegativeInteger|) (|NonNegativeInteger|)))) (|Symbol|) (|Field|)) (T |RationalInterpolation|)) 
((|interpolate| (*1 *2 *3 *3 *4 *4) (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *6 (|Field|)) (|isDomain| *2 (|Fraction| (|Polynomial| *6))) (|isDomain| *1 (|RationalInterpolation| *5 *6)) (|ofType| *5 (|Symbol|))))) 
(CATEGORY |package| (SIGNATURE |interpolate| ((|Fraction| (|Polynomial| |#2|)) (|List| |#2|) (|List| |#2|) (|NonNegativeInteger|) (|NonNegativeInteger|)))) 
((|symmetric?| (((|Boolean|) $) 27)) (|square?| (((|Boolean|) $) 16)) (|nrows| (((|NonNegativeInteger|) $) 13)) (|ncols| (((|NonNegativeInteger|) $) 14)) (|diagonal?| (((|Boolean|) $) 25)) (|antisymmetric?| (((|Boolean|) $) 29))) 
(((|RectangularMatrixCategory&| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |domain| (SIGNATURE |ncols| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |nrows| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |antisymmetric?| ((|Boolean|) |#1|)) (SIGNATURE |symmetric?| ((|Boolean|) |#1|)) (SIGNATURE |diagonal?| ((|Boolean|) |#1|)) (SIGNATURE |square?| ((|Boolean|) |#1|))) (|RectangularMatrixCategory| |#2| |#3| |#4| |#5| |#6|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Ring|) (|DirectProductCategory| |#3| |#4|) (|DirectProductCategory| |#2| |#4|)) (T |RectangularMatrixCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |ncols| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |nrows| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |antisymmetric?| ((|Boolean|) |#1|)) (SIGNATURE |symmetric?| ((|Boolean|) |#1|)) (SIGNATURE |diagonal?| ((|Boolean|) |#1|)) (SIGNATURE |square?| ((|Boolean|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|symmetric?| (((|Boolean|) $) 48)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|square?| (((|Boolean|) $) 50)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 58)) (|sample| (($) 16 T CONST)) (|rowEchelon| (($ $) 31 (|has| |#3| (|EuclideanDomain|)))) (|row| ((|#4| $ (|Integer|)) 36)) (|rank| (((|NonNegativeInteger|) $) 30 (|has| |#3| (|IntegralDomain|)))) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) 38)) (|parts| (((|List| |#3|) $) 65 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nullity| (((|NonNegativeInteger|) $) 29 (|has| |#3| (|IntegralDomain|)))) (|nullSpace| (((|List| |#5|) $) 28 (|has| |#3| (|IntegralDomain|)))) (|nrows| (((|NonNegativeInteger|) $) 42)) (|ncols| (((|NonNegativeInteger|) $) 41)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 57)) (|minRowIndex| (((|Integer|) $) 46)) (|minColIndex| (((|Integer|) $) 44)) (|members| (((|List| |#3|) $) 66 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#3| $) 68 (AND (|has| |#3| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|maxRowIndex| (((|Integer|) $) 45)) (|maxColIndex| (((|Integer|) $) 43)) (|matrix| (($ (|List| (|List| |#3|))) 51)) (|map!| (($ (|Mapping| |#3| |#3|) $) 61 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#3| |#3|) $) 60) (($ (|Mapping| |#3| |#3| |#3|) $ $) 34)) (|listOfLists| (((|List| (|List| |#3|)) $) 40)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 56)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|exquo| (((|Union| $ "failed") $ |#3|) 33 (|has| |#3| (|IntegralDomain|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#3|) $) 63 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| |#3|) (|List| |#3|)) 72 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|)))) (($ $ |#3| |#3|) 71 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|)))) (($ $ (|Equation| |#3|)) 70 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|)))) (($ $ (|List| (|Equation| |#3|))) 69 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 52)) (|empty?| (((|Boolean|) $) 55)) (|empty| (($) 54)) (|elt| ((|#3| $ (|Integer|) (|Integer|)) 39) ((|#3| $ (|Integer|) (|Integer|) |#3|) 37)) (|diagonal?| (((|Boolean|) $) 49)) (|count| (((|NonNegativeInteger|) |#3| $) 67 (AND (|has| |#3| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#3|) $) 64 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) 53)) (|column| ((|#5| $ (|Integer|)) 35)) (|coerce| (((|OutputForm|) $) 11)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#3|) $) 62 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|antisymmetric?| (((|Boolean|) $) 47)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (/ (($ $ |#3|) 32 (|has| |#3| (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ |#3| $) 22) (($ $ |#3|) 24)) (|#| (((|NonNegativeInteger|) $) 59 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|RectangularMatrixCategory| |#1| |#2| |#3| |#4| |#5|) (|Category|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Ring|) (|DirectProductCategory| |t#2| |t#3|) (|DirectProductCategory| |t#1| |t#3|)) (T |RectangularMatrixCategory|)) 
((|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *5 *5)) (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)))) (|matrix| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|List| *5))) (|ofCategory| *5 (|Ring|)) (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)))) (|square?| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|Boolean|)))) (|diagonal?| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|Boolean|)))) (|symmetric?| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|Boolean|)))) (|antisymmetric?| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|Boolean|)))) (|minRowIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|Integer|)))) (|maxRowIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|Integer|)))) (|minColIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|Integer|)))) (|maxColIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|Integer|)))) (|nrows| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|NonNegativeInteger|)))) (|ncols| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|NonNegativeInteger|)))) (|listOfLists| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|List| (|List| *5))))) (|elt| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|RectangularMatrixCategory| *4 *5 *2 *6 *7)) (|ofCategory| *6 (|DirectProductCategory| *5 *2)) (|ofCategory| *7 (|DirectProductCategory| *4 *2)) (|ofCategory| *2 (|Ring|)))) (|qelt| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|RectangularMatrixCategory| *4 *5 *2 *6 *7)) (|ofCategory| *6 (|DirectProductCategory| *5 *2)) (|ofCategory| *7 (|DirectProductCategory| *4 *2)) (|ofCategory| *2 (|Ring|)))) (|elt| (*1 *2 *1 *3 *3 *2) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|RectangularMatrixCategory| *4 *5 *2 *6 *7)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *5 *2)) (|ofCategory| *7 (|DirectProductCategory| *4 *2)))) (|row| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|RectangularMatrixCategory| *4 *5 *6 *2 *7)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *7 (|DirectProductCategory| *4 *6)) (|ofCategory| *2 (|DirectProductCategory| *5 *6)))) (|column| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|RectangularMatrixCategory| *4 *5 *6 *7 *2)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *7 (|DirectProductCategory| *5 *6)) (|ofCategory| *2 (|DirectProductCategory| *4 *6)))) (|map| (*1 *1 *2 *1 *1) (AND (|isDomain| *2 (|Mapping| *5 *5 *5)) (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)))) (|exquo| (*1 *1 *1 *2) (|partial| AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *2 *5 *6)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *4 *2)) (|ofCategory| *6 (|DirectProductCategory| *3 *2)) (|ofCategory| *2 (|IntegralDomain|)))) (/ (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *2 *5 *6)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *4 *2)) (|ofCategory| *6 (|DirectProductCategory| *3 *2)) (|ofCategory| *2 (|Field|)))) (|rowEchelon| (*1 *1 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *2 *3 *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *3 *4)) (|ofCategory| *6 (|DirectProductCategory| *2 *4)) (|ofCategory| *4 (|EuclideanDomain|)))) (|rank| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|nullity| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|nullSpace| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|List| *7))))) 
(|Join| (|BiModule| |t#3| |t#3|) (|HomogeneousAggregate| |t#3|) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (IF (|has| |t#3| (|CommutativeRing|)) (ATTRIBUTE (|Module| |t#3|)) |noBranch|) (SIGNATURE |matrix| ($ (|List| (|List| |t#3|)))) (SIGNATURE |square?| ((|Boolean|) $)) (SIGNATURE |diagonal?| ((|Boolean|) $)) (SIGNATURE |symmetric?| ((|Boolean|) $)) (SIGNATURE |antisymmetric?| ((|Boolean|) $)) (SIGNATURE |minRowIndex| ((|Integer|) $)) (SIGNATURE |maxRowIndex| ((|Integer|) $)) (SIGNATURE |minColIndex| ((|Integer|) $)) (SIGNATURE |maxColIndex| ((|Integer|) $)) (SIGNATURE |nrows| ((|NonNegativeInteger|) $)) (SIGNATURE |ncols| ((|NonNegativeInteger|) $)) (SIGNATURE |listOfLists| ((|List| (|List| |t#3|)) $)) (SIGNATURE |elt| (|t#3| $ (|Integer|) (|Integer|))) (SIGNATURE |qelt| (|t#3| $ (|Integer|) (|Integer|))) (SIGNATURE |elt| (|t#3| $ (|Integer|) (|Integer|) |t#3|)) (SIGNATURE |row| (|t#4| $ (|Integer|))) (SIGNATURE |column| (|t#5| $ (|Integer|))) (SIGNATURE |map| ($ (|Mapping| |t#3| |t#3|) $)) (SIGNATURE |map| ($ (|Mapping| |t#3| |t#3| |t#3|) $ $)) (IF (|has| |t#3| (|IntegralDomain|)) (SIGNATURE |exquo| ((|Union| $ "failed") $ |t#3|)) |noBranch|) (IF (|has| |t#3| (|Field|)) (SIGNATURE / ($ $ |t#3|)) |noBranch|) (IF (|has| |t#3| (|EuclideanDomain|)) (SIGNATURE |rowEchelon| ($ $)) |noBranch|) (IF (|has| |t#3| (|IntegralDomain|)) (PROGN (SIGNATURE |rank| ((|NonNegativeInteger|) $)) (SIGNATURE |nullity| ((|NonNegativeInteger|) $)) (SIGNATURE |nullSpace| ((|List| |t#5|) $))) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Aggregate|) . T) ((|BasicType|) . T) ((|BiModule| |#3| |#3|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Evalable| |#3|) AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|))) ((|HomogeneousAggregate| |#3|) . T) ((|InnerEvalable| |#3| |#3|) AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|))) ((|LeftModule| |#3|) . T) ((|Module| |#3|) |has| |#3| (|CommutativeRing|)) ((|RightModule| |#3|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|symmetric?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|square?| (((|Boolean|) $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|sample| (($) NIL T CONST)) (|rowEchelon| (($ $) 40 (|has| |#3| (|EuclideanDomain|)))) (|row| (((|DirectProduct| |#2| |#3|) $ (|Integer|)) 29)) (|rectangularMatrix| (($ (|Matrix| |#3|)) 38)) (|rank| (((|NonNegativeInteger|) $) 42 (|has| |#3| (|IntegralDomain|)))) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) NIL)) (|parts| (((|List| |#3|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nullity| (((|NonNegativeInteger|) $) 44 (|has| |#3| (|IntegralDomain|)))) (|nullSpace| (((|List| (|DirectProduct| |#1| |#3|)) $) 48 (|has| |#3| (|IntegralDomain|)))) (|nrows| (((|NonNegativeInteger|) $) NIL)) (|ncols| (((|NonNegativeInteger|) $) NIL)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minRowIndex| (((|Integer|) $) NIL)) (|minColIndex| (((|Integer|) $) NIL)) (|members| (((|List| |#3|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#3| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#3| (|SetCategory|))))) (|maxRowIndex| (((|Integer|) $) NIL)) (|maxColIndex| (((|Integer|) $) NIL)) (|matrix| (($ (|List| (|List| |#3|))) 24)) (|map!| (($ (|Mapping| |#3| |#3|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#3| |#3|) $) NIL) (($ (|Mapping| |#3| |#3| |#3|) $ $) NIL)) (|listOfLists| (((|List| (|List| |#3|)) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|exquo| (((|Union| $ "failed") $ |#3|) NIL (|has| |#3| (|IntegralDomain|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#3|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| |#3|) (|List| |#3|)) NIL (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|)))) (($ $ |#3| |#3|) NIL (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|)))) (($ $ (|Equation| |#3|)) NIL (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|)))) (($ $ (|List| (|Equation| |#3|))) NIL (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#3| $ (|Integer|) (|Integer|)) NIL) ((|#3| $ (|Integer|) (|Integer|) |#3|) NIL)) (|dimension| (((|CardinalNumber|)) 51 (|has| |#3| (|Field|)))) (|diagonal?| (((|Boolean|) $) NIL)) (|count| (((|NonNegativeInteger|) |#3| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#3| (|SetCategory|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#3|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) 60 (|has| |#3| (|ConvertibleTo| (|InputForm|))))) (|column| (((|DirectProduct| |#1| |#3|) $ (|Integer|)) 33)) (|coerce| (((|OutputForm|) $) 16) (((|Matrix| |#3|) $) 35)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#3|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|antisymmetric?| (((|Boolean|) $) NIL)) (|Zero| (($) 13 T CONST)) (= (((|Boolean|) $ $) NIL)) (/ (($ $ |#3|) NIL (|has| |#3| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ |#3| $) NIL) (($ $ |#3|) NIL)) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|RectangularMatrix| |#1| |#2| |#3|) (|Join| (|RectangularMatrixCategory| |#1| |#2| |#3| (|DirectProduct| |#2| |#3|) (|DirectProduct| |#1| |#3|)) (|CoercibleTo| (|Matrix| |#3|)) (CATEGORY |domain| (IF (|has| |#3| (|Field|)) (ATTRIBUTE (|VectorSpace| |#3|)) |noBranch|) (IF (|has| |#3| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |noBranch|) (SIGNATURE |rectangularMatrix| ($ (|Matrix| |#3|))) (SIGNATURE |coerce| ((|Matrix| |#3|) $)))) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Ring|)) (T |RectangularMatrix|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Matrix| *5)) (|isDomain| *1 (|RectangularMatrix| *3 *4 *5)) (|ofType| *3 (|NonNegativeInteger|)) (|ofType| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|Ring|)))) (|rectangularMatrix| (*1 *1 *2) (AND (|isDomain| *2 (|Matrix| *5)) (|ofCategory| *5 (|Ring|)) (|isDomain| *1 (|RectangularMatrix| *3 *4 *5)) (|ofType| *3 (|NonNegativeInteger|)) (|ofType| *4 (|NonNegativeInteger|))))) 
(|Join| (|RectangularMatrixCategory| |#1| |#2| |#3| (|DirectProduct| |#2| |#3|) (|DirectProduct| |#1| |#3|)) (|CoercibleTo| (|Matrix| |#3|)) (CATEGORY |domain| (IF (|has| |#3| (|Field|)) (ATTRIBUTE (|VectorSpace| |#3|)) |noBranch|) (IF (|has| |#3| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |noBranch|) (SIGNATURE |rectangularMatrix| ($ (|Matrix| |#3|))) (SIGNATURE |coerce| ((|Matrix| |#3|) $)))) 
((|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) 34)) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) 32))) 
(((|RectangularMatrixCategoryFunctions2| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8| |#9| |#10|) (CATEGORY |package| (SIGNATURE |map| (|#10| (|Mapping| |#7| |#3|) |#6|)) (SIGNATURE |reduce| (|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|))) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Ring|) (|DirectProductCategory| |#2| |#3|) (|DirectProductCategory| |#1| |#3|) (|RectangularMatrixCategory| |#1| |#2| |#3| |#4| |#5|) (|Ring|) (|DirectProductCategory| |#2| |#7|) (|DirectProductCategory| |#1| |#7|) (|RectangularMatrixCategory| |#1| |#2| |#7| |#8| |#9|)) (T |RectangularMatrixCategoryFunctions2|)) 
((|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *7 *2)) (|ofCategory| *7 (|Ring|)) (|ofCategory| *2 (|Ring|)) (|ofType| *5 (|NonNegativeInteger|)) (|ofType| *6 (|NonNegativeInteger|)) (|ofCategory| *8 (|DirectProductCategory| *6 *7)) (|ofCategory| *9 (|DirectProductCategory| *5 *7)) (|ofCategory| *10 (|DirectProductCategory| *6 *2)) (|ofCategory| *11 (|DirectProductCategory| *5 *2)) (|isDomain| *1 (|RectangularMatrixCategoryFunctions2| *5 *6 *7 *8 *9 *4 *2 *10 *11 *12)) (|ofCategory| *4 (|RectangularMatrixCategory| *5 *6 *7 *8 *9)) (|ofCategory| *12 (|RectangularMatrixCategory| *5 *6 *2 *10 *11)))) (|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *10 *7)) (|ofCategory| *7 (|Ring|)) (|ofCategory| *10 (|Ring|)) (|ofType| *5 (|NonNegativeInteger|)) (|ofType| *6 (|NonNegativeInteger|)) (|ofCategory| *8 (|DirectProductCategory| *6 *7)) (|ofCategory| *9 (|DirectProductCategory| *5 *7)) (|ofCategory| *2 (|RectangularMatrixCategory| *5 *6 *10 *11 *12)) (|isDomain| *1 (|RectangularMatrixCategoryFunctions2| *5 *6 *7 *8 *9 *4 *10 *11 *12 *2)) (|ofCategory| *4 (|RectangularMatrixCategory| *5 *6 *7 *8 *9)) (|ofCategory| *11 (|DirectProductCategory| *6 *10)) (|ofCategory| *12 (|DirectProductCategory| *5 *10))))) 
(CATEGORY |package| (SIGNATURE |map| (|#10| (|Mapping| |#7| |#3|) |#6|)) (SIGNATURE |reduce| (|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ |#1|) 22))) 
(((|RightModule| |#1|) (|Category|) (|Rng|)) (T |RightModule|)) 
((* (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RightModule| *2)) (|ofCategory| *2 (|Rng|))))) 
(|Join| (|AbelianGroup|) (CATEGORY |domain| (SIGNATURE * ($ $ |t#1|)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (^ (($ $ (|PositiveInteger|)) 25)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|Rng|) (|Category|)) (T |Rng|)) 
NIL 
(|Join| (|AbelianGroup|) (|SemiGroup|)) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|truncate| (($ $) 16)) (|round| (($ $) 22)) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) 49)) (|norm| (($ $) 24)) (|fractionPart| (($ $) 11)) (|floor| (($ $) 38)) (|convert| (((|Float|) $) NIL) (((|DoubleFloat|) $) NIL) (((|Pattern| (|Float|)) $) 33)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL) (($ (|Fraction| (|Integer|))) 28) (($ (|Integer|)) NIL) (($ (|Fraction| (|Integer|))) 28)) (|characteristic| (((|NonNegativeInteger|)) 8)) (|ceiling| (($ $) 39))) 
(((|RealNumberSystem&| |#1|) (CATEGORY |domain| (SIGNATURE |round| (|#1| |#1|)) (SIGNATURE |truncate| (|#1| |#1|)) (SIGNATURE |fractionPart| (|#1| |#1|)) (SIGNATURE |floor| (|#1| |#1|)) (SIGNATURE |ceiling| (|#1| |#1|)) (SIGNATURE |norm| (|#1| |#1|)) (SIGNATURE |patternMatch| ((|PatternMatchResult| (|Float|) |#1|) |#1| (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) |#1|))) (SIGNATURE |convert| ((|Pattern| (|Float|)) |#1|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |convert| ((|DoubleFloat|) |#1|)) (SIGNATURE |convert| ((|Float|) |#1|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |coerce| (|#1| |#1|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |characteristic| ((|NonNegativeInteger|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|RealNumberSystem|)) (T |RealNumberSystem&|)) 
((|characteristic| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|RealNumberSystem&| *3)) (|ofCategory| *3 (|RealNumberSystem|))))) 
(CATEGORY |domain| (SIGNATURE |round| (|#1| |#1|)) (SIGNATURE |truncate| (|#1| |#1|)) (SIGNATURE |fractionPart| (|#1| |#1|)) (SIGNATURE |floor| (|#1| |#1|)) (SIGNATURE |ceiling| (|#1| |#1|)) (SIGNATURE |norm| (|#1| |#1|)) (SIGNATURE |patternMatch| ((|PatternMatchResult| (|Float|) |#1|) |#1| (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) |#1|))) (SIGNATURE |convert| ((|Pattern| (|Float|)) |#1|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |convert| ((|DoubleFloat|) |#1|)) (SIGNATURE |convert| ((|Float|) |#1|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |coerce| (|#1| |#1|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |characteristic| ((|NonNegativeInteger|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|wholePart| (((|Integer|) $) 87)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|truncate| (($ $) 85)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 73)) (|squareFree| (((|Factored| $) $) 72)) (|sqrt| (($ $) 95)) (|sizeLess?| (((|Boolean|) $ $) 58)) (|sign| (((|Integer|) $) 112)) (|sample| (($) 16 T CONST)) (|round| (($ $) 84)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 100) (((|Union| (|Fraction| (|Integer|)) "failed") $) 97)) (|retract| (((|Integer|) $) 99) (((|Fraction| (|Integer|)) $) 96)) (|rem| (($ $ $) 54)) (|recip| (((|Union| $ "failed") $) 33)) (|quo| (($ $ $) 55)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 50)) (|prime?| (((|Boolean|) $) 71)) (|positive?| (((|Boolean|) $) 110)) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) 91)) (|one?| (((|Boolean|) $) 30)) (|nthRoot| (($ $ (|Integer|)) 94)) (|norm| (($ $) 90)) (|negative?| (((|Boolean|) $) 111)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 51)) (|min| (($ $ $) 109)) (|max| (($ $ $) 108)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 70)) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|fractionPart| (($ $) 86)) (|floor| (($ $) 88)) (|factor| (((|Factored| $) $) 74)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 53) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 52)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 49)) (|euclideanSize| (((|NonNegativeInteger|) $) 57)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 56)) (|convert| (((|Float|) $) 103) (((|DoubleFloat|) $) 102) (((|Pattern| (|Float|)) $) 92)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42) (($ (|Fraction| (|Integer|))) 65) (($ (|Integer|)) 101) (($ (|Fraction| (|Integer|))) 98)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|ceiling| (($ $) 89)) (|associates?| (((|Boolean|) $ $) 38)) (|abs| (($ $) 113)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 69)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (>= (((|Boolean|) $ $) 106)) (> (((|Boolean|) $ $) 105)) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 107)) (< (((|Boolean|) $ $) 104)) (/ (($ $ $) 64)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 68) (($ $ (|Fraction| (|Integer|))) 93)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ (|Fraction| (|Integer|))) 67) (($ (|Fraction| (|Integer|)) $) 66))) 
(((|RealNumberSystem|) (|Category|)) (T |RealNumberSystem|)) 
((|abs| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|))) (|norm| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|))) (|ceiling| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|))) (|floor| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|))) (|wholePart| (*1 *2 *1) (AND (|ofCategory| *1 (|RealNumberSystem|)) (|isDomain| *2 (|Integer|)))) (|fractionPart| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|))) (|truncate| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|))) (|round| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|)))) 
(|Join| (|Field|) (|OrderedRing|) (|RealConstant|) (|RetractableTo| (|Integer|)) (|RetractableTo| (|Fraction| (|Integer|))) (|RadicalCategory|) (|ConvertibleTo| (|Pattern| (|Float|))) (|PatternMatchable| (|Float|)) (|CharacteristicZero|) (CATEGORY |domain| (SIGNATURE |norm| ($ $)) (SIGNATURE |ceiling| ($ $)) (SIGNATURE |floor| ($ $)) (SIGNATURE |wholePart| ((|Integer|) $)) (SIGNATURE |fractionPart| ($ $)) (SIGNATURE |truncate| ($ $)) (SIGNATURE |round| ($ $)) (SIGNATURE |abs| ($ $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|DoubleFloat|)) . T) ((|ConvertibleTo| (|Float|)) . T) ((|ConvertibleTo| (|Pattern| (|Float|))) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| (|Fraction| (|Integer|))) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| (|Fraction| (|Integer|))) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|PatternMatchable| (|Float|)) . T) ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T) ((|RealConstant|) . T) ((|RetractableTo| (|Fraction| (|Integer|))) . T) ((|RetractableTo| (|Integer|)) . T) ((|RightModule| (|Fraction| (|Integer|))) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|UniqueFactorizationDomain|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) |#2| $) 23)) (|size| ((|#1| $) 10)) (|sign| (((|Integer|) |#2| $) 88)) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) 58)) (|right| ((|#1| $) 28)) (|relativeApprox| ((|#1| |#2| $ |#1|) 37)) (|refine| (($ $) 25)) (|recip| (((|Union| |#2| "failed") |#2| $) 87)) (|positive?| (((|Boolean|) |#2| $) NIL)) (|negative?| (((|Boolean|) |#2| $) NIL)) (|mightHaveRoots| (((|Boolean|) |#2| $) 24)) (|middle| ((|#1| $) 89)) (|left| ((|#1| $) 27)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|definingPolynomial| ((|#2| $) 79)) (|coerce| (((|OutputForm|) $) 71)) (|approximate| ((|#1| |#2| $ |#1|) 38)) (|allRootsOf| (((|List| $) |#2|) 60)) (= (((|Boolean|) $ $) 74))) 
(((|RightOpenIntervalRootCharacterization| |#1| |#2|) (|Join| (|RealRootCharacterizationCategory| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |left| (|#1| $)) (SIGNATURE |right| (|#1| $)) (SIGNATURE |size| (|#1| $)) (SIGNATURE |middle| (|#1| $)) (SIGNATURE |refine| ($ $)) (SIGNATURE |mightHaveRoots| ((|Boolean|) |#2| $)) (SIGNATURE |relativeApprox| (|#1| |#2| $ |#1|)))) (|Join| (|OrderedRing|) (|Field|)) (|UnivariatePolynomialCategory| |#1|)) (T |RightOpenIntervalRootCharacterization|)) 
((|relativeApprox| (*1 *2 *3 *1 *2) (AND (|ofCategory| *2 (|Join| (|OrderedRing|) (|Field|))) (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|left| (*1 *2 *1) (AND (|ofCategory| *2 (|Join| (|OrderedRing|) (|Field|))) (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|right| (*1 *2 *1) (AND (|ofCategory| *2 (|Join| (|OrderedRing|) (|Field|))) (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|size| (*1 *2 *1) (AND (|ofCategory| *2 (|Join| (|OrderedRing|) (|Field|))) (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|middle| (*1 *2 *1) (AND (|ofCategory| *2 (|Join| (|OrderedRing|) (|Field|))) (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|refine| (*1 *1 *1) (AND (|ofCategory| *2 (|Join| (|OrderedRing|) (|Field|))) (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|mightHaveRoots| (*1 *2 *3 *1) (AND (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(|Join| (|RealRootCharacterizationCategory| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |left| (|#1| $)) (SIGNATURE |right| (|#1| $)) (SIGNATURE |size| (|#1| $)) (SIGNATURE |middle| (|#1| $)) (SIGNATURE |refine| ($ $)) (SIGNATURE |mightHaveRoots| ((|Boolean|) |#2| $)) (SIGNATURE |relativeApprox| (|#1| |#2| $ |#1|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|symmetricRemainder| (($ $ $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|submod| (($ $ $ $) NIL)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sign| (((|Integer|) $) NIL)) (|shift| (($ $ $) NIL)) (|sample| (($) NIL T CONST)) (|roman| (($ (|Symbol|)) 10) (($ (|Integer|)) 7)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL)) (|retract| (((|Integer|) $) NIL)) (|rem| (($ $ $) NIL)) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| (|Integer|)) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL)) (|rational?| (((|Boolean|) $) NIL)) (|rational| (((|Fraction| (|Integer|)) $) NIL)) (|random| (($) NIL) (($ $) NIL)) (|quo| (($ $ $) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|powmod| (($ $ $ $) NIL)) (|positiveRemainder| (($ $ $) NIL)) (|positive?| (((|Boolean|) $) NIL)) (|permutation| (($ $ $) NIL)) (|patternMatch| (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL)) (|one?| (((|Boolean|) $) NIL)) (|odd?| (((|Boolean|) $) NIL)) (|nextItem| (((|Union| $ "failed") $) NIL)) (|negative?| (((|Boolean|) $) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|mulmod| (($ $ $ $) NIL)) (|min| (($ $ $) NIL)) (|max| (($ $ $) NIL)) (|mask| (($ $) NIL)) (|length| (($ $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|invmod| (($ $ $) NIL)) (|init| (($) NIL T CONST)) (|inc| (($ $) NIL)) (|hash| (((|SingleInteger|) $) NIL) (($ $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) NIL) (($ (|List| $)) NIL)) (|factorial| (($ $) NIL)) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|even?| (((|Boolean|) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|differentiate| (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (|dec| (($ $) NIL)) (|copy| (($ $) NIL)) (|convert| (((|Integer|) $) 16) (((|InputForm|) $) NIL) (((|Pattern| (|Integer|)) $) NIL) (((|Float|) $) NIL) (((|DoubleFloat|) $) NIL) (($ (|Symbol|)) 9)) (|coerce| (((|OutputForm|) $) 20) (($ (|Integer|)) 6) (($ $) NIL) (($ (|Integer|)) 6)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|bit?| (((|Boolean|) $ $) NIL)) (|binomial| (($ $ $) NIL)) (|base| (($) NIL)) (|associates?| (((|Boolean|) $ $) NIL)) (|addmod| (($ $ $ $) NIL)) (|abs| (($ $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) NIL)) (- (($ $) 19) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL))) 
(((|RomanNumeral|) (|Join| (|IntegerNumberSystem|) (CATEGORY |domain| (ATTRIBUTE |canonical|) (ATTRIBUTE |canonicalsClosed|) (ATTRIBUTE |noetherian|) (SIGNATURE |convert| ($ (|Symbol|))) (SIGNATURE |roman| ($ (|Symbol|))) (SIGNATURE |roman| ($ (|Integer|)))))) (T |RomanNumeral|)) 
((|convert| (*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|RomanNumeral|)))) (|roman| (*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|RomanNumeral|)))) (|roman| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|RomanNumeral|))))) 
(|Join| (|IntegerNumberSystem|) (CATEGORY |domain| (ATTRIBUTE |canonical|) (ATTRIBUTE |canonicalsClosed|) (ATTRIBUTE |noetherian|) (SIGNATURE |convert| ($ (|Symbol|))) (SIGNATURE |roman| ($ (|Symbol|))) (SIGNATURE |roman| ($ (|Integer|))))) 
((~= (((|Boolean|) $ $) NIL (OR (|has| (|Any|) (|SetCategory|)) (|has| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|SetCategory|))))) (|table| (($) NIL) (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))))) NIL)) (|swap!| (((|Void|) $ (|Symbol|) (|Symbol|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|showTheRoutinesTable| (($) 9)) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) NIL)) (|selectSumOfSquaresRoutines| (($ $) 23)) (|selectPDERoutines| (($ $) 21)) (|selectOptimizationRoutines| (($ $) 20)) (|selectODEIVPRoutines| (($ $) 22)) (|selectNonFiniteRoutines| (($ $) 25)) (|selectMultiDimensionalRoutines| (($ $) 26)) (|selectIntegrationRoutines| (($ $) 19)) (|selectFiniteRoutines| (($ $) 24)) (|select!| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|)))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|select| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|)))) $) 18 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|search| (((|Union| (|Any|) "failed") (|Symbol|) $) 34)) (|sample| (($) NIL T CONST)) (|routines| (($) 7)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|SetCategory|))))) (|remove!| (($ (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) $) 46 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|)))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| (|Any|) "failed") (|Symbol|) $) NIL)) (|remove| (($ (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|SetCategory|)))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|)))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| (((|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|Mapping| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|)))) $ (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|)))) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|SetCategory|)))) (((|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|Mapping| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|)))) $ (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|)))) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|Mapping| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|Any|))) 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(|Join| (|TableAggregate| (|Symbol|) (|Any|)) (CATEGORY |domain| (SIGNATURE |concat| ($ $ $)) (SIGNATURE |routines| ($)) (SIGNATURE |selectIntegrationRoutines| ($ $)) (SIGNATURE |selectOptimizationRoutines| ($ $)) (SIGNATURE |selectPDERoutines| ($ $)) (SIGNATURE |selectODEIVPRoutines| ($ $)) (SIGNATURE |selectFiniteRoutines| ($ $)) (SIGNATURE |selectSumOfSquaresRoutines| ($ $)) (SIGNATURE |selectNonFiniteRoutines| ($ $)) (SIGNATURE |selectMultiDimensionalRoutines| ($ $)) (SIGNATURE |changeThreshhold| ($ $ (|Symbol|) (|Float|))) (SIGNATURE |changeMeasure| ($ $ (|Symbol|) (|Float|))) (SIGNATURE |getMeasure| ((|Float|) $ (|Symbol|))) (SIGNATURE |getExplanations| ((|List| (|String|)) $ (|String|))) (SIGNATURE |deleteRoutine!| ($ $ (|Symbol|))) (SIGNATURE |showTheRoutinesTable| ($)) (SIGNATURE |recoverAfterFail| ((|Union| (|String|) "failed") $ (|String|) (|Integer|))) (ATTRIBUTE |finiteAggregate|))) 
((|tail| (($ $) 45)) (|supRittWu?| (((|Boolean|) $ $) 74)) (|retractIfCan| (((|Union| |#2| "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL) (((|Union| (|Integer|) "failed") $) NIL) (((|Union| |#4| "failed") $) NIL) (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) 226) (((|Union| $ "failed") (|Polynomial| (|Integer|))) 225) (((|Union| $ "failed") (|Polynomial| |#2|)) 228)) (|retract| ((|#2| $) NIL) (((|Fraction| (|Integer|)) $) NIL) (((|Integer|) $) NIL) ((|#4| $) NIL) (($ (|Polynomial| (|Fraction| (|Integer|)))) 214) (($ (|Polynomial| (|Integer|))) 210) (($ (|Polynomial| |#2|)) 230)) (|reductum| (($ $) NIL) (($ $ |#4|) 43)) (|reduced?| (((|Boolean|) $ $) 111) (((|Boolean|) $ (|List| $)) 112)) (|quasiMonic?| (((|Boolean|) $) 56)) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 106)) (|primitivePart!| (($ $) 137)) (|primPartElseUnitCanonical!| (($ $) 133)) (|primPartElseUnitCanonical| (($ $) 132)) (|prem| (($ $ $) 79) (($ $ $ |#4|) 84)) (|pquo| (($ $ $) 82) (($ $ $ |#4|) 86)) (|normalized?| (((|Boolean|) $ $) 120) (((|Boolean|) $ (|List| $)) 121)) (|mvar| ((|#4| $) 33)) (|monicModulo| (($ $ $) 109)) (|monic?| (((|Boolean|) $) 55)) (|mdeg| (((|NonNegativeInteger|) $) 35)) (|mainSquareFreePart| (($ $) 151)) (|mainPrimitivePart| (($ $) 148)) (|mainMonomials| (((|List| $) $) 68)) (|mainMonomial| (($ $) 57)) (|mainContent| (($ $) 144)) (|mainCoefficients| (((|List| $) $) 65)) (|leastMonomial| (($ $) 59)) (|leadingCoefficient| ((|#2| $) NIL) (($ $ |#4|) 38)) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) 110)) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) 107) (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) 108)) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) 103) (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) 104)) (|lazyPrem| (($ $ $) 89) (($ $ $ |#4|) 94)) (|lazyPquo| (($ $ $) 90) (($ $ $ |#4|) 95)) (|iteratedInitials| (((|List| $) $) 51)) (|initiallyReduced?| (((|Boolean|) $ $) 117) (((|Boolean|) $ (|List| $)) 118)) (|initiallyReduce| (($ $ $) 102)) (|init| (($ $) 37)) (|infRittWu?| (((|Boolean|) $ $) 72)) (|headReduced?| (((|Boolean|) $ $) 113) (((|Boolean|) $ (|List| $)) 115)) (|headReduce| (($ $ $) 100)) (|head| (($ $) 40)) (|gcd| ((|#2| |#2| $) 141) (($ (|List| $)) NIL) (($ $ $) NIL)) (|exactQuotient!| (($ $ |#2|) NIL) (($ $ $) 130)) (|exactQuotient| (($ $ |#2|) 125) (($ $ $) 128)) (|deepestTail| (($ $) 48)) (|deepestInitial| (($ $) 52)) (|convert| (((|Pattern| (|Float|)) $) NIL) (((|Pattern| (|Integer|)) $) NIL) (((|InputForm|) $) NIL) (($ (|Polynomial| (|Fraction| (|Integer|)))) 216) (($ (|Polynomial| (|Integer|))) 212) (($ (|Polynomial| |#2|)) 227) (((|String|) $) 249) (((|Polynomial| |#2|) $) 161)) (|coerce| (((|OutputForm|) $) 30) (($ (|Integer|)) NIL) (($ |#2|) NIL) (($ |#4|) NIL) (((|Polynomial| |#2|) $) 162) (($ (|Fraction| (|Integer|))) NIL) (($ $) NIL)) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) 71))) 
(((|RecursivePolynomialCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |coerce| (|#1| |#1|)) (SIGNATURE |gcd| (|#1| |#1| |#1|)) (SIGNATURE |gcd| (|#1| (|List| |#1|))) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |coerce| ((|Polynomial| |#2|) |#1|)) (SIGNATURE |convert| ((|Polynomial| |#2|) |#1|)) (SIGNATURE |convert| ((|String|) |#1|)) (SIGNATURE |mainSquareFreePart| (|#1| |#1|)) (SIGNATURE |mainPrimitivePart| (|#1| |#1|)) (SIGNATURE |mainContent| (|#1| |#1|)) (SIGNATURE |primitivePart!| (|#1| |#1|)) (SIGNATURE |gcd| (|#2| |#2| |#1|)) (SIGNATURE |exactQuotient!| (|#1| |#1| |#1|)) (SIGNATURE |exactQuotient| (|#1| |#1| |#1|)) (SIGNATURE |exactQuotient!| (|#1| |#1| |#2|)) (SIGNATURE |exactQuotient| (|#1| |#1| |#2|)) (SIGNATURE |primPartElseUnitCanonical!| (|#1| |#1|)) (SIGNATURE |primPartElseUnitCanonical| (|#1| |#1|)) (SIGNATURE |convert| (|#1| (|Polynomial| |#2|))) (SIGNATURE |retract| (|#1| (|Polynomial| |#2|))) (SIGNATURE |retractIfCan| ((|Union| |#1| "failed") (|Polynomial| |#2|))) (SIGNATURE |convert| (|#1| (|Polynomial| (|Integer|)))) (SIGNATURE |retract| (|#1| (|Polynomial| (|Integer|)))) (SIGNATURE |retractIfCan| ((|Union| |#1| "failed") (|Polynomial| (|Integer|)))) (SIGNATURE |convert| (|#1| (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |retract| (|#1| (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |retractIfCan| ((|Union| |#1| "failed") (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |initiallyReduce| (|#1| |#1| |#1|)) (SIGNATURE |headReduce| (|#1| |#1| |#1|)) (SIGNATURE |lazyResidueClass| ((|Record| (|:| |polnum| |#1|) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) |#1| |#1|)) (SIGNATURE |monicModulo| (|#1| |#1| |#1|)) (SIGNATURE |pseudoDivide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |lazyPseudoDivide| ((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1| |#4|)) (SIGNATURE |lazyPseudoDivide| ((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |lazyPremWithDefault| ((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| |#1|)) |#1| |#1| |#4|)) (SIGNATURE |lazyPremWithDefault| ((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |lazyPquo| (|#1| |#1| |#1| |#4|)) (SIGNATURE |lazyPrem| (|#1| |#1| |#1| |#4|)) (SIGNATURE |lazyPquo| (|#1| |#1| |#1|)) (SIGNATURE |lazyPrem| (|#1| |#1| |#1|)) (SIGNATURE |pquo| (|#1| |#1| |#1| |#4|)) (SIGNATURE |prem| (|#1| |#1| |#1| |#4|)) (SIGNATURE |pquo| (|#1| |#1| |#1|)) (SIGNATURE |prem| (|#1| |#1| |#1|)) (SIGNATURE |normalized?| ((|Boolean|) |#1| (|List| |#1|))) (SIGNATURE |normalized?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |initiallyReduced?| ((|Boolean|) |#1| (|List| |#1|))) (SIGNATURE |initiallyReduced?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |headReduced?| ((|Boolean|) |#1| (|List| |#1|))) (SIGNATURE |headReduced?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |reduced?| ((|Boolean|) |#1| (|List| |#1|))) (SIGNATURE |reduced?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |supRittWu?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |infRittWu?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |RittWuCompare| ((|Union| (|Boolean|) "failed") |#1| |#1|)) (SIGNATURE |mainMonomials| ((|List| |#1|) |#1|)) (SIGNATURE |mainCoefficients| ((|List| |#1|) |#1|)) (SIGNATURE |leastMonomial| (|#1| |#1|)) (SIGNATURE |mainMonomial| (|#1| |#1|)) (SIGNATURE |quasiMonic?| ((|Boolean|) |#1|)) (SIGNATURE |monic?| ((|Boolean|) |#1|)) (SIGNATURE |reductum| (|#1| |#1| |#4|)) (SIGNATURE |leadingCoefficient| (|#1| |#1| |#4|)) (SIGNATURE |deepestInitial| (|#1| |#1|)) (SIGNATURE |iteratedInitials| ((|List| |#1|) |#1|)) (SIGNATURE |deepestTail| (|#1| |#1|)) (SIGNATURE |tail| (|#1| |#1|)) (SIGNATURE |head| (|#1| |#1|)) (SIGNATURE |init| (|#1| |#1|)) (SIGNATURE |mdeg| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |mvar| (|#4| |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |convert| ((|Pattern| (|Integer|)) |#1|)) (SIGNATURE |convert| ((|Pattern| (|Float|)) |#1|)) (SIGNATURE |retract| (|#4| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#4| "failed") |#1|)) (SIGNATURE |coerce| (|#1| |#4|)) (SIGNATURE |leadingCoefficient| (|#2| |#1|)) (SIGNATURE |reductum| (|#1| |#1|)) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|RecursivePolynomialCategory| |#2| |#3| |#4|) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|)) (T |RecursivePolynomialCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |coerce| (|#1| |#1|)) (SIGNATURE |gcd| (|#1| |#1| |#1|)) (SIGNATURE |gcd| (|#1| (|List| |#1|))) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |coerce| ((|Polynomial| |#2|) |#1|)) (SIGNATURE |convert| ((|Polynomial| |#2|) |#1|)) (SIGNATURE |convert| ((|String|) |#1|)) (SIGNATURE |mainSquareFreePart| (|#1| |#1|)) (SIGNATURE |mainPrimitivePart| (|#1| |#1|)) (SIGNATURE |mainContent| (|#1| |#1|)) (SIGNATURE |primitivePart!| (|#1| |#1|)) (SIGNATURE |gcd| (|#2| |#2| |#1|)) (SIGNATURE |exactQuotient!| (|#1| |#1| |#1|)) (SIGNATURE |exactQuotient| (|#1| |#1| |#1|)) (SIGNATURE |exactQuotient!| (|#1| |#1| |#2|)) (SIGNATURE |exactQuotient| (|#1| |#1| |#2|)) (SIGNATURE |primPartElseUnitCanonical!| (|#1| |#1|)) (SIGNATURE |primPartElseUnitCanonical| (|#1| |#1|)) (SIGNATURE |convert| (|#1| (|Polynomial| |#2|))) (SIGNATURE |retract| (|#1| (|Polynomial| |#2|))) (SIGNATURE |retractIfCan| ((|Union| |#1| "failed") (|Polynomial| |#2|))) (SIGNATURE |convert| (|#1| (|Polynomial| (|Integer|)))) (SIGNATURE |retract| (|#1| (|Polynomial| (|Integer|)))) (SIGNATURE |retractIfCan| ((|Union| |#1| "failed") (|Polynomial| (|Integer|)))) (SIGNATURE |convert| (|#1| (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |retract| (|#1| (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |retractIfCan| ((|Union| |#1| "failed") (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |initiallyReduce| (|#1| |#1| |#1|)) (SIGNATURE |headReduce| (|#1| |#1| |#1|)) (SIGNATURE |lazyResidueClass| ((|Record| (|:| |polnum| |#1|) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) |#1| |#1|)) (SIGNATURE |monicModulo| (|#1| |#1| |#1|)) (SIGNATURE |pseudoDivide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |lazyPseudoDivide| ((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1| |#4|)) (SIGNATURE |lazyPseudoDivide| ((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |lazyPremWithDefault| ((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| |#1|)) |#1| |#1| |#4|)) (SIGNATURE |lazyPremWithDefault| ((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |lazyPquo| (|#1| |#1| |#1| |#4|)) (SIGNATURE |lazyPrem| (|#1| |#1| |#1| |#4|)) (SIGNATURE |lazyPquo| (|#1| |#1| |#1|)) (SIGNATURE |lazyPrem| (|#1| |#1| |#1|)) (SIGNATURE |pquo| (|#1| |#1| |#1| |#4|)) (SIGNATURE |prem| (|#1| |#1| |#1| |#4|)) (SIGNATURE |pquo| (|#1| |#1| |#1|)) (SIGNATURE |prem| (|#1| |#1| |#1|)) (SIGNATURE |normalized?| ((|Boolean|) |#1| (|List| |#1|))) (SIGNATURE |normalized?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |initiallyReduced?| ((|Boolean|) |#1| (|List| |#1|))) (SIGNATURE |initiallyReduced?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |headReduced?| ((|Boolean|) |#1| (|List| |#1|))) (SIGNATURE |headReduced?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |reduced?| ((|Boolean|) |#1| (|List| |#1|))) (SIGNATURE |reduced?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |supRittWu?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |infRittWu?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |RittWuCompare| ((|Union| (|Boolean|) "failed") |#1| |#1|)) (SIGNATURE |mainMonomials| ((|List| |#1|) |#1|)) (SIGNATURE |mainCoefficients| ((|List| |#1|) |#1|)) (SIGNATURE |leastMonomial| (|#1| |#1|)) (SIGNATURE |mainMonomial| (|#1| |#1|)) (SIGNATURE |quasiMonic?| ((|Boolean|) |#1|)) (SIGNATURE |monic?| ((|Boolean|) |#1|)) (SIGNATURE |reductum| (|#1| |#1| |#4|)) (SIGNATURE |leadingCoefficient| (|#1| |#1| |#4|)) (SIGNATURE |deepestInitial| (|#1| |#1|)) (SIGNATURE |iteratedInitials| ((|List| |#1|) |#1|)) (SIGNATURE |deepestTail| (|#1| |#1|)) (SIGNATURE |tail| (|#1| |#1|)) (SIGNATURE |head| (|#1| |#1|)) (SIGNATURE |init| (|#1| |#1|)) (SIGNATURE |mdeg| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |mvar| (|#4| |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |convert| ((|Pattern| (|Integer|)) |#1|)) (SIGNATURE |convert| ((|Pattern| (|Float|)) |#1|)) (SIGNATURE |retract| (|#4| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#4| "failed") |#1|)) (SIGNATURE |coerce| (|#1| |#4|)) (SIGNATURE |leadingCoefficient| (|#2| |#1|)) (SIGNATURE |reductum| (|#1| |#1|)) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|variables| (((|List| |#3|) $) 109)) (|univariate| (((|SparseUnivariatePolynomial| $) $ |#3|) 124) (((|SparseUnivariatePolynomial| |#1|) $) 123)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 85 (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) 86 (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) 88 (|has| |#1| (|IntegralDomain|)))) (|totalDegree| (((|NonNegativeInteger|) $) 111) (((|NonNegativeInteger|) $ (|List| |#3|)) 110)) (|tail| (($ $) 251)) (|supRittWu?| (((|Boolean|) $ $) 237)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|subResultantGcd| (($ $ $) 196 (|has| |#1| (|IntegralDomain|)))) (|subResultantChain| (((|List| $) $ $) 191 (|has| |#1| (|IntegralDomain|)))) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 99 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) 97 (|has| |#1| (|GcdDomain|)))) (|squareFree| (((|Factored| $) $) 96 (|has| |#1| (|GcdDomain|)))) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 102 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 163) (((|Union| (|Fraction| (|Integer|)) "failed") $) 161 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Integer|) "failed") $) 159 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| |#3| "failed") $) 135) (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) 211 (AND (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Symbol|))))) (((|Union| $ "failed") (|Polynomial| (|Integer|))) 208 (OR (AND (|not| (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (|has| |#1| (|Algebra| (|Integer|))) (|has| |#3| (|ConvertibleTo| (|Symbol|)))) (AND (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Symbol|)))))) (((|Union| $ "failed") (|Polynomial| |#1|)) 205 (OR (AND (|not| (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (|not| (|has| |#1| (|Algebra| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Symbol|)))) (AND (|not| (|has| |#1| (|IntegerNumberSystem|))) (|not| (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (|has| |#1| (|Algebra| (|Integer|))) (|has| |#3| (|ConvertibleTo| (|Symbol|)))) (AND (|not| (|has| |#1| (|QuotientFieldCategory| (|Integer|)))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Symbol|))))))) (|retract| ((|#1| $) 164) (((|Fraction| (|Integer|)) $) 160 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Integer|) $) 158 (|has| |#1| (|RetractableTo| (|Integer|)))) ((|#3| $) 134) (($ (|Polynomial| (|Fraction| (|Integer|)))) 210 (AND (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Symbol|))))) (($ 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(((|RecursivePolynomialCategory| |#1| |#2| |#3|) (|Category|) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|)) (T |RecursivePolynomialCategory|)) 
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(|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|mainMonomials| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|RittWuCompare| (*1 *2 *1 *1) (|partial| AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|infRittWu?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|supRittWu?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|reduced?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|reduced?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|headReduced?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|headReduced?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|initiallyReduced?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|initiallyReduced?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|normalized?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|normalized?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|prem| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|pquo| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|prem| (*1 *1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|pquo| (*1 *1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|lazyPrem| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|lazyPquo| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|lazyPrem| (*1 *1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|lazyPquo| (*1 *1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|lazyPremWithDefault| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |coef| *1) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|lazyPremWithDefault| (*1 *2 *1 *1 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |coef| *1) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *3)))) (|lazyPseudoDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |coef| *1) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|lazyPseudoDivide| (*1 *2 *1 *1 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |coef| *1) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *3)))) (|pseudoDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|monicModulo| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|lazyResidueClass| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |polnum| *1) (|:| |polden| *1) (|:| |power| (|NonNegativeInteger|)))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|headReduce| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|initiallyReduce| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Polynomial| (|Fraction| (|Integer|)))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| (|Fraction| (|Integer|)))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| (|Fraction| (|Integer|)))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (|retractIfCan| (*1 *1 *2) (|partial| OR (AND (|isDomain| *2 (|Polynomial| (|Integer|))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|))) (AND (|isDomain| *2 (|Polynomial| (|Integer|))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|))))) (|retract| (*1 *1 *2) (OR (AND (|isDomain| *2 (|Polynomial| (|Integer|))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|))) (AND (|isDomain| *2 (|Polynomial| (|Integer|))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|))))) (|convert| (*1 *1 *2) (OR (AND (|isDomain| *2 (|Polynomial| (|Integer|))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|))) (AND (|isDomain| *2 (|Polynomial| (|Integer|))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|))))) (|retractIfCan| (*1 *1 *2) (|partial| OR (AND (|isDomain| *2 (|Polynomial| *3)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|not| (|ofCategory| *3 (|Algebra| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|))) (AND (|isDomain| *2 (|Polynomial| *3)) (AND (|not| (|ofCategory| *3 (|IntegerNumberSystem|))) (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|))) (AND (|isDomain| *2 (|Polynomial| *3)) (AND (|not| (|ofCategory| *3 (|QuotientFieldCategory| (|Integer|)))) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|))))) (|retract| (*1 *1 *2) (OR (AND (|isDomain| *2 (|Polynomial| *3)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|not| (|ofCategory| *3 (|Algebra| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|))) (AND (|isDomain| *2 (|Polynomial| *3)) (AND (|not| (|ofCategory| *3 (|IntegerNumberSystem|))) (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|))) (AND (|isDomain| *2 (|Polynomial| *3)) (AND (|not| (|ofCategory| *3 (|QuotientFieldCategory| (|Integer|)))) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|))))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (|primPartElseUnitCanonical| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|primPartElseUnitCanonical!| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|exactQuotient| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|exactQuotient!| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|exactQuotient| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|exactQuotient!| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|subResultantGcd| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|extendedSubResultantGcd| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |gcd| *1) (|:| |coef1| *1) (|:| |coef2| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|halfExtendedSubResultantGcd1| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |gcd| *1) (|:| |coef1| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|halfExtendedSubResultantGcd2| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |gcd| *1) (|:| |coef2| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|resultant| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|subResultantChain| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|lastSubResultant| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|LazardQuotient| (*1 *1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *3 (|IntegralDomain|)))) (|LazardQuotient2| (*1 *1 *1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *3 (|IntegralDomain|)))) (|nextsubResultant2| (*1 *1 *1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|gcd| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|)))) (|primitivePart!| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|)))) (|mainContent| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|)))) (|mainPrimitivePart| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|)))) (|mainSquareFreePart| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|))))) 
(|Join| (|PolynomialCategory| |t#1| |t#2| |t#3|) (CATEGORY |domain| (SIGNATURE |mvar| (|t#3| $)) (SIGNATURE |mdeg| ((|NonNegativeInteger|) $)) (SIGNATURE |init| ($ $)) (SIGNATURE |head| ($ $)) (SIGNATURE |tail| ($ $)) (SIGNATURE |deepestTail| ($ $)) (SIGNATURE |iteratedInitials| ((|List| $) $)) (SIGNATURE |deepestInitial| ($ $)) (SIGNATURE |leadingCoefficient| ($ $ |t#3|)) (SIGNATURE |reductum| ($ $ |t#3|)) (SIGNATURE |monic?| ((|Boolean|) $)) (SIGNATURE |quasiMonic?| ((|Boolean|) $)) (SIGNATURE |mainMonomial| ($ $)) (SIGNATURE |leastMonomial| ($ $)) (SIGNATURE |mainCoefficients| ((|List| $) $)) (SIGNATURE |mainMonomials| ((|List| $) $)) (SIGNATURE |RittWuCompare| ((|Union| (|Boolean|) "failed") $ $)) (SIGNATURE |infRittWu?| ((|Boolean|) $ $)) (SIGNATURE |supRittWu?| ((|Boolean|) $ $)) (SIGNATURE |reduced?| ((|Boolean|) $ $)) (SIGNATURE |reduced?| ((|Boolean|) $ (|List| $))) (SIGNATURE |headReduced?| ((|Boolean|) $ $)) (SIGNATURE |headReduced?| ((|Boolean|) $ (|List| $))) (SIGNATURE |initiallyReduced?| ((|Boolean|) $ $)) (SIGNATURE |initiallyReduced?| ((|Boolean|) $ (|List| $))) (SIGNATURE |normalized?| ((|Boolean|) $ $)) (SIGNATURE |normalized?| ((|Boolean|) $ (|List| $))) (SIGNATURE |prem| ($ $ $)) (SIGNATURE |pquo| ($ $ $)) (SIGNATURE |prem| ($ $ $ |t#3|)) (SIGNATURE |pquo| ($ $ $ |t#3|)) (SIGNATURE |lazyPrem| ($ $ $)) (SIGNATURE |lazyPquo| ($ $ $)) (SIGNATURE |lazyPrem| ($ $ $ |t#3|)) (SIGNATURE |lazyPquo| ($ $ $ |t#3|)) (SIGNATURE |lazyPremWithDefault| ((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $)) (SIGNATURE |lazyPremWithDefault| ((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |t#3|)) (SIGNATURE |lazyPseudoDivide| ((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |lazyPseudoDivide| ((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |t#3|)) (SIGNATURE |pseudoDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |monicModulo| ($ $ $)) (SIGNATURE |lazyResidueClass| ((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $)) (SIGNATURE |headReduce| ($ $ $)) (SIGNATURE |initiallyReduce| ($ $ $)) (IF (|has| |t#3| (|ConvertibleTo| (|Symbol|))) (PROGN (ATTRIBUTE (|CoercibleTo| (|Polynomial| |t#1|))) (ATTRIBUTE (|ConvertibleTo| (|Polynomial| |t#1|))) (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |retract| ($ (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |convert| ($ (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| (|Integer|)))) (SIGNATURE |retract| ($ (|Polynomial| (|Integer|)))) (SIGNATURE |convert| ($ (|Polynomial| (|Integer|)))) (IF (|has| |t#1| (|QuotientFieldCategory| (|Integer|))) |noBranch| (PROGN (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| |t#1|))) (SIGNATURE |retract| ($ (|Polynomial| |t#1|)))))) |noBranch|) (IF (|has| |t#1| (|Algebra| (|Integer|))) (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) |noBranch| (PROGN (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| (|Integer|)))) (SIGNATURE |retract| ($ (|Polynomial| (|Integer|)))) (SIGNATURE |convert| ($ (|Polynomial| (|Integer|)))) (IF (|has| |t#1| (|IntegerNumberSystem|)) |noBranch| (PROGN (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| |t#1|))) (SIGNATURE |retract| ($ (|Polynomial| |t#1|))))))) |noBranch|) (IF (|has| |t#1| (|Algebra| (|Integer|))) |noBranch| (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) |noBranch| (PROGN (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| |t#1|))) (SIGNATURE |retract| ($ (|Polynomial| |t#1|)))))) (SIGNATURE |convert| ($ (|Polynomial| |t#1|))) (IF (|has| |t#1| (|RetractableTo| (|Integer|))) (ATTRIBUTE (|ConvertibleTo| (|String|))) |noBranch|)) |noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |primPartElseUnitCanonical| ($ $)) (SIGNATURE |primPartElseUnitCanonical!| ($ $)) (SIGNATURE |exactQuotient| ($ $ |t#1|)) (SIGNATURE |exactQuotient!| ($ $ |t#1|)) (SIGNATURE |exactQuotient| ($ $ $)) (SIGNATURE |exactQuotient!| ($ $ $)) (SIGNATURE |subResultantGcd| ($ $ $)) (SIGNATURE |extendedSubResultantGcd| ((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $)) (SIGNATURE |halfExtendedSubResultantGcd1| ((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $)) (SIGNATURE |halfExtendedSubResultantGcd2| ((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $)) (SIGNATURE |resultant| ($ $ $)) (SIGNATURE |subResultantChain| ((|List| $) $ $)) (SIGNATURE |lastSubResultant| ($ $ $)) (SIGNATURE |LazardQuotient| ($ $ $ (|NonNegativeInteger|))) (SIGNATURE |LazardQuotient2| ($ $ $ $ (|NonNegativeInteger|))) (SIGNATURE |nextsubResultant2| ($ $ $ $ $))) |noBranch|) (IF (|has| |t#1| (|GcdDomain|)) (PROGN (SIGNATURE |gcd| (|t#1| |t#1| $)) (SIGNATURE |primitivePart!| ($ $)) (SIGNATURE |mainContent| ($ $)) (SIGNATURE |mainPrimitivePart| ($ $)) (SIGNATURE |mainSquareFreePart| ($ $))) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| |#2|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CoercibleTo| (|Polynomial| |#1|)) |has| |#3| (|ConvertibleTo| (|Symbol|))) ((|CommutativeRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|ConvertibleTo| (|InputForm|)) AND (|has| |#1| (|ConvertibleTo| (|InputForm|))) (|has| |#3| (|ConvertibleTo| (|InputForm|)))) ((|ConvertibleTo| (|Pattern| (|Float|))) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#3| (|ConvertibleTo| (|Pattern| (|Float|))))) ((|ConvertibleTo| (|Pattern| (|Integer|))) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Pattern| (|Integer|))))) ((|ConvertibleTo| (|Polynomial| |#1|)) |has| |#3| (|ConvertibleTo| (|Symbol|))) ((|ConvertibleTo| (|String|)) AND (|has| |#1| (|RetractableTo| (|Integer|))) (|has| |#3| (|ConvertibleTo| (|Symbol|)))) ((|EntireRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|Evalable| $) . T) ((|FiniteAbelianMonoidRing| |#1| |#2|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|GcdDomain|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|GcdDomain|))) ((|InnerEvalable| |#3| |#1|) . T) ((|InnerEvalable| |#3| $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|LeftModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|GcdDomain|))) ((|LinearlyExplicitRingOver| (|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|Monoid|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|PartialDifferentialRing| |#3|) . T) ((|PatternMatchable| (|Float|)) AND (|has| |#1| (|PatternMatchable| (|Float|))) (|has| |#3| (|PatternMatchable| (|Float|)))) ((|PatternMatchable| (|Integer|)) AND (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#3| (|PatternMatchable| (|Integer|)))) ((|PolynomialCategory| |#1| |#2| |#3|) . T) ((|PolynomialFactorizationExplicit|) |has| |#1| (|PolynomialFactorizationExplicit|)) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RetractableTo| |#3|) . T) ((|RightModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|PolynomialFactorizationExplicit|))) 
((|zero?| (((|Boolean|) |#3| $) 13)) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) 23)) (|recip| (((|Union| |#3| "failed") |#3| $) 37)) (|positive?| (((|Boolean|) |#3| $) 16)) (|negative?| (((|Boolean|) |#3| $) 14))) 
(((|RealRootCharacterizationCategory&| |#1| |#2| |#3|) (CATEGORY |domain| (SIGNATURE |rootOf| ((|Union| |#1| "failed") |#3| (|PositiveInteger|))) (SIGNATURE |recip| ((|Union| |#3| "failed") |#3| |#1|)) (SIGNATURE |positive?| ((|Boolean|) |#3| |#1|)) (SIGNATURE |negative?| ((|Boolean|) |#3| |#1|)) (SIGNATURE |zero?| ((|Boolean|) |#3| |#1|))) (|RealRootCharacterizationCategory| |#2| |#3|) (|Join| (|OrderedRing|) (|Field|)) (|UnivariatePolynomialCategory| |#2|)) (T |RealRootCharacterizationCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |rootOf| ((|Union| |#1| "failed") |#3| (|PositiveInteger|))) (SIGNATURE |recip| ((|Union| |#3| "failed") |#3| |#1|)) (SIGNATURE |positive?| ((|Boolean|) |#3| |#1|)) (SIGNATURE |negative?| ((|Boolean|) |#3| |#1|)) (SIGNATURE |zero?| ((|Boolean|) |#3| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) |#2| $) 20)) (|sign| (((|Integer|) |#2| $) 21)) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) 14)) (|relativeApprox| ((|#1| |#2| $ |#1|) 12)) (|recip| (((|Union| |#2| "failed") |#2| $) 17)) (|positive?| (((|Boolean|) |#2| $) 18)) (|negative?| (((|Boolean|) |#2| $) 19)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|definingPolynomial| ((|#2| $) 16)) (|coerce| (((|OutputForm|) $) 11)) (|approximate| ((|#1| |#2| $ |#1|) 13)) (|allRootsOf| (((|List| $) |#2|) 15)) (= (((|Boolean|) $ $) 6))) 
(((|RealRootCharacterizationCategory| |#1| |#2|) (|Category|) (|Join| (|OrderedRing|) (|Field|)) (|UnivariatePolynomialCategory| |t#1|)) (T |RealRootCharacterizationCategory|)) 
((|sign| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|RealRootCharacterizationCategory| *4 *3)) (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|))) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Integer|)))) (|zero?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|RealRootCharacterizationCategory| *4 *3)) (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|))) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Boolean|)))) (|negative?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|RealRootCharacterizationCategory| *4 *3)) (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|))) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Boolean|)))) (|positive?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|RealRootCharacterizationCategory| *4 *3)) (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|))) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Boolean|)))) (|recip| (*1 *2 *2 *1) (|partial| AND (|ofCategory| *1 (|RealRootCharacterizationCategory| *3 *2)) (|ofCategory| *3 (|Join| (|OrderedRing|) (|Field|))) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|definingPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|RealRootCharacterizationCategory| *3 *2)) (|ofCategory| *3 (|Join| (|OrderedRing|) (|Field|))) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|allRootsOf| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|))) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RealRootCharacterizationCategory| *4 *3)))) (|rootOf| (*1 *1 *2 *3) (|partial| AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|))) (|ofCategory| *1 (|RealRootCharacterizationCategory| *4 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)))) (|approximate| (*1 *2 *3 *1 *2) (AND (|ofCategory| *1 (|RealRootCharacterizationCategory| *2 *3)) (|ofCategory| *2 (|Join| (|OrderedRing|) (|Field|))) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|relativeApprox| (*1 *2 *3 *1 *2) (AND (|ofCategory| *1 (|RealRootCharacterizationCategory| *2 *3)) (|ofCategory| *2 (|Join| (|OrderedRing|) (|Field|))) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |sign| ((|Integer|) |t#2| $)) (SIGNATURE |zero?| ((|Boolean|) |t#2| $)) (SIGNATURE |negative?| ((|Boolean|) |t#2| $)) (SIGNATURE |positive?| ((|Boolean|) |t#2| $)) (SIGNATURE |recip| ((|Union| |t#2| "failed") |t#2| $)) (SIGNATURE |definingPolynomial| (|t#2| $)) (SIGNATURE |allRootsOf| ((|List| $) |t#2|)) (SIGNATURE |rootOf| ((|Union| $ "failed") |t#2| (|PositiveInteger|))) (SIGNATURE |approximate| (|t#1| |t#2| $ |t#1|)) (SIGNATURE |relativeApprox| (|t#1| |t#2| $ |t#1|)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((|upDateBranches| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| |#4|) (|List| |#5|) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) (|NonNegativeInteger|)) 95)) (|transcendentalDecompose| (((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5|) 56) (((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|)) 55)) (|printInfo| (((|Void|) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|NonNegativeInteger|)) 87)) (|numberOfVariables| (((|NonNegativeInteger|) (|List| |#4|) (|List| |#5|)) 27)) (|internalDecompose| (((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5|) 58) (((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|)) 57) (((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|) (|Boolean|)) 59)) (|decompose| (((|List| |#5|) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) 78) (((|List| |#5|) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) 79)) (|convert| (((|String|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) 82)) (|algebraicDecompose| (((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|Boolean|)) 54)) (|KrullNumber| (((|NonNegativeInteger|) (|List| |#4|) (|List| |#5|)) 19))) 
(((|RegularSetDecompositionPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |KrullNumber| ((|NonNegativeInteger|) (|List| |#4|) (|List| |#5|))) (SIGNATURE |numberOfVariables| ((|NonNegativeInteger|) (|List| |#4|) (|List| |#5|))) (SIGNATURE |algebraicDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|Boolean|))) (SIGNATURE |transcendentalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|))) (SIGNATURE |transcendentalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5|)) (SIGNATURE |internalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|) (|Boolean|))) (SIGNATURE |internalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|))) (SIGNATURE |internalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5|)) (SIGNATURE |decompose| ((|List| |#5|) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|))) (SIGNATURE |decompose| ((|List| |#5|) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |upDateBranches| ((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| |#4|) (|List| |#5|) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) (|NonNegativeInteger|))) (SIGNATURE |convert| ((|String|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) (SIGNATURE |printInfo| ((|Void|) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|NonNegativeInteger|)))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |RegularSetDecompositionPackage|)) 
((|printInfo| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Record| (|:| |val| (|List| *8)) (|:| |tower| *9)))) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *9 (|RegularTriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|RegularSetDecompositionPackage| *5 *6 *7 *8 *9)))) (|convert| (*1 *2 *3) (AND (|isDomain| *3 (|Record| (|:| |val| (|List| *7)) (|:| |tower| *8))) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|String|)) (|isDomain| *1 (|RegularSetDecompositionPackage| *4 *5 *6 *7 *8)))) (|upDateBranches| (*1 *2 *3 *4 *2 *5 *6) (AND (|isDomain| *5 (|Record| (|:| |done| (|List| *11)) (|:| |todo| (|List| (|Record| (|:| |val| *3) (|:| |tower| *11)))))) (|isDomain| *6 (|NonNegativeInteger|)) (|isDomain| *2 (|List| (|Record| (|:| |val| (|List| *10)) (|:| |tower| *11)))) (|isDomain| *3 (|List| *10)) (|isDomain| *4 (|List| *11)) (|ofCategory| *10 (|RecursivePolynomialCategory| *7 *8 *9)) (|ofCategory| *11 (|RegularTriangularSetCategory| *7 *8 *9 *10)) (|ofCategory| *7 (|GcdDomain|)) (|ofCategory| *8 (|OrderedAbelianMonoidSup|)) (|ofCategory| *9 (|OrderedSet|)) (|isDomain| *1 (|RegularSetDecompositionPackage| *7 *8 *9 *10 *11)))) (|decompose| (*1 *2 *3 *2 *4 *4 *4 *4 *4) (AND (|isDomain| *2 (|List| *9)) (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *9 (|RegularTriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *1 (|RegularSetDecompositionPackage| *5 *6 *7 *8 *9)))) (|decompose| (*1 *2 *3 *2 *4 *4) (AND (|isDomain| *2 (|List| *9)) (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *9 (|RegularTriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *1 (|RegularSetDecompositionPackage| *5 *6 *7 *8 *9)))) (|internalDecompose| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Record| (|:| |done| (|List| *4)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4)))))) (|isDomain| *1 (|RegularSetDecompositionPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|internalDecompose| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|NonNegativeInteger|)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8)) (|isDomain| *2 (|Record| (|:| |done| (|List| *4)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4)))))) (|isDomain| *1 (|RegularSetDecompositionPackage| *6 *7 *8 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *3)))) (|internalDecompose| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *5 (|NonNegativeInteger|)) (|isDomain| *6 (|Boolean|)) (|ofCategory| *7 (|GcdDomain|)) (|ofCategory| *8 (|OrderedAbelianMonoidSup|)) (|ofCategory| *9 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *7 *8 *9)) (|isDomain| *2 (|Record| (|:| |done| (|List| *4)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4)))))) (|isDomain| *1 (|RegularSetDecompositionPackage| *7 *8 *9 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *7 *8 *9 *3)))) (|transcendentalDecompose| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Record| (|:| |done| (|List| *4)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4)))))) (|isDomain| *1 (|RegularSetDecompositionPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|transcendentalDecompose| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|NonNegativeInteger|)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8)) (|isDomain| *2 (|Record| (|:| |done| (|List| *4)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4)))))) (|isDomain| *1 (|RegularSetDecompositionPackage| *6 *7 *8 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *3)))) (|algebraicDecompose| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|Boolean|)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8)) (|isDomain| *2 (|Record| (|:| |done| (|List| *4)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4)))))) (|isDomain| *1 (|RegularSetDecompositionPackage| *6 *7 *8 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *3)))) (|numberOfVariables| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|List| *9)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *9 (|RegularTriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|RegularSetDecompositionPackage| *5 *6 *7 *8 *9)))) (|KrullNumber| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|List| *9)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *9 (|RegularTriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|RegularSetDecompositionPackage| *5 *6 *7 *8 *9))))) 
(CATEGORY |package| (SIGNATURE |KrullNumber| ((|NonNegativeInteger|) (|List| |#4|) (|List| |#5|))) (SIGNATURE |numberOfVariables| ((|NonNegativeInteger|) (|List| |#4|) (|List| |#5|))) (SIGNATURE |algebraicDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|Boolean|))) (SIGNATURE |transcendentalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|))) (SIGNATURE |transcendentalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5|)) (SIGNATURE |internalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|) (|Boolean|))) (SIGNATURE |internalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|))) (SIGNATURE |internalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5|)) (SIGNATURE |decompose| ((|List| |#5|) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|))) (SIGNATURE |decompose| ((|List| |#5|) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |upDateBranches| ((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| |#4|) (|List| |#5|) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) (|NonNegativeInteger|))) (SIGNATURE |convert| ((|String|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) (SIGNATURE |printInfo| ((|Void|) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|NonNegativeInteger|)))) 
((|purelyTranscendental?| (((|Boolean|) |#5| $) 20)) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) 23)) (|purelyAlgebraic?| (((|Boolean|) |#5| $) 16) (((|Boolean|) $) 44)) (|intersect| (((|List| $) |#5| $) NIL) (((|List| $) (|List| |#5|) $) 76) (((|List| $) (|List| |#5|) (|List| $)) 74) (((|List| $) |#5| (|List| $)) 77)) (|extend| (($ $ |#5|) NIL) (((|List| $) |#5| $) NIL) (((|List| $) |#5| (|List| $)) 59) (((|List| $) (|List| |#5|) $) 61) (((|List| $) (|List| |#5|) (|List| $)) 63)) (|augment| (((|List| $) |#5| $) NIL) (((|List| $) |#5| (|List| $)) 53) (((|List| $) (|List| |#5|) $) 55) (((|List| $) (|List| |#5|) (|List| $)) 57)) (|algebraicCoefficients?| (((|Boolean|) |#5| $) 26))) 
(((|RegularTriangularSetCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |domain| (SIGNATURE |extend| ((|List| |#1|) (|List| |#5|) (|List| |#1|))) (SIGNATURE |extend| ((|List| |#1|) (|List| |#5|) |#1|)) (SIGNATURE |extend| ((|List| |#1|) |#5| (|List| |#1|))) (SIGNATURE |extend| ((|List| |#1|) |#5| |#1|)) (SIGNATURE |augment| ((|List| |#1|) (|List| |#5|) (|List| |#1|))) (SIGNATURE |augment| ((|List| |#1|) (|List| |#5|) |#1|)) (SIGNATURE |augment| ((|List| |#1|) |#5| (|List| |#1|))) (SIGNATURE |augment| ((|List| |#1|) |#5| |#1|)) (SIGNATURE |intersect| ((|List| |#1|) |#5| (|List| |#1|))) (SIGNATURE |intersect| ((|List| |#1|) (|List| |#5|) (|List| |#1|))) (SIGNATURE |intersect| ((|List| |#1|) (|List| |#5|) |#1|)) (SIGNATURE |intersect| ((|List| |#1|) |#5| |#1|)) (SIGNATURE |purelyAlgebraicLeadingMonomial?| ((|Boolean|) |#5| |#1|)) (SIGNATURE |purelyAlgebraic?| ((|Boolean|) |#1|)) (SIGNATURE |algebraicCoefficients?| ((|Boolean|) |#5| |#1|)) (SIGNATURE |purelyTranscendental?| ((|Boolean|) |#5| |#1|)) (SIGNATURE |purelyAlgebraic?| ((|Boolean|) |#5| |#1|)) (SIGNATURE |extend| (|#1| |#1| |#5|))) (|RegularTriangularSetCategory| |#2| |#3| |#4| |#5|) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#2| |#3| |#4|)) (T |RegularTriangularSetCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |extend| ((|List| |#1|) (|List| |#5|) (|List| |#1|))) (SIGNATURE |extend| ((|List| |#1|) (|List| |#5|) |#1|)) (SIGNATURE |extend| ((|List| |#1|) |#5| (|List| |#1|))) (SIGNATURE |extend| ((|List| |#1|) |#5| |#1|)) (SIGNATURE |augment| ((|List| |#1|) (|List| |#5|) (|List| |#1|))) (SIGNATURE |augment| ((|List| |#1|) (|List| |#5|) |#1|)) (SIGNATURE |augment| ((|List| |#1|) |#5| (|List| |#1|))) (SIGNATURE |augment| ((|List| |#1|) |#5| |#1|)) (SIGNATURE |intersect| ((|List| |#1|) |#5| (|List| |#1|))) (SIGNATURE |intersect| ((|List| |#1|) (|List| |#5|) (|List| |#1|))) (SIGNATURE |intersect| ((|List| |#1|) (|List| |#5|) |#1|)) (SIGNATURE |intersect| ((|List| |#1|) |#5| |#1|)) (SIGNATURE |purelyAlgebraicLeadingMonomial?| ((|Boolean|) |#5| |#1|)) (SIGNATURE |purelyAlgebraic?| ((|Boolean|) |#1|)) (SIGNATURE |algebraicCoefficients?| ((|Boolean|) |#5| |#1|)) (SIGNATURE |purelyTranscendental?| ((|Boolean|) |#5| |#1|)) (SIGNATURE |purelyAlgebraic?| ((|Boolean|) |#5| |#1|)) (SIGNATURE |extend| (|#1| |#1| |#5|))) 
((~= (((|Boolean|) $ $) 7)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 78)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 79) (((|List| $) (|List| |#4|) (|Boolean|)) 104)) (|variables| (((|List| |#3|) $) 32)) (|trivialIdeal?| (((|Boolean|) $) 25)) (|triangular?| (((|Boolean|) $) 16 (|has| |#1| (|IntegralDomain|)))) (|stronglyReduced?| (((|Boolean|) |#4| $) 94) (((|Boolean|) $) 90)) (|stronglyReduce| ((|#4| |#4| $) 85)) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) 119)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 26)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 43)) (|select| (($ (|Mapping| (|Boolean|) |#4|) $) 64 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| |#4| "failed") $ |#3|) 72)) (|sample| (($) 44 T CONST)) (|roughUnitIdeal?| (((|Boolean|) $) 21 (|has| |#1| (|IntegralDomain|)))) (|roughSubIdeal?| (((|Boolean|) $ $) 23 (|has| |#1| (|IntegralDomain|)))) (|roughEqualIdeals?| (((|Boolean|) $ $) 22 (|has| |#1| (|IntegralDomain|)))) (|roughBase?| (((|Boolean|) $) 24 (|has| |#1| (|IntegralDomain|)))) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 86)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) 17 (|has| |#1| (|IntegralDomain|)))) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) 18 (|has| |#1| (|IntegralDomain|)))) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 35)) (|retract| (($ (|List| |#4|)) 34)) (|rest| (((|Union| $ "failed") $) 75)) (|removeZero| ((|#4| |#4| $) 82)) (|removeDuplicates| (($ $) 67 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove| (($ |#4| $) 66 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#4|) $) 63 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 19 (|has| |#1| (|IntegralDomain|)))) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) 95)) (|reduceByQuasiMonic| ((|#4| |#4| $) 80)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 65 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 62 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 61 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 87)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 98)) (|purelyTranscendental?| (((|Boolean|) |#4| $) 129)) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) 126)) (|purelyAlgebraic?| (((|Boolean|) |#4| $) 130) (((|Boolean|) $) 127)) (|parts| (((|List| |#4|) $) 51 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|normalized?| (((|Boolean|) |#4| $) 97) (((|Boolean|) $) 96)) (|mvar| ((|#3| $) 33)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 42)) (|members| (((|List| |#4|) $) 52 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#4| $) 54 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#4| |#4|) $) 47 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#4| |#4|) $) 46)) (|mainVariables| (((|List| |#3|) $) 31)) (|mainVariable?| (((|Boolean|) |#3| $) 30)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 41)) (|latex| (((|String|) $) 9)) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) 121)) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) 120)) (|last| (((|Union| |#4| "failed") $) 76)) (|invertibleSet| (((|List| $) |#4| $) 122)) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) 125)) (|invertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) 124) (((|Boolean|) |#4| $) 123)) (|intersect| (((|List| $) |#4| $) 118) (((|List| $) (|List| |#4|) $) 117) (((|List| $) (|List| |#4|) (|List| $)) 116) (((|List| $) |#4| (|List| $)) 115)) (|internalAugment| (($ |#4| $) 110) (($ (|List| |#4|) $) 109)) (|initials| (((|List| |#4|) $) 100)) (|initiallyReduced?| (((|Boolean|) |#4| $) 92) (((|Boolean|) $) 88)) (|initiallyReduce| ((|#4| |#4| $) 83)) (|infRittWu?| (((|Boolean|) $ $) 103)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 20 (|has| |#1| (|IntegralDomain|)))) (|headReduced?| (((|Boolean|) |#4| $) 93) (((|Boolean|) $) 89)) (|headReduce| ((|#4| |#4| $) 84)) (|hash| (((|SingleInteger|) $) 10)) (|first| (((|Union| |#4| "failed") $) 77)) (|find| (((|Union| |#4| "failed") (|Mapping| (|Boolean|) |#4|) $) 60)) (|extendIfCan| (((|Union| $ "failed") $ |#4|) 71)) (|extend| (($ $ |#4|) 70) (((|List| $) |#4| $) 108) (((|List| $) |#4| (|List| $)) 107) (((|List| $) (|List| |#4|) $) 106) (((|List| $) (|List| |#4|) (|List| $)) 105)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) 49 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 58 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ |#4| |#4|) 57 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|Equation| |#4|)) 56 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|List| (|Equation| |#4|))) 55 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 37)) (|empty?| (((|Boolean|) $) 40)) (|empty| (($) 39)) (|degree| (((|NonNegativeInteger|) $) 99)) (|count| (((|NonNegativeInteger|) |#4| $) 53 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#4|) $) 50 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) 38)) (|convert| (((|InputForm|) $) 68 (|has| |#4| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#4|)) 59)) (|collectUpper| (($ $ |#3|) 27)) (|collectUnder| (($ $ |#3|) 29)) (|collectQuasiMonic| (($ $) 81)) (|collect| (($ $ |#3|) 28)) (|coerce| (((|OutputForm|) $) 11) (((|List| |#4|) $) 36)) (|coHeight| (((|NonNegativeInteger|) $) 69 (|has| |#3| (|Finite|)))) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 102) (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 101)) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) 91)) (|augment| (((|List| $) |#4| $) 114) (((|List| $) |#4| (|List| $)) 113) (((|List| $) (|List| |#4|) $) 112) (((|List| $) (|List| |#4|) (|List| $)) 111)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) 48 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|algebraicVariables| (((|List| |#3|) $) 74)) (|algebraicCoefficients?| (((|Boolean|) |#4| $) 128)) (|algebraic?| (((|Boolean|) |#3| $) 73)) (= (((|Boolean|) $ $) 6)) (|#| (((|NonNegativeInteger|) $) 45 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) (|Category|) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |t#1| |t#2| |t#3|)) (T |RegularTriangularSetCategory|)) 
((|purelyAlgebraic?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|purelyTranscendental?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|algebraicCoefficients?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|purelyAlgebraic?| (*1 *2 *1) (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Boolean|)))) (|purelyAlgebraicLeadingMonomial?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|invertibleElseSplit?| (*1 *2 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Union| (|Boolean|) (|List| *1))) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|invertible?| (*1 *2 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| *1)))) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|invertible?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|invertibleSet| (*1 *2 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|lastSubResultantElseSplit| (*1 *2 *3 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Union| *3 (|List| *1))) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|lastSubResultant| (*1 *2 *3 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *1)))) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|squareFreePart| (*1 *2 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *1)))) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|intersect| (*1 *2 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|intersect| (*1 *2 *3 *1) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|intersect| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| *1)) (|isDomain| *3 (|List| *7)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)))) (|intersect| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)))) (|augment| (*1 *2 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|augment| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)))) (|augment| (*1 *2 *3 *1) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|augment| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| *1)) (|isDomain| *3 (|List| *7)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)))) (|internalAugment| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|internalAugment| (*1 *1 *2 *1) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *1 (|RegularTriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)))) (|extend| (*1 *2 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|extend| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)))) (|extend| (*1 *2 *3 *1) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|extend| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| *1)) (|isDomain| *3 (|List| *7)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)))) (|zeroSetSplit| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *5 *6 *7 *8))))) 
(|Join| (|TriangularSetCategory| |t#1| |t#2| |t#3| |t#4|) (CATEGORY |domain| (SIGNATURE |purelyAlgebraic?| ((|Boolean|) |t#4| $)) (SIGNATURE |purelyTranscendental?| ((|Boolean|) |t#4| $)) (SIGNATURE |algebraicCoefficients?| ((|Boolean|) |t#4| $)) (SIGNATURE |purelyAlgebraic?| ((|Boolean|) $)) (SIGNATURE |purelyAlgebraicLeadingMonomial?| ((|Boolean|) |t#4| $)) (SIGNATURE |invertibleElseSplit?| ((|Union| (|Boolean|) (|List| $)) |t#4| $)) (SIGNATURE |invertible?| ((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |t#4| $)) (SIGNATURE |invertible?| ((|Boolean|) |t#4| $)) (SIGNATURE |invertibleSet| ((|List| $) |t#4| $)) (SIGNATURE |lastSubResultantElseSplit| ((|Union| |t#4| (|List| $)) |t#4| |t#4| $)) (SIGNATURE |lastSubResultant| ((|List| (|Record| (|:| |val| |t#4|) (|:| |tower| $))) |t#4| |t#4| $)) (SIGNATURE |squareFreePart| ((|List| (|Record| (|:| |val| |t#4|) (|:| |tower| $))) |t#4| $)) (SIGNATURE |intersect| ((|List| $) |t#4| $)) (SIGNATURE |intersect| ((|List| $) (|List| |t#4|) $)) (SIGNATURE |intersect| ((|List| $) (|List| |t#4|) (|List| $))) (SIGNATURE |intersect| ((|List| $) |t#4| (|List| $))) (SIGNATURE |augment| ((|List| $) |t#4| $)) (SIGNATURE |augment| ((|List| $) |t#4| (|List| $))) (SIGNATURE |augment| ((|List| $) (|List| |t#4|) $)) (SIGNATURE |augment| ((|List| $) (|List| |t#4|) (|List| $))) (SIGNATURE |internalAugment| ($ |t#4| $)) (SIGNATURE |internalAugment| ($ (|List| |t#4|) $)) (SIGNATURE |extend| ((|List| $) |t#4| $)) (SIGNATURE |extend| ((|List| $) |t#4| (|List| $))) (SIGNATURE |extend| ((|List| $) (|List| |t#4|) $)) (SIGNATURE |extend| ((|List| $) (|List| |t#4|) (|List| $))) (SIGNATURE |zeroSetSplit| ((|List| $) (|List| |t#4|) (|Boolean|))))) 
(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|TriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|Type|) . T)) 
((|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) 81)) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) 112)) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) 70)) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) 44) (((|Boolean|) |#4| |#5|) 52)) (|stopTableInvSet!| (((|Void|)) 35)) (|stopTableGcd!| (((|Void|)) 25)) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) 31)) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) 20)) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) 95)) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) 106) (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) 49)) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) 101))) 
(((|RegularTriangularSetGcdPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |startTableGcd!| ((|Void|) (|String|) (|String|) (|String|))) (SIGNATURE |stopTableGcd!| ((|Void|))) (SIGNATURE |startTableInvSet!| ((|Void|) (|String|) (|String|) (|String|))) (SIGNATURE |stopTableInvSet!| ((|Void|))) (SIGNATURE |prepareSubResAlgo| ((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|)) (SIGNATURE |internalLastSubResultant| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|))) (SIGNATURE |internalLastSubResultant| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|))) (SIGNATURE |integralLastSubResultant| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|)) (SIGNATURE |toseLastSubResultant| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|)) (SIGNATURE |toseInvertible?| ((|Boolean|) |#4| |#5|)) (SIGNATURE |toseInvertible?| ((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|)) (SIGNATURE |toseInvertibleSet| ((|List| |#5|) |#4| |#5|)) (SIGNATURE |toseSquareFreePart| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |RegularTriangularSetGcdPackage|)) 
((|toseSquareFreePart| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4)))) (|isDomain| *1 (|RegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|toseInvertibleSet| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|RegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|toseInvertible?| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| *4)))) (|isDomain| *1 (|RegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|toseInvertible?| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|RegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|toseLastSubResultant| (*1 *2 *3 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4)))) (|isDomain| *1 (|RegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|integralLastSubResultant| (*1 *2 *3 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4)))) (|isDomain| *1 (|RegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|internalLastSubResultant| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| (|Record| (|:| |val| (|List| *8)) (|:| |tower| *9)))) (|isDomain| *5 (|Boolean|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *6 *7 *4)) (|ofCategory| *9 (|RegularTriangularSetCategory| *6 *7 *4 *8)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|List| (|Record| (|:| |val| *8) (|:| |tower| *9)))) (|isDomain| *1 (|RegularTriangularSetGcdPackage| *6 *7 *4 *8 *9)))) (|internalLastSubResultant| (*1 *2 *3 *3 *4 *5 *5) (AND (|isDomain| *5 (|Boolean|)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8)) (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4)))) (|isDomain| *1 (|RegularTriangularSetGcdPackage| *6 *7 *8 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *3)))) (|prepareSubResAlgo| (*1 *2 *3 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4)))) (|isDomain| *1 (|RegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|stopTableInvSet!| (*1 *2) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|RegularTriangularSetGcdPackage| *3 *4 *5 *6 *7)) (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)))) (|startTableInvSet!| (*1 *2 *3 *3 *3) (AND (|isDomain| *3 (|String|)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|RegularTriangularSetGcdPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|stopTableGcd!| (*1 *2) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|RegularTriangularSetGcdPackage| *3 *4 *5 *6 *7)) (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)))) (|startTableGcd!| (*1 *2 *3 *3 *3) (AND (|isDomain| *3 (|String|)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|RegularTriangularSetGcdPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))) 
(CATEGORY |package| (SIGNATURE |startTableGcd!| ((|Void|) (|String|) (|String|) (|String|))) (SIGNATURE |stopTableGcd!| ((|Void|))) (SIGNATURE |startTableInvSet!| ((|Void|) (|String|) (|String|) (|String|))) (SIGNATURE |stopTableInvSet!| ((|Void|))) (SIGNATURE |prepareSubResAlgo| ((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|)) (SIGNATURE |internalLastSubResultant| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|))) (SIGNATURE |internalLastSubResultant| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|))) (SIGNATURE |integralLastSubResultant| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|)) (SIGNATURE |toseLastSubResultant| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|)) (SIGNATURE |toseInvertible?| ((|Boolean|) |#4| |#5|)) (SIGNATURE |toseInvertible?| ((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|)) (SIGNATURE |toseInvertibleSet| ((|List| |#5|) |#4| |#5|)) (SIGNATURE |toseSquareFreePart| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|))) 
((~= (((|Boolean|) $ $) NIL)) (|name| (((|Symbol|) $) 8)) (|latex| (((|String|) $) 16)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 11)) (= (((|Boolean|) $ $) 13))) 
(((|RuleCalled| |#1|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |name| ((|Symbol|) $)))) (|Symbol|)) (T |RuleCalled|)) 
((|name| (*1 *2 *1) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|RuleCalled| *3)) (|ofType| *3 *2)))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |name| ((|Symbol|) $)))) 
((~= (((|Boolean|) $ $) NIL)) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) 29)) (|rule| (($ |#3| |#3|) 21) (($ |#3| |#3| (|List| (|Symbol|))) 19)) (|rhs| ((|#3| $) 13)) (|retractIfCan| (((|Union| (|Equation| |#3|) "failed") $) 56)) (|retract| (((|Equation| |#3|) $) NIL)) (|quotedOperators| (((|List| (|Symbol|)) $) 15)) (|pattern| (((|Pattern| |#1|) $) 11)) (|lhs| ((|#3| $) 12)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|elt| ((|#3| $ |#3|) 25) ((|#3| $ |#3| (|PositiveInteger|)) 36)) (|coerce| (((|OutputForm|) $) 84) (($ (|Equation| |#3|)) 20)) (= (((|Boolean|) $ $) 33))) 
(((|RewriteRule| |#1| |#2| |#3|) (|Join| (|SetCategory|) (|Eltable| |#3| |#3|) (|RetractableTo| (|Equation| |#3|)) (CATEGORY |domain| (SIGNATURE |rule| ($ |#3| |#3|)) (SIGNATURE |rule| ($ |#3| |#3| (|List| (|Symbol|)))) (SIGNATURE |suchThat| ($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|)))) (SIGNATURE |pattern| ((|Pattern| |#1|) $)) (SIGNATURE |lhs| (|#3| $)) (SIGNATURE |rhs| (|#3| $)) (SIGNATURE |elt| (|#3| $ |#3| (|PositiveInteger|))) (SIGNATURE |quotedOperators| ((|List| (|Symbol|)) $)))) (|SetCategory|) (|Join| (|Ring|) (|PatternMatchable| |#1|) (|OrderedSet|) (|ConvertibleTo| (|Pattern| |#1|))) (|Join| (|FunctionSpace| |#2|) (|PatternMatchable| |#1|) (|ConvertibleTo| (|Pattern| |#1|)))) (T |RewriteRule|)) 
((|rule| (*1 *1 *2 *2) (AND (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|Join| (|Ring|) (|PatternMatchable| *3) (|OrderedSet|) (|ConvertibleTo| (|Pattern| *3)))) (|isDomain| *1 (|RewriteRule| *3 *4 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *4) (|PatternMatchable| *3) (|ConvertibleTo| (|Pattern| *3)))))) (|rule| (*1 *1 *2 *2 *3) (AND (|isDomain| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|Join| (|Ring|) (|PatternMatchable| *4) (|OrderedSet|) (|ConvertibleTo| (|Pattern| *4)))) (|isDomain| *1 (|RewriteRule| *4 *5 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *5) (|PatternMatchable| *4) (|ConvertibleTo| (|Pattern| *4)))))) (|suchThat| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *3 (|Mapping| (|Boolean|) (|List| *6))) (|ofCategory| *6 (|Join| (|FunctionSpace| *5) (|PatternMatchable| *4) (|ConvertibleTo| (|Pattern| *4)))) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|Join| (|Ring|) (|PatternMatchable| *4) (|OrderedSet|) (|ConvertibleTo| (|Pattern| *4)))) (|isDomain| *1 (|RewriteRule| *4 *5 *6)))) (|pattern| (*1 *2 *1) (AND (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|Join| (|Ring|) (|PatternMatchable| *3) (|OrderedSet|) (|ConvertibleTo| *2))) (|isDomain| *2 (|Pattern| *3)) (|isDomain| *1 (|RewriteRule| *3 *4 *5)) (|ofCategory| *5 (|Join| (|FunctionSpace| *4) (|PatternMatchable| *3) (|ConvertibleTo| *2))))) (|lhs| (*1 *2 *1) (AND (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|Join| (|FunctionSpace| *4) (|PatternMatchable| *3) (|ConvertibleTo| (|Pattern| *3)))) (|isDomain| *1 (|RewriteRule| *3 *4 *2)) (|ofCategory| *4 (|Join| (|Ring|) (|PatternMatchable| *3) (|OrderedSet|) (|ConvertibleTo| (|Pattern| *3)))))) (|rhs| (*1 *2 *1) (AND (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|Join| (|FunctionSpace| *4) (|PatternMatchable| *3) (|ConvertibleTo| (|Pattern| *3)))) (|isDomain| *1 (|RewriteRule| *3 *4 *2)) (|ofCategory| *4 (|Join| (|Ring|) (|PatternMatchable| *3) (|OrderedSet|) (|ConvertibleTo| (|Pattern| *3)))))) (|elt| (*1 *2 *1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|Join| (|Ring|) (|PatternMatchable| *4) (|OrderedSet|) (|ConvertibleTo| (|Pattern| *4)))) (|isDomain| *1 (|RewriteRule| *4 *5 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *5) (|PatternMatchable| *4) (|ConvertibleTo| (|Pattern| *4)))))) (|quotedOperators| (*1 *2 *1) (AND (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|Join| (|Ring|) (|PatternMatchable| *3) (|OrderedSet|) (|ConvertibleTo| (|Pattern| *3)))) (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *1 (|RewriteRule| *3 *4 *5)) (|ofCategory| *5 (|Join| (|FunctionSpace| *4) (|PatternMatchable| *3) (|ConvertibleTo| (|Pattern| *3))))))) 
(|Join| (|SetCategory|) (|Eltable| |#3| |#3|) (|RetractableTo| (|Equation| |#3|)) (CATEGORY |domain| (SIGNATURE |rule| ($ |#3| |#3|)) (SIGNATURE |rule| ($ |#3| |#3| (|List| (|Symbol|)))) (SIGNATURE |suchThat| ($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|)))) (SIGNATURE |pattern| ((|Pattern| |#1|) $)) (SIGNATURE |lhs| (|#3| $)) (SIGNATURE |rhs| (|#3| $)) (SIGNATURE |elt| (|#3| $ |#3| (|PositiveInteger|))) (SIGNATURE |quotedOperators| ((|List| (|Symbol|)) $)))) 
((~= (((|Boolean|) $ $) NIL)) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) 12)) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) 19)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|elt| ((|#3| $ |#3|) 22) ((|#3| $ |#3| (|PositiveInteger|)) 25)) (|coerce| (((|OutputForm|) $) 15)) (= (((|Boolean|) $ $) 18))) 
(((|Ruleset| |#1| |#2| |#3|) (|Join| (|SetCategory|) (|Eltable| |#3| |#3|) (CATEGORY |domain| (SIGNATURE |ruleset| ($ (|List| (|RewriteRule| |#1| |#2| |#3|)))) (SIGNATURE |rules| ((|List| (|RewriteRule| |#1| |#2| |#3|)) $)) (SIGNATURE |elt| (|#3| $ |#3| (|PositiveInteger|))))) (|SetCategory|) (|Join| (|Ring|) (|PatternMatchable| |#1|) (|OrderedSet|) (|ConvertibleTo| (|Pattern| |#1|))) (|Join| (|FunctionSpace| |#2|) (|PatternMatchable| |#1|) (|ConvertibleTo| (|Pattern| |#1|)))) (T |Ruleset|)) 
((|ruleset| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|RewriteRule| *3 *4 *5))) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|Join| (|Ring|) (|PatternMatchable| *3) (|OrderedSet|) (|ConvertibleTo| (|Pattern| *3)))) (|ofCategory| *5 (|Join| (|FunctionSpace| *4) (|PatternMatchable| *3) (|ConvertibleTo| (|Pattern| *3)))) (|isDomain| *1 (|Ruleset| *3 *4 *5)))) (|rules| (*1 *2 *1) (AND (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|Join| (|Ring|) (|PatternMatchable| *3) (|OrderedSet|) (|ConvertibleTo| (|Pattern| *3)))) (|isDomain| *2 (|List| (|RewriteRule| *3 *4 *5))) (|isDomain| *1 (|Ruleset| *3 *4 *5)) (|ofCategory| *5 (|Join| (|FunctionSpace| *4) (|PatternMatchable| *3) (|ConvertibleTo| (|Pattern| *3)))))) (|elt| (*1 *2 *1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|Join| (|Ring|) (|PatternMatchable| *4) (|OrderedSet|) (|ConvertibleTo| (|Pattern| *4)))) (|isDomain| *1 (|Ruleset| *4 *5 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *5) (|PatternMatchable| *4) (|ConvertibleTo| (|Pattern| *4))))))) 
(|Join| (|SetCategory|) (|Eltable| |#3| |#3|) (CATEGORY |domain| (SIGNATURE |ruleset| ($ (|List| (|RewriteRule| |#1| |#2| |#3|)))) (SIGNATURE |rules| ((|List| (|RewriteRule| |#1| |#2| |#3|)) $)) (SIGNATURE |elt| (|#3| $ |#3| (|PositiveInteger|))))) 
((|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) 73) (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) 75) (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) 74))) 
(((|RationalUnivariateRepresentationPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rur| ((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|))) (SIGNATURE |rur| ((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)))) (SIGNATURE |rur| ((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|)) (|List| (|Symbol|))) (T |RationalUnivariateRepresentationPackage|)) 
((|rur| (*1 *2 *3 *4 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *5)) (|:| |coordinates| (|List| (|Polynomial| *5)))))) (|isDomain| *1 (|RationalUnivariateRepresentationPackage| *5 *6)) (|isDomain| *3 (|List| (|Polynomial| *5))) (|ofType| *6 (|List| (|Symbol|))))) (|rur| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *4)) (|:| |coordinates| (|List| (|Polynomial| *4)))))) (|isDomain| *1 (|RationalUnivariateRepresentationPackage| *4 *5)) (|isDomain| *3 (|List| (|Polynomial| *4))) (|ofType| *5 (|List| (|Symbol|))))) (|rur| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *5)) (|:| |coordinates| (|List| (|Polynomial| *5)))))) (|isDomain| *1 (|RationalUnivariateRepresentationPackage| *5 *6)) (|isDomain| *3 (|List| (|Polynomial| *5))) (|ofType| *6 (|List| (|Symbol|)))))) 
(CATEGORY |package| (SIGNATURE |rur| ((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|))) (SIGNATURE |rur| ((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)))) (SIGNATURE |rur| ((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)))) 
((|factor| (((|Factored| |#3|) |#3|) 16))) 
(((|SimpleAlgebraicExtensionAlgFactor| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#3|) |#3|))) (|UnivariatePolynomialCategory| (|Fraction| (|Integer|))) (|Join| (|Field|) (|CharacteristicZero|) (|MonogenicAlgebra| (|Fraction| (|Integer|)) |#1|)) (|UnivariatePolynomialCategory| |#2|)) (T |SimpleAlgebraicExtensionAlgFactor|)) 
((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|MonogenicAlgebra| (|Fraction| (|Integer|)) *4))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|SimpleAlgebraicExtensionAlgFactor| *4 *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#3|) |#3|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 125)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|Field|)))) (|unitCanonical| (($ $) NIL (|has| |#1| (|Field|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|Field|)))) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) NIL) (((|Matrix| |#1|)) 115)) (|trace| ((|#1| $) 119)) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL (|has| |#1| (|Field|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#1| (|Field|)))) (|sizeLess?| (((|Boolean|) $ $) NIL (|has| |#1| (|Field|)))) (|size| (((|NonNegativeInteger|)) 40 (|has| |#1| (|Finite|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) NIL)) (|retract| (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) NIL)) (|represents| (($ (|Vector| |#1|) (|Vector| $)) NIL) (($ (|Vector| |#1|)) 43)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|rem| (($ $ $) NIL (|has| |#1| (|Field|)))) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) NIL) (((|Matrix| |#1|) $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) 106) (((|Matrix| |#1|) (|Matrix| $)) 100)) (|reduce| (($ |#2|) 61) (((|Union| $ "failed") (|Fraction| |#2|)) NIL (|has| |#1| (|Field|)))) (|recip| (((|Union| $ "failed") $) NIL)) (|rank| (((|PositiveInteger|)) 77)) (|random| (($) 44 (|has| |#1| (|Finite|)))) (|quo| (($ $ $) NIL (|has| |#1| (|Field|)))) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL (|has| |#1| (|Field|)))) (|primitiveElement| (($) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|primitive?| (((|Boolean|) $) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|FiniteFieldCategory|))) (($ $) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|prime?| (((|Boolean|) $) NIL (|has| |#1| (|Field|)))) (|order| (((|PositiveInteger|) $) NIL (|has| |#1| (|FiniteFieldCategory|))) (((|OnePointCompletion| (|PositiveInteger|)) $) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|one?| (((|Boolean|) $) NIL)) (|norm| ((|#1| $) NIL)) (|nextItem| (((|Union| $ "failed") $) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) (|minimalPolynomial| ((|#2| $) 84 (|has| |#1| (|Field|)))) (|lookup| (((|PositiveInteger|) $) 129 (|has| |#1| (|Finite|)))) (|lift| ((|#2| $) 58)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| |#1| (|Field|)))) (|lcm| (($ (|List| $)) NIL (|has| |#1| (|Field|))) (($ $ $) NIL (|has| |#1| (|Field|)))) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL (|has| |#1| (|Field|)))) (|init| (($) NIL (|has| |#1| (|FiniteFieldCategory|)) CONST)) (|index| (($ (|PositiveInteger|)) 124 (|has| |#1| (|Finite|)))) (|hash| (((|SingleInteger|) $) NIL)) (|generator| (($) 121)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|Field|)))) (|gcd| (($ (|List| $)) NIL (|has| |#1| (|Field|))) (($ $ $) NIL (|has| |#1| (|Field|)))) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|factor| (((|Factored| $) $) NIL (|has| |#1| (|Field|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL (|has| |#1| (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|exquo| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|Field|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) (|euclideanSize| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|Field|)))) (|enumerate| (((|List| $)) NIL (|has| |#1| (|Finite|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|Field|)))) (|discriminant| ((|#1| (|Vector| $)) NIL) ((|#1|) 109)) (|discreteLog| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|FiniteFieldCategory|))) (((|Union| (|NonNegativeInteger|) "failed") $ $) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|differentiate| (($ $) NIL (OR (AND (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|))) (|has| |#1| (|FiniteFieldCategory|)))) (($ $ (|NonNegativeInteger|)) NIL (OR (AND (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|))) (|has| |#1| (|FiniteFieldCategory|)))) (($ $ (|Symbol|)) NIL (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL (|has| |#1| (|Field|))) (($ $ (|Mapping| |#1| |#1|)) NIL (|has| |#1| (|Field|)))) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) NIL (|has| |#1| (|Field|)))) (|definingPolynomial| ((|#2|) 73)) (|createPrimitiveElement| (($) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|coordinates| (((|Vector| |#1|) $ (|Vector| $)) 89) (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) NIL) (((|Vector| |#1|) $) 71) (((|Matrix| |#1|) (|Vector| $)) 85)) (|convert| (((|Vector| |#1|) $) NIL) (($ (|Vector| |#1|)) NIL) ((|#2| $) NIL) (($ |#2|) NIL)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (|has| |#1| (|FiniteFieldCategory|)))) (|coerce| (((|OutputForm|) $) 57) (($ (|Integer|)) 53) (($ |#1|) 54) (($ $) NIL (|has| |#1| (|Field|))) (($ (|Fraction| (|Integer|))) NIL (OR (|has| |#1| (|Field|)) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))))) (|charthRoot| (($ $) NIL (|has| |#1| (|FiniteFieldCategory|))) (((|Union| $ "failed") $) NIL (|has| |#1| (|CharacteristicNonZero|)))) (|characteristicPolynomial| ((|#2| $) 82)) (|characteristic| (((|NonNegativeInteger|)) 75)) (|basis| (((|Vector| $)) 81)) (|associates?| (((|Boolean|) $ $) NIL (|has| |#1| (|Field|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| |#1| (|Field|)))) (|Zero| (($) 30 T CONST)) (|One| (($) 19 T CONST)) (D (($ $) NIL (OR (AND (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|))) (|has| |#1| (|FiniteFieldCategory|)))) (($ $ (|NonNegativeInteger|)) NIL (OR (AND (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|))) (|has| |#1| (|FiniteFieldCategory|)))) (($ $ (|Symbol|)) NIL (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL (|has| |#1| (|Field|))) (($ $ (|Mapping| |#1| |#1|)) NIL (|has| |#1| (|Field|)))) (= (((|Boolean|) $ $) 63)) (/ (($ $ $) NIL (|has| |#1| (|Field|)))) (- (($ $) 67) (($ $ $) NIL)) (+ (($ $ $) 65)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| |#1| (|Field|)))) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 51) (($ $ $) 69) (($ $ |#1|) NIL) (($ |#1| $) 48) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Field|))) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Field|))))) 
(((|SimpleAlgebraicExtension| |#1| |#2| |#3|) (|MonogenicAlgebra| |#1| |#2|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#1|) |#2|) (T |SimpleAlgebraicExtension|)) 
NIL 
(|MonogenicAlgebra| |#1| |#2|) 
((|factor| (((|Factored| |#3|) |#3|) 16))) 
(((|SAERationalFunctionAlgFactor| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#3|) |#3|))) (|UnivariatePolynomialCategory| (|Fraction| (|Polynomial| (|Integer|)))) (|Join| (|Field|) (|CharacteristicZero|) (|MonogenicAlgebra| (|Fraction| (|Polynomial| (|Integer|))) |#1|)) (|UnivariatePolynomialCategory| |#2|)) (T |SAERationalFunctionAlgFactor|)) 
((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| (|Polynomial| (|Integer|))))) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|MonogenicAlgebra| (|Fraction| (|Polynomial| (|Integer|))) *4))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|SAERationalFunctionAlgFactor| *4 *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#3|) |#3|))) 
((~= (((|Boolean|) $ $) NIL)) (|min| (($ $ $) 14)) (|max| (($ $ $) 15)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|create| (($) 6)) (|convert| (((|Symbol|) $) 18)) (|coerce| (((|OutputForm|) $) 12)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 13)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 8))) 
(((|SingletonAsOrderedSet|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |create| ($)) (SIGNATURE |convert| ((|Symbol|) $))))) (T |SingletonAsOrderedSet|)) 
((|create| (*1 *1) (|isDomain| *1 (|SingletonAsOrderedSet|))) (|convert| (*1 *2 *1) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|SingletonAsOrderedSet|))))) 
(|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |create| ($)) (SIGNATURE |convert| ((|Symbol|) $)))) 
((|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) 21) ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) 18)) (|clearCache| (((|Void|)) 15)) (|cache| (((|List| |#1|)) 9))) 
(((|SortedCache| |#1|) (CATEGORY |package| (SIGNATURE |clearCache| ((|Void|))) (SIGNATURE |cache| ((|List| |#1|))) (SIGNATURE |enterInCache| (|#1| |#1| (|Mapping| (|Boolean|) |#1|))) (SIGNATURE |enterInCache| (|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)))) (|CachableSet|)) (T |SortedCache|)) 
((|enterInCache| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Mapping| (|Integer|) *2 *2)) (|ofCategory| *2 (|CachableSet|)) (|isDomain| *1 (|SortedCache| *2)))) (|enterInCache| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *2)) (|ofCategory| *2 (|CachableSet|)) (|isDomain| *1 (|SortedCache| *2)))) (|cache| (*1 *2) (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|SortedCache| *3)) (|ofCategory| *3 (|CachableSet|)))) (|clearCache| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SortedCache| *3)) (|ofCategory| *3 (|CachableSet|))))) 
(CATEGORY |package| (SIGNATURE |clearCache| ((|Void|))) (SIGNATURE |cache| ((|List| |#1|))) (SIGNATURE |enterInCache| (|#1| |#1| (|Mapping| (|Boolean|) |#1|))) (SIGNATURE |enterInCache| (|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)))) 
((|variableOf| (((|Symbol|) $) 14)) (|stablePol| ((|#2| $) 10)) (|separe| (((|List| |#1|) (|List| |#1|) |#1| |#1|) 33)) (|samplePoint| ((|#1| $) 9)) (|pointToCell| (($ |#1| (|Boolean|) (|Symbol|)) 35)) (|hasDimension?| (((|Boolean|) $) 12)) (|coerce| (((|OutputForm|) $) 22)) (|allSimpleCells| (((|List| $) |#2| (|Symbol|)) 38) (((|List| $) (|List| |#2|) (|Symbol|)) 37))) 
(((|SimpleCell| |#1| |#2|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |allSimpleCells| ((|List| $) |#2| (|Symbol|))) (SIGNATURE |allSimpleCells| ((|List| $) (|List| |#2|) (|Symbol|))) (SIGNATURE |hasDimension?| ((|Boolean|) $)) (SIGNATURE |samplePoint| (|#1| $)) (SIGNATURE |stablePol| (|#2| $)) (SIGNATURE |variableOf| ((|Symbol|) $)) (SIGNATURE |separe| ((|List| |#1|) (|List| |#1|) |#1| |#1|)) (SIGNATURE |pointToCell| ($ |#1| (|Boolean|) (|Symbol|))))) (|RealClosedField|) (|UnivariatePolynomialCategory| |#1|)) (T |SimpleCell|)) 
((|allSimpleCells| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|RealClosedField|)) (|isDomain| *2 (|List| (|SimpleCell| *5 *3))) (|isDomain| *1 (|SimpleCell| *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|allSimpleCells| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|RealClosedField|)) (|isDomain| *2 (|List| (|SimpleCell| *5 *6))) (|isDomain| *1 (|SimpleCell| *5 *6)))) (|hasDimension?| (*1 *2 *1) (AND (|ofCategory| *3 (|RealClosedField|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SimpleCell| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|samplePoint| (*1 *2 *1) (AND (|ofCategory| *2 (|RealClosedField|)) (|isDomain| *1 (|SimpleCell| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|stablePol| (*1 *2 *1) (AND (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)) (|isDomain| *1 (|SimpleCell| *3 *2)) (|ofCategory| *3 (|RealClosedField|)))) (|variableOf| (*1 *2 *1) (AND (|ofCategory| *3 (|RealClosedField|)) (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|SimpleCell| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|separe| (*1 *2 *2 *3 *3) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|RealClosedField|)) (|isDomain| *1 (|SimpleCell| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|pointToCell| (*1 *1 *2 *3 *4) (AND (|isDomain| *3 (|Boolean|)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *2 (|RealClosedField|)) (|isDomain| *1 (|SimpleCell| *2 *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *2))))) 
(|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |allSimpleCells| ((|List| $) |#2| (|Symbol|))) (SIGNATURE |allSimpleCells| ((|List| $) (|List| |#2|) (|Symbol|))) (SIGNATURE |hasDimension?| ((|Boolean|) $)) (SIGNATURE |samplePoint| (|#1| $)) (SIGNATURE |stablePol| (|#2| $)) (SIGNATURE |variableOf| ((|Symbol|) $)) (SIGNATURE |separe| ((|List| |#1|) (|List| |#1|) |#1| |#1|)) (SIGNATURE |pointToCell| ($ |#1| (|Boolean|) (|Symbol|))))) 
((|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) 41) (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|))) 60) (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) 76)) (|coordinates| (((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))) 35))) 
(((|StructuralConstantsPackage| |#1|) (CATEGORY |package| (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|)))) (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)))) (SIGNATURE |coordinates| ((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))))) (|Field|)) (T |StructuralConstantsPackage|)) 
((|coordinates| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| (|Matrix| *5))) (|isDomain| *3 (|Matrix| *5)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Vector| *5)) (|isDomain| *1 (|StructuralConstantsPackage| *5)))) (|structuralConstants| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Matrix| *4))) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|Vector| (|Matrix| *4))) (|isDomain| *1 (|StructuralConstantsPackage| *4)))) (|structuralConstants| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Symbol|))) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Vector| (|Matrix| (|Polynomial| *5)))) (|isDomain| *1 (|StructuralConstantsPackage| *5)) (|isDomain| *4 (|Matrix| (|Polynomial| *5))))) (|structuralConstants| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Symbol|))) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Vector| (|Matrix| (|Fraction| (|Polynomial| *5))))) (|isDomain| *1 (|StructuralConstantsPackage| *5)) (|isDomain| *4 (|Matrix| (|Fraction| (|Polynomial| *5))))))) 
(CATEGORY |package| (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|)))) (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)))) (SIGNATURE |coordinates| ((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|uncorrelated?| (((|Boolean|) $ $) 89) (((|Boolean|) (|List| $) (|List| $)) 94) (((|Boolean|) (|List| (|List| $))) 97)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|statusIto| (((|OutputForm|)) 88)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|BasicStochasticDifferential|) "failed") $) NIL)) (|retract| (((|BasicStochasticDifferential|) $) 68)) (|listSD| (((|List| (|BasicStochasticDifferential|)) $) 70)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|freeOf?| (((|Boolean|) $ (|BasicStochasticDifferential|)) 64)) (|equation| (((|Union| (|Equation| $) "failed") $ |#1|) 75) (((|Union| (|Equation| $) "failed") |#1| $) 76)) (|drift| (($ $) 62)) (|copyQuadVar| (((|Table| $ $)) 79)) (|copyDrift| (((|Table| $ $)) 78)) (|coerce| (((|OutputForm|) $) 47) (($ (|BasicStochasticDifferential|)) 35)) (|coefficient| (((|Expression| |#1|) $ (|BasicStochasticDifferential|)) 66)) (|alterQuadVar!| (((|Union| $ "failed") (|BasicStochasticDifferential|) (|BasicStochasticDifferential|) $) 39)) (|alterDrift!| (((|Union| $ "failed") (|BasicStochasticDifferential|) $) 40)) (^ (($ $ (|PositiveInteger|)) 61)) (|Zero| (($) 21 T CONST)) (= (((|Boolean|) $ $) 33)) (/ (($ $ (|Expression| |#1|)) 11)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) 56)) (** (($ $ (|PositiveInteger|)) 60)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 32) (($ $ (|Expression| |#1|)) NIL) (($ (|Expression| |#1|) $) 10))) 
(((|StochasticDifferential| |#1|) (|Join| (|Rng|) (|Module| (|Expression| |#1|)) (CATEGORY |domain| (ATTRIBUTE (|RetractableTo| (|BasicStochasticDifferential|))) (SIGNATURE |alterQuadVar!| ((|Union| $ "failed") (|BasicStochasticDifferential|) (|BasicStochasticDifferential|) $)) (SIGNATURE |alterDrift!| ((|Union| $ "failed") (|BasicStochasticDifferential|) $)) (SIGNATURE |drift| ($ $)) (SIGNATURE |freeOf?| ((|Boolean|) $ (|BasicStochasticDifferential|))) (SIGNATURE |coefficient| ((|Expression| |#1|) $ (|BasicStochasticDifferential|))) (SIGNATURE |listSD| ((|List| (|BasicStochasticDifferential|)) $)) (SIGNATURE |equation| ((|Union| (|Equation| $) "failed") $ |#1|)) (SIGNATURE |equation| ((|Union| (|Equation| $) "failed") |#1| $)) (SIGNATURE |copyDrift| ((|Table| $ $))) (SIGNATURE |copyQuadVar| ((|Table| $ $))) (SIGNATURE / ($ $ (|Expression| |#1|))) (SIGNATURE ** ($ $ (|PositiveInteger|))) (SIGNATURE ^ ($ $ (|PositiveInteger|))) (SIGNATURE |statusIto| ((|OutputForm|))) (SIGNATURE |uncorrelated?| ((|Boolean|) $ $)) (SIGNATURE |uncorrelated?| ((|Boolean|) (|List| $) (|List| $))) (SIGNATURE |uncorrelated?| ((|Boolean|) (|List| (|List| $)))))) (|Join| (|OrderedSet|) (|IntegralDomain|))) (T |StochasticDifferential|)) 
((^ (*1 *1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|StochasticDifferential| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (** (*1 *1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|StochasticDifferential| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|alterQuadVar!| (*1 *1 *2 *2 *1) (|partial| AND (|isDomain| *2 (|BasicStochasticDifferential|)) (|isDomain| *1 (|StochasticDifferential| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|alterDrift!| (*1 *1 *2 *1) (|partial| AND (|isDomain| *2 (|BasicStochasticDifferential|)) (|isDomain| *1 (|StochasticDifferential| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|drift| (*1 *1 *1) (AND (|isDomain| *1 (|StochasticDifferential| *2)) (|ofCategory| *2 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|freeOf?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|BasicStochasticDifferential|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|StochasticDifferential| *4)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|coefficient| (*1 *2 *1 *3) (AND (|isDomain| *3 (|BasicStochasticDifferential|)) (|isDomain| *2 (|Expression| *4)) (|isDomain| *1 (|StochasticDifferential| *4)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|listSD| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|BasicStochasticDifferential|))) (|isDomain| *1 (|StochasticDifferential| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|equation| (*1 *2 *1 *3) (|partial| AND (|isDomain| *2 (|Equation| (|StochasticDifferential| *3))) (|isDomain| *1 (|StochasticDifferential| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|equation| (*1 *2 *3 *1) (|partial| AND (|isDomain| *2 (|Equation| (|StochasticDifferential| *3))) (|isDomain| *1 (|StochasticDifferential| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|copyDrift| (*1 *2) (AND (|isDomain| *2 (|Table| (|StochasticDifferential| *3) (|StochasticDifferential| *3))) (|isDomain| *1 (|StochasticDifferential| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|copyQuadVar| (*1 *2) (AND (|isDomain| *2 (|Table| (|StochasticDifferential| *3) (|StochasticDifferential| *3))) (|isDomain| *1 (|StochasticDifferential| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (/ (*1 *1 *1 *2) (AND (|isDomain| *2 (|Expression| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))) (|isDomain| *1 (|StochasticDifferential| *3)))) (|statusIto| (*1 *2) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|StochasticDifferential| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|uncorrelated?| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|StochasticDifferential| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|uncorrelated?| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| (|StochasticDifferential| *4))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|StochasticDifferential| *4)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|))))) (|uncorrelated?| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|List| (|StochasticDifferential| *4)))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|StochasticDifferential| *4)) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|)))))) 
(|Join| (|Rng|) (|Module| (|Expression| |#1|)) (CATEGORY |domain| (ATTRIBUTE (|RetractableTo| (|BasicStochasticDifferential|))) (SIGNATURE |alterQuadVar!| ((|Union| $ "failed") (|BasicStochasticDifferential|) (|BasicStochasticDifferential|) $)) (SIGNATURE |alterDrift!| ((|Union| $ "failed") (|BasicStochasticDifferential|) $)) (SIGNATURE |drift| ($ $)) (SIGNATURE |freeOf?| ((|Boolean|) $ (|BasicStochasticDifferential|))) (SIGNATURE |coefficient| ((|Expression| |#1|) $ (|BasicStochasticDifferential|))) (SIGNATURE |listSD| ((|List| (|BasicStochasticDifferential|)) $)) (SIGNATURE |equation| ((|Union| (|Equation| $) "failed") $ |#1|)) (SIGNATURE |equation| ((|Union| (|Equation| $) "failed") |#1| $)) (SIGNATURE |copyDrift| ((|Table| $ $))) (SIGNATURE |copyQuadVar| ((|Table| $ $))) (SIGNATURE / ($ $ (|Expression| |#1|))) (SIGNATURE ** ($ $ (|PositiveInteger|))) (SIGNATURE ^ ($ $ (|PositiveInteger|))) (SIGNATURE |statusIto| ((|OutputForm|))) (SIGNATURE |uncorrelated?| ((|Boolean|) $ $)) (SIGNATURE |uncorrelated?| ((|Boolean|) (|List| $) (|List| $))) (SIGNATURE |uncorrelated?| ((|Boolean|) (|List| (|List| $)))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|weights| (((|List| (|NonNegativeInteger|)) $) NIL) (((|List| (|NonNegativeInteger|)) $ (|Symbol|)) NIL)) (|weight| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|Symbol|)) NIL)) (|variables| (((|List| (|SequentialDifferentialVariable| (|Symbol|))) $) NIL)) (|univariate| (((|SparseUnivariatePolynomial| $) $ (|SequentialDifferentialVariable| (|Symbol|))) NIL) (((|SparseUnivariatePolynomial| |#1|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|totalDegree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|List| (|SequentialDifferentialVariable| (|Symbol|)))) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL (|has| |#1| (|GcdDomain|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#1| (|GcdDomain|)))) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|separant| (($ $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|SequentialDifferentialVariable| (|Symbol|)) "failed") $) NIL) (((|Union| (|Symbol|) "failed") $) NIL) (((|Union| (|SparseMultivariatePolynomial| |#1| (|Symbol|)) "failed") $) NIL)) (|retract| ((|#1| $) NIL) (((|Fraction| (|Integer|)) $) NIL (|has| 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NIL 
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(|Join| (|SegmentCategory| |t#1|) (CATEGORY |domain| (SIGNATURE |expand| (|t#2| (|List| $))) (SIGNATURE |expand| (|t#2| $)) (SIGNATURE |map| (|t#2| (|Mapping| |t#1| |t#1|) $)))) 
(((|SegmentCategory| |#1|) . T) ((|Type|) . T)) 
((|sortedPurge!| (((|Void|) $ (|Mapping| (|Boolean|) |#1|)) 71)) (|setelt!| (((|Void|) $ (|Integer|) |#1| |#2|) 48)) (|setRow!| (((|Void|) $ (|Integer|) (|Record| (|:| |Indices| (|List| |#1|)) (|:| |Entries| (|List| |#2|)))) 37) (((|Void|) $ (|Integer|) (|List| |#1|) (|List| |#2|)) 39)) (|setGcdMode| (((|Symbol|) (|Symbol|)) 105 (|has| |#2| (|GcdDomain|)))) (|rowEchelon| (((|Record| (|:| |Ech| $) (|:| |Lt| (|Matrix| |#2|)) (|:| |Pivots| (|List| |#2|)) (|:| |Rank| (|NonNegativeInteger|))) $) 104)) (|row| (((|Record| (|:| |Indices| (|List| |#1|)) (|:| |Entries| (|List| |#2|))) $ (|Integer|)) 33)) (|purge!| (((|Void|) $ (|Mapping| (|Boolean|) |#1|)) 70)) (|primitiveRowEchelon| (((|Record| (|:| |Ech| $) (|:| |Lt| (|Matrix| (|Fraction| |#2|))) (|:| |Pivots| (|List| |#2|)) (|:| |Rank| (|NonNegativeInteger|))) $) 130 (|has| |#2| (|GcdDomain|)))) (|pivots| (((|Record| (|:| |Indices| (|List| |#1|)) (|:| |Entries| (|List| |#2|))) $) 93)) (|pivot| (((|Record| (|:| |Index| |#1|) (|:| |Entry| |#2|)) $ (|Integer|)) 92)) (|nrows| (((|NonNegativeInteger|) $) 26)) (|new| (($ (|List| |#1|) (|Integer|)) 40)) (|ncols| (((|NonNegativeInteger|) $) 25)) (|join| (($ $ $) 81)) (|horizSplit| (((|Record| (|:| |Left| $) (|:| |Right| $)) $ |#1|) 84)) (|horizJoin| (($ $ $) 82)) (|extract| (($ $ (|Integer|) (|Integer|)) 80)) (|elt| ((|#2| $ (|Integer|) |#1|) 44)) (|elimZeroCols!| (((|Void|) $) 68)) (|deleteRow!| (((|Void|) $ (|Integer|)) 72)) (|copy| (($ $) 64)) (|consRow!| (((|Void|) $ (|Record| (|:| |Indices| (|List| |#1|)) (|:| |Entries| (|List| |#2|)))) 77)) (|coerce| (((|OutputForm|) $) 61) (((|Matrix| |#2|) $) 57)) (|appendRow!| (((|Void|) $ (|Record| (|:| |Indices| (|List| |#1|)) (|:| |Entries| (|List| |#2|)))) 79)) (|allIndices| (((|List| |#1|) $) 29)) (* (($ (|Matrix| |#2|) $) 136) (($ (|Matrix| (|Fraction| |#2|)) $) 148 (|has| |#2| (|IntegralDomain|))))) 
(((|SparseEchelonMatrix| |#1| |#2|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (ATTRIBUTE |shallowlyMutable|) (ATTRIBUTE |finiteAggregate|) (SIGNATURE |coerce| ((|Matrix| |#2|) $)) (SIGNATURE |copy| ($ $)) (SIGNATURE |ncols| ((|NonNegativeInteger|) $)) (SIGNATURE |nrows| ((|NonNegativeInteger|) $)) (SIGNATURE |allIndices| ((|List| |#1|) $)) (SIGNATURE |elimZeroCols!| ((|Void|) $)) (SIGNATURE |purge!| ((|Void|) $ (|Mapping| (|Boolean|) |#1|))) (SIGNATURE |sortedPurge!| ((|Void|) $ (|Mapping| (|Boolean|) |#1|))) (SIGNATURE |new| ($ (|List| |#1|) (|Integer|))) (SIGNATURE |elt| (|#2| $ (|Integer|) |#1|)) (SIGNATURE |setelt!| ((|Void|) $ (|Integer|) |#1| |#2|)) (SIGNATURE |row| ((|Record| (|:| |Indices| (|List| |#1|)) (|:| |Entries| (|List| |#2|))) $ (|Integer|))) (SIGNATURE |setRow!| ((|Void|) $ (|Integer|) (|Record| (|:| |Indices| (|List| |#1|)) (|:| |Entries| (|List| |#2|))))) (SIGNATURE |setRow!| ((|Void|) $ (|Integer|) (|List| |#1|) (|List| |#2|))) (SIGNATURE |deleteRow!| ((|Void|) $ (|Integer|))) (SIGNATURE |consRow!| ((|Void|) $ (|Record| (|:| |Indices| (|List| |#1|)) (|:| |Entries| (|List| |#2|))))) (SIGNATURE |appendRow!| ((|Void|) $ (|Record| (|:| |Indices| (|List| |#1|)) (|:| |Entries| (|List| |#2|))))) (SIGNATURE |extract| ($ $ (|Integer|) (|Integer|))) (SIGNATURE |rowEchelon| ((|Record| (|:| |Ech| $) (|:| |Lt| (|Matrix| |#2|)) (|:| |Pivots| (|List| |#2|)) (|:| |Rank| (|NonNegativeInteger|))) $)) (IF (|has| |#2| (|GcdDomain|)) (PROGN (SIGNATURE |setGcdMode| ((|Symbol|) (|Symbol|))) (SIGNATURE |primitiveRowEchelon| ((|Record| (|:| |Ech| $) (|:| |Lt| (|Matrix| (|Fraction| |#2|))) (|:| |Pivots| (|List| |#2|)) (|:| |Rank| (|NonNegativeInteger|))) $))) |noBranch|) (SIGNATURE |pivot| ((|Record| (|:| |Index| |#1|) (|:| |Entry| |#2|)) $ (|Integer|))) (SIGNATURE |pivots| ((|Record| (|:| |Indices| (|List| |#1|)) (|:| |Entries| (|List| |#2|))) $)) (SIGNATURE * ($ (|Matrix| |#2|) $)) (IF (|has| |#2| (|IntegralDomain|)) (SIGNATURE * ($ (|Matrix| (|Fraction| |#2|)) $)) |noBranch|) (SIGNATURE |join| ($ $ $)) (SIGNATURE |horizJoin| ($ $ $)) (SIGNATURE |horizSplit| ((|Record| (|:| |Left| $) (|:| |Right| $)) $ |#1|)))) (|OrderedSet|) (|Ring|)) (T |SparseEchelonMatrix|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|SparseEchelonMatrix| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)))) (|copy| (*1 *1 *1) (AND (|isDomain| *1 (|SparseEchelonMatrix| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|)))) (|ncols| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|SparseEchelonMatrix| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)))) (|nrows| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|SparseEchelonMatrix| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)))) (|allIndices| (*1 *2 *1) (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|SparseEchelonMatrix| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)))) (|elimZeroCols!| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SparseEchelonMatrix| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)))) (|purge!| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SparseEchelonMatrix| *4 *5)) (|ofCategory| *5 (|Ring|)))) (|sortedPurge!| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SparseEchelonMatrix| *4 *5)) (|ofCategory| *5 (|Ring|)))) (|new| (*1 *1 *2 *3) (AND (|isDomain| *2 (|List| *4)) (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|SparseEchelonMatrix| *4 *5)) (|ofCategory| *5 (|Ring|)))) (|elt| (*1 *2 *1 *3 *4) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|SparseEchelonMatrix| *4 *2)) (|ofCategory| *4 (|OrderedSet|)))) (|setelt!| (*1 *2 *1 *3 *4 *5) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SparseEchelonMatrix| *4 *5)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|Ring|)))) (|row| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Record| (|:| |Indices| (|List| *4)) (|:| |Entries| (|List| *5)))) (|isDomain| *1 (|SparseEchelonMatrix| *4 *5)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|Ring|)))) (|setRow!| (*1 *2 *1 *3 *4) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *4 (|Record| (|:| |Indices| (|List| *5)) (|:| |Entries| (|List| *6)))) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Ring|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SparseEchelonMatrix| *5 *6)))) (|setRow!| (*1 *2 *1 *3 *4 *5) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *4 (|List| *6)) (|isDomain| *5 (|List| *7)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|Ring|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SparseEchelonMatrix| *6 *7)))) (|deleteRow!| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SparseEchelonMatrix| *4 *5)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|Ring|)))) (|consRow!| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Record| (|:| |Indices| (|List| *4)) (|:| |Entries| (|List| *5)))) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SparseEchelonMatrix| *4 *5)))) (|appendRow!| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Record| (|:| |Indices| (|List| *4)) (|:| |Entries| (|List| *5)))) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SparseEchelonMatrix| *4 *5)))) (|extract| (*1 *1 *1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|SparseEchelonMatrix| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)))) (|rowEchelon| (*1 *2 *1) (AND (|isDomain| *2 (|Record| (|:| |Ech| (|SparseEchelonMatrix| *3 *4)) (|:| |Lt| (|Matrix| *4)) (|:| |Pivots| (|List| *4)) (|:| |Rank| (|NonNegativeInteger|)))) (|isDomain| *1 (|SparseEchelonMatrix| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)))) (|setGcdMode| (*1 *2 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|SparseEchelonMatrix| *3 *4)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)))) (|primitiveRowEchelon| (*1 *2 *1) (AND (|isDomain| *2 (|Record| (|:| |Ech| (|SparseEchelonMatrix| *3 *4)) (|:| |Lt| (|Matrix| (|Fraction| *4))) (|:| |Pivots| (|List| *4)) (|:| |Rank| (|NonNegativeInteger|)))) (|isDomain| *1 (|SparseEchelonMatrix| *3 *4)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)))) (|pivot| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Record| (|:| |Index| *4) (|:| |Entry| *5))) (|isDomain| *1 (|SparseEchelonMatrix| *4 *5)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|Ring|)))) (|pivots| (*1 *2 *1) (AND (|isDomain| *2 (|Record| (|:| |Indices| (|List| *3)) (|:| |Entries| (|List| *4)))) (|isDomain| *1 (|SparseEchelonMatrix| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)))) (* (*1 *1 *2 *1) (AND (|isDomain| *2 (|Matrix| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|SparseEchelonMatrix| *3 *4)) (|ofCategory| *3 (|OrderedSet|)))) (* (*1 *1 *2 *1) (AND (|isDomain| *2 (|Matrix| (|Fraction| *4))) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|SparseEchelonMatrix| *3 *4)) (|ofCategory| *3 (|OrderedSet|)))) (|join| (*1 *1 *1 *1) (AND (|isDomain| *1 (|SparseEchelonMatrix| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|)))) (|horizJoin| (*1 *1 *1 *1) (AND (|isDomain| *1 (|SparseEchelonMatrix| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|)))) (|horizSplit| (*1 *2 *1 *3) (AND (|isDomain| *2 (|Record| (|:| |Left| (|SparseEchelonMatrix| *3 *4)) (|:| |Right| (|SparseEchelonMatrix| *3 *4)))) (|isDomain| *1 (|SparseEchelonMatrix| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))))) 
(|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (ATTRIBUTE |shallowlyMutable|) (ATTRIBUTE |finiteAggregate|) (SIGNATURE |coerce| ((|Matrix| |#2|) $)) (SIGNATURE |copy| ($ $)) (SIGNATURE |ncols| ((|NonNegativeInteger|) $)) (SIGNATURE |nrows| ((|NonNegativeInteger|) $)) (SIGNATURE |allIndices| ((|List| |#1|) $)) (SIGNATURE |elimZeroCols!| ((|Void|) $)) (SIGNATURE |purge!| ((|Void|) $ (|Mapping| (|Boolean|) |#1|))) (SIGNATURE |sortedPurge!| ((|Void|) $ (|Mapping| (|Boolean|) |#1|))) (SIGNATURE |new| ($ (|List| |#1|) (|Integer|))) (SIGNATURE |elt| (|#2| $ (|Integer|) |#1|)) (SIGNATURE |setelt!| ((|Void|) $ (|Integer|) |#1| |#2|)) (SIGNATURE |row| ((|Record| (|:| |Indices| (|List| |#1|)) (|:| |Entries| (|List| |#2|))) $ (|Integer|))) (SIGNATURE |setRow!| ((|Void|) $ (|Integer|) (|Record| (|:| |Indices| (|List| |#1|)) (|:| |Entries| (|List| |#2|))))) (SIGNATURE |setRow!| ((|Void|) $ (|Integer|) (|List| |#1|) (|List| |#2|))) (SIGNATURE |deleteRow!| ((|Void|) $ (|Integer|))) (SIGNATURE |consRow!| ((|Void|) $ (|Record| (|:| |Indices| (|List| |#1|)) (|:| |Entries| (|List| |#2|))))) (SIGNATURE |appendRow!| ((|Void|) $ (|Record| (|:| |Indices| (|List| |#1|)) (|:| |Entries| (|List| |#2|))))) (SIGNATURE |extract| ($ $ (|Integer|) (|Integer|))) (SIGNATURE |rowEchelon| ((|Record| (|:| |Ech| $) (|:| |Lt| (|Matrix| |#2|)) (|:| |Pivots| (|List| |#2|)) (|:| |Rank| (|NonNegativeInteger|))) $)) (IF (|has| |#2| (|GcdDomain|)) (PROGN (SIGNATURE |setGcdMode| ((|Symbol|) (|Symbol|))) (SIGNATURE |primitiveRowEchelon| ((|Record| (|:| |Ech| $) (|:| |Lt| (|Matrix| (|Fraction| |#2|))) (|:| |Pivots| (|List| |#2|)) (|:| |Rank| (|NonNegativeInteger|))) $))) |noBranch|) (SIGNATURE |pivot| ((|Record| (|:| |Index| |#1|) (|:| |Entry| |#2|)) $ (|Integer|))) (SIGNATURE |pivots| ((|Record| (|:| |Indices| (|List| |#1|)) (|:| |Entries| (|List| |#2|))) $)) (SIGNATURE * ($ (|Matrix| |#2|) $)) (IF (|has| |#2| (|IntegralDomain|)) (SIGNATURE * ($ (|Matrix| (|Fraction| |#2|)) $)) |noBranch|) (SIGNATURE |join| ($ $ $)) (SIGNATURE |horizJoin| ($ $ $)) (SIGNATURE |horizSplit| ((|Record| (|:| |Left| $) (|:| |Right| $)) $ |#1|)))) 
((|union| (($ $ $) NIL) (($ $ |#2|) 13) (($ |#2| $) 14)) (|symmetricDifference| (($ $ $) 10)) (|difference| (($ $ $) NIL) (($ $ |#2|) 15))) 
(((|SetAggregate&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |union| (|#1| |#2| |#1|)) (SIGNATURE |union| (|#1| |#1| |#2|)) (SIGNATURE |union| (|#1| |#1| |#1|)) (SIGNATURE |symmetricDifference| (|#1| |#1| |#1|)) (SIGNATURE |difference| (|#1| |#1| |#2|)) (SIGNATURE |difference| (|#1| |#1| |#1|))) (|SetAggregate| |#2|) (|SetCategory|)) (T |SetAggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |union| (|#1| |#2| |#1|)) (SIGNATURE |union| (|#1| |#1| |#2|)) (SIGNATURE |union| (|#1| |#1| |#1|)) (SIGNATURE |symmetricDifference| (|#1| |#1| |#1|)) (SIGNATURE |difference| (|#1| |#1| |#2|)) (SIGNATURE |difference| (|#1| |#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|union| (($ $ $) 17) (($ $ |#1|) 16) (($ |#1| $) 15)) (|symmetricDifference| (($ $ $) 19)) (|subset?| (((|Boolean|) $ $) 18)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 34)) (|set| (($) 24) (($ (|List| |#1|)) 23)) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 55 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) 35 T CONST)) (|removeDuplicates| (($ $) 58 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove| (($ |#1| $) 57 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#1|) $) 54 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 56 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 53 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 52 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|parts| (((|List| |#1|) $) 42 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 33)) (|members| (((|List| |#1|) $) 43 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 45 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 37)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 32)) (|latex| (((|String|) $) 9)) (|intersect| (($ $ $) 22)) (|hash| (((|SingleInteger|) $) 10)) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) 51)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 40 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) 49 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 48 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 47 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| (|Equation| |#1|))) 46 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 28)) (|empty?| (((|Boolean|) $) 31)) (|empty| (($) 30)) (|difference| (($ $ $) 21) (($ $ |#1|) 20)) (|count| (((|NonNegativeInteger|) |#1| $) 44 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 41 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) 29)) (|convert| (((|InputForm|) $) 59 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 50)) (|coerce| (((|OutputForm|) $) 11)) (|brace| (($) 26) (($ (|List| |#1|)) 25)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 39 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 6)) (< (((|Boolean|) $ $) 27)) (|#| (((|NonNegativeInteger|) $) 36 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|SetAggregate| |#1|) (|Category|) (|SetCategory|)) (T |SetAggregate|)) 
((< (*1 *2 *1 *1) (AND (|ofCategory| *1 (|SetAggregate| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|brace| (*1 *1) (AND (|ofCategory| *1 (|SetAggregate| *2)) (|ofCategory| *2 (|SetCategory|)))) (|brace| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *1 (|SetAggregate| *3)))) (|set| (*1 *1) (AND (|ofCategory| *1 (|SetAggregate| *2)) (|ofCategory| *2 (|SetCategory|)))) (|set| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *1 (|SetAggregate| *3)))) (|intersect| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|SetAggregate| *2)) (|ofCategory| *2 (|SetCategory|)))) (|difference| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|SetAggregate| *2)) (|ofCategory| *2 (|SetCategory|)))) (|difference| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|SetAggregate| *2)) (|ofCategory| *2 (|SetCategory|)))) (|symmetricDifference| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|SetAggregate| *2)) (|ofCategory| *2 (|SetCategory|)))) (|subset?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|SetAggregate| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|union| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|SetAggregate| *2)) (|ofCategory| *2 (|SetCategory|)))) (|union| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|SetAggregate| *2)) (|ofCategory| *2 (|SetCategory|)))) (|union| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|SetAggregate| *2)) (|ofCategory| *2 (|SetCategory|))))) 
(|Join| (|SetCategory|) (|Collection| |t#1|) (CATEGORY |domain| (ATTRIBUTE |partiallyOrderedSet|) (SIGNATURE < ((|Boolean|) $ $)) (SIGNATURE |brace| ($)) (SIGNATURE |brace| ($ (|List| |t#1|))) (SIGNATURE |set| ($)) (SIGNATURE |set| ($ (|List| |t#1|))) (SIGNATURE |intersect| ($ $ $)) (SIGNATURE |difference| ($ $ $)) (SIGNATURE |difference| ($ $ |t#1|)) (SIGNATURE |symmetricDifference| ($ $ $)) (SIGNATURE |subset?| ((|Boolean|) $ $)) (SIGNATURE |union| ($ $ $)) (SIGNATURE |union| ($ $ |t#1|)) (SIGNATURE |union| ($ |t#1| $)))) 
(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= (((|Boolean|) $ $) 7)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|degree| (((|PositiveInteger|) $) 12)) (|coerce| (((|OutputForm|) $) 11)) (= (((|Boolean|) $ $) 6))) 
(((|SetCategoryWithDegree|) (|Category|)) (T |SetCategoryWithDegree|)) 
((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|SetCategoryWithDegree|)) (|isDomain| *2 (|PositiveInteger|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |degree| ((|PositiveInteger|) $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((|latex| (((|String|) $) 10)) (|hash| (((|SingleInteger|) $) 8))) 
(((|SetCategory&| |#1|) (CATEGORY |domain| (SIGNATURE |latex| ((|String|) |#1|)) (SIGNATURE |hash| ((|SingleInteger|) |#1|))) (|SetCategory|)) (T |SetCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |latex| ((|String|) |#1|)) (SIGNATURE |hash| ((|SingleInteger|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (= (((|Boolean|) $ $) 6))) 
(((|SetCategory|) (|Category|)) (T |SetCategory|)) 
((|hash| (*1 *2 *1) (AND (|ofCategory| *1 (|SetCategory|)) (|isDomain| *2 (|SingleInteger|)))) (|latex| (*1 *2 *1) (AND (|ofCategory| *1 (|SetCategory|)) (|isDomain| *2 (|String|))))) 
(|Join| (|BasicType|) (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |hash| ((|SingleInteger|) $)) (SIGNATURE |latex| ((|String|) $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|size| (((|NonNegativeInteger|)) 30)) (|setOfMinN| (($ (|List| (|PositiveInteger|))) 52)) (|replaceKthElement| (((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) 57)) (|random| (($) 32)) (|member?| (((|Boolean|) (|PositiveInteger|) $) 35)) (|lookup| (((|PositiveInteger|) $) 50)) (|latex| (((|String|) $) NIL)) (|index| (($ (|PositiveInteger|)) 31)) (|incrementKthElement| (((|Union| $ "failed") $ (|PositiveInteger|)) 55)) (|hash| (((|SingleInteger|) $) NIL)) (|enumerate| (((|List| $)) NIL) (((|Vector| $)) 40)) (|elements| (((|List| (|PositiveInteger|)) $) 23)) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) 56)) (|coerce| (((|OutputForm|) $) 29)) (= (((|Boolean|) $ $) 21))) 
(((|SetOfMIntegersInOneToN| |#1| |#2|) (|Join| (|Finite|) (CATEGORY |domain| (SIGNATURE |incrementKthElement| ((|Union| $ "failed") $ (|PositiveInteger|))) (SIGNATURE |replaceKthElement| ((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |elements| ((|List| (|PositiveInteger|)) $)) (SIGNATURE |setOfMinN| ($ (|List| (|PositiveInteger|)))) (SIGNATURE |enumerate| ((|Vector| $))) (SIGNATURE |member?| ((|Boolean|) (|PositiveInteger|) $)) (SIGNATURE |delta| ((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|))))) (|PositiveInteger|) (|PositiveInteger|)) (T |SetOfMIntegersInOneToN|)) 
((|incrementKthElement| (*1 *1 *1 *2) (|partial| AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|SetOfMIntegersInOneToN| *3 *4)) (|ofType| *3 *2) (|ofType| *4 *2))) (|replaceKthElement| (*1 *1 *1 *2 *2) (|partial| AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|SetOfMIntegersInOneToN| *3 *4)) (|ofType| *3 *2) (|ofType| *4 *2))) (|elements| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|PositiveInteger|))) (|isDomain| *1 (|SetOfMIntegersInOneToN| *3 *4)) (|ofType| *3 (|PositiveInteger|)) (|ofType| *4 (|PositiveInteger|)))) (|setOfMinN| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|PositiveInteger|))) (|isDomain| *1 (|SetOfMIntegersInOneToN| *3 *4)) (|ofType| *3 (|PositiveInteger|)) (|ofType| *4 (|PositiveInteger|)))) (|enumerate| (*1 *2) (AND (|isDomain| *2 (|Vector| (|SetOfMIntegersInOneToN| *3 *4))) (|isDomain| *1 (|SetOfMIntegersInOneToN| *3 *4)) (|ofType| *3 (|PositiveInteger|)) (|ofType| *4 (|PositiveInteger|)))) (|member?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SetOfMIntegersInOneToN| *4 *5)) (|ofType| *4 *3) (|ofType| *5 *3))) (|delta| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|SetOfMIntegersInOneToN| *4 *5)) (|ofType| *4 *3) (|ofType| *5 *3)))) 
(|Join| (|Finite|) (CATEGORY |domain| (SIGNATURE |incrementKthElement| ((|Union| $ "failed") $ (|PositiveInteger|))) (SIGNATURE |replaceKthElement| ((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |elements| ((|List| (|PositiveInteger|)) $)) (SIGNATURE |setOfMinN| ($ (|List| (|PositiveInteger|)))) (SIGNATURE |enumerate| ((|Vector| $))) (SIGNATURE |member?| ((|Boolean|) (|PositiveInteger|) $)) (SIGNATURE |delta| ((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|))))) 
((~= (((|Boolean|) $ $) NIL)) (|universe| (($) NIL (|has| |#1| (|Finite|)))) (|union| (($ |#1| $) NIL) (($ $ |#1|) NIL) (($ $ $) 73)) (|symmetricDifference| (($ $ $) 71)) (|subset?| (((|Boolean|) $ $) 72)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|size| (((|NonNegativeInteger|)) NIL (|has| |#1| (|Finite|)))) (|set| (($ (|List| |#1|)) NIL) (($) 13)) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) NIL T CONST)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|remove!| (($ |#1| $) 67 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remove| (($ |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) (($ (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 43 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|)))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 41 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 39 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|random| (($) NIL (|has| |#1| (|Finite|)))) (|parts| (((|List| |#1|) $) 19 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|min| ((|#1| $) 57 (|has| |#1| (|OrderedSet|)))) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 66 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|max| ((|#1| $) 55 (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| |#1| |#1|) $) 33 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 34)) (|lookup| (((|PositiveInteger|) $) NIL (|has| |#1| (|Finite|)))) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL)) (|intersect| (($ $ $) 69)) (|inspect| ((|#1| $) 25)) (|insert!| (($ |#1| $) 65)) (|index| (($ (|PositiveInteger|)) NIL (|has| |#1| (|Finite|)))) (|hash| (((|SingleInteger|) $) NIL)) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) 31)) (|extract!| ((|#1| $) 27)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|enumerate| (((|List| $)) NIL (|has| |#1| (|Finite|)))) (|empty?| (((|Boolean|) $) 21)) (|empty| (($) 11)) (|difference| (($ $ |#1|) NIL) (($ $ $) 70)) (|dictionary| (($) NIL) (($ (|List| |#1|)) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) 16)) (|convert| (((|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 61)) (|complement| (($ $) NIL (|has| |#1| (|Finite|)))) (|coerce| (((|OutputForm|) $) NIL)) (|cardinality| (((|NonNegativeInteger|) $) NIL)) (|brace| (($ (|List| |#1|)) NIL) (($) 12)) (|bag| (($ (|List| |#1|)) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 54)) (< (((|Boolean|) $ $) NIL)) (|#| (((|NonNegativeInteger|) $) 10 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|Set| |#1|) (|FiniteSetAggregate| |#1|) (|SetCategory|)) (T |Set|)) 
NIL 
(|FiniteSetAggregate| |#1|) 
((~= (((|Boolean|) $ $) 7)) (|symbol?| (((|Boolean|) $) 31)) (|symbol| ((|#2| $) 26)) (|string?| (((|Boolean|) $) 32)) (|string| ((|#1| $) 27)) (|pair?| (((|Boolean|) $) 34)) (|null?| (((|Boolean|) $) 36)) (|list?| (((|Boolean|) $) 33)) (|latex| (((|String|) $) 9)) (|integer?| (((|Boolean|) $) 30)) (|integer| ((|#3| $) 25)) (|hash| (((|SingleInteger|) $) 10)) (|float?| (((|Boolean|) $) 29)) (|float| ((|#4| $) 24)) (|expr| ((|#5| $) 23)) (|eq| (((|Boolean|) $ $) 37)) (|elt| (($ $ (|Integer|)) 13) (($ $ (|List| (|Integer|))) 12)) (|destruct| (((|List| $) $) 28)) (|convert| (($ (|List| $)) 22) (($ |#1|) 21) (($ |#2|) 20) (($ |#3|) 19) (($ |#4|) 18) (($ |#5|) 17)) (|coerce| (((|OutputForm|) $) 11)) (|cdr| (($ $) 15)) (|car| (($ $) 16)) (|atom?| (((|Boolean|) $) 35)) (= (((|Boolean|) $ $) 6)) (|#| (((|Integer|) $) 14))) 
(((|SExpressionCategory| |#1| |#2| |#3| |#4| |#5|) (|Category|) (|SetCategory|) (|SetCategory|) (|SetCategory|) (|SetCategory|) (|SetCategory|)) (T |SExpressionCategory|)) 
((|eq| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|null?| (*1 *2 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|atom?| (*1 *2 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|pair?| (*1 *2 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|list?| (*1 *2 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|string?| (*1 *2 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|symbol?| (*1 *2 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|integer?| (*1 *2 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|float?| (*1 *2 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|destruct| (*1 *2 *1) (AND (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7)))) (|string| (*1 *2 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *2 *3 *4 *5 *6)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)))) (|symbol| (*1 *2 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *2 *4 *5 *6)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)))) (|integer| (*1 *2 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *2 *5 *6)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)))) (|float| (*1 *2 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *2 *6)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)))) (|expr| (*1 *2 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *7 (|SetCategory|)))) (|convert| (*1 *1 *2) (AND (|ofCategory| *1 (|SExpressionCategory| *2 *3 *4 *5 *6)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)))) (|convert| (*1 *1 *2) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *2 *4 *5 *6)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)))) (|convert| (*1 *1 *2) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *2 *5 *6)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)))) (|convert| (*1 *1 *2) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *2 *6)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)))) (|convert| (*1 *1 *2) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)))) (|car| (*1 *1 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *2 *3 *4 *5 *6)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)))) (|cdr| (*1 *1 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *2 *3 *4 *5 *6)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)))) (|#| (*1 *2 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Integer|)))) (|elt| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *7 (|SetCategory|)))) (|elt| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *7 (|SetCategory|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |eq| ((|Boolean|) $ $)) (SIGNATURE |null?| ((|Boolean|) $)) (SIGNATURE |atom?| ((|Boolean|) $)) (SIGNATURE |pair?| ((|Boolean|) $)) (SIGNATURE |list?| ((|Boolean|) $)) (SIGNATURE |string?| ((|Boolean|) $)) (SIGNATURE |symbol?| ((|Boolean|) $)) (SIGNATURE |integer?| ((|Boolean|) $)) (SIGNATURE |float?| ((|Boolean|) $)) (SIGNATURE |destruct| ((|List| $) $)) (SIGNATURE |string| (|t#1| $)) (SIGNATURE |symbol| (|t#2| $)) (SIGNATURE |integer| (|t#3| $)) (SIGNATURE |float| (|t#4| $)) (SIGNATURE |expr| (|t#5| $)) (SIGNATURE |convert| ($ (|List| $))) (SIGNATURE |convert| ($ |t#1|)) (SIGNATURE |convert| ($ |t#2|)) (SIGNATURE |convert| ($ |t#3|)) (SIGNATURE |convert| ($ |t#4|)) (SIGNATURE |convert| ($ |t#5|)) (SIGNATURE |car| ($ $)) (SIGNATURE |cdr| ($ $)) (SIGNATURE |#| ((|Integer|) $)) (SIGNATURE |elt| ($ $ (|Integer|))) (SIGNATURE |elt| ($ $ (|List| (|Integer|)))))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|symbol?| (((|Boolean|) $) NIL)) (|symbol| (((|Symbol|) $) NIL)) (|string?| (((|Boolean|) $) NIL)) (|string| (((|String|) $) NIL)) (|pair?| (((|Boolean|) $) NIL)) (|null?| (((|Boolean|) $) NIL)) (|list?| (((|Boolean|) $) NIL)) (|latex| (((|String|) $) NIL)) (|integer?| (((|Boolean|) $) NIL)) (|integer| (((|Integer|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|float?| (((|Boolean|) $) NIL)) (|float| (((|DoubleFloat|) $) NIL)) (|expr| (((|OutputForm|) $) NIL)) (|eq| (((|Boolean|) $ $) NIL)) (|elt| (($ $ (|Integer|)) NIL) (($ $ (|List| (|Integer|))) NIL)) (|destruct| (((|List| $) $) NIL)) (|convert| (($ (|List| $)) NIL) (($ (|String|)) NIL) (($ (|Symbol|)) NIL) (($ (|Integer|)) NIL) (($ (|DoubleFloat|)) NIL) (($ (|OutputForm|)) NIL)) (|coerce| (((|OutputForm|) $) NIL)) (|cdr| (($ $) NIL)) (|car| (($ $) NIL)) (|atom?| (((|Boolean|) $) NIL)) (= (((|Boolean|) $ $) NIL)) (|#| (((|Integer|) $) NIL))) 
(((|SExpression|) (|SExpressionCategory| (|String|) (|Symbol|) (|Integer|) (|DoubleFloat|) (|OutputForm|))) (T |SExpression|)) 
NIL 
(|SExpressionCategory| (|String|) (|Symbol|) (|Integer|) (|DoubleFloat|) (|OutputForm|)) 
((~= (((|Boolean|) $ $) NIL)) (|symbol?| (((|Boolean|) $) 37)) (|symbol| ((|#2| $) 41)) (|string?| (((|Boolean|) $) 36)) (|string| ((|#1| $) 40)) (|pair?| (((|Boolean|) $) 34)) (|null?| (((|Boolean|) $) 14)) (|list?| (((|Boolean|) $) 35)) (|latex| (((|String|) $) NIL)) (|integer?| (((|Boolean|) $) 38)) (|integer| ((|#3| $) 43)) (|hash| (((|SingleInteger|) $) NIL)) (|float?| (((|Boolean|) $) 39)) (|float| ((|#4| $) 42)) (|expr| ((|#5| $) 44)) (|eq| (((|Boolean|) $ $) 33)) (|elt| (($ $ (|Integer|)) 55) (($ $ (|List| (|Integer|))) 57)) (|destruct| (((|List| $) $) 21)) (|convert| (($ (|List| $)) 45) (($ |#1|) 46) (($ |#2|) 47) (($ |#3|) 48) (($ |#4|) 49) (($ |#5|) 50)) (|coerce| (((|OutputForm|) $) 22)) (|cdr| (($ $) 20)) (|car| (($ $) 51)) (|atom?| (((|Boolean|) $) 18)) (= (((|Boolean|) $ $) 32)) (|#| (((|Integer|) $) 53))) 
(((|SExpressionOf| |#1| |#2| |#3| |#4| |#5|) (|SExpressionCategory| |#1| |#2| |#3| |#4| |#5|) (|SetCategory|) (|SetCategory|) (|SetCategory|) (|SetCategory|) (|SetCategory|)) (T |SExpressionOf|)) 
NIL 
(|SExpressionCategory| |#1| |#2| |#3| |#4| |#5|) 
((|outputAsFortran| (((|Void|) $) 23)) (|fortran| (($ (|Symbol|) (|FortranScalarType|) |#2|) 11)) (|coerce| (((|OutputForm|) $) 16))) 
(((|SimpleFortranProgram| |#1| |#2|) (|Join| (|FortranProgramCategory|) (CATEGORY |domain| (SIGNATURE |fortran| ($ (|Symbol|) (|FortranScalarType|) |#2|)))) (|OrderedSet|) (|FunctionSpace| |#1|)) (T |SimpleFortranProgram|)) 
((|fortran| (*1 *1 *2 *3 *4) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|FortranScalarType|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|SimpleFortranProgram| *5 *4)) (|ofCategory| *4 (|FunctionSpace| *5))))) 
(|Join| (|FortranProgramCategory|) (CATEGORY |domain| (SIGNATURE |fortran| ($ (|Symbol|) (|FortranScalarType|) |#2|)))) 
((|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) 37)) (|subTriSet?| (((|Boolean|) |#5| |#5|) 51)) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) 74) (((|Boolean|) |#5| |#5|) 60)) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) 57)) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) 62)) (|stopTable!| (((|Void|)) 33)) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) 29)) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) 81)) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) 79)) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) 101)) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) 46)) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) 70)) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) 56)) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) 58)) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) 59)) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) 97)) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) 42))) 
(((|SquareFreeQuasiComponentPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |startTable!| ((|Void|) (|String|) (|String|) (|String|))) (SIGNATURE |stopTable!| ((|Void|))) (SIGNATURE |supDimElseRittWu?| ((|Boolean|) |#5| |#5|)) (SIGNATURE |algebraicSort| ((|List| |#5|) (|List| |#5|))) (SIGNATURE |moreAlgebraic?| ((|Boolean|) |#5| |#5|)) (SIGNATURE |subTriSet?| ((|Boolean|) |#5| |#5|)) (SIGNATURE |subPolSet?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |internalSubPolSet?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |internalInfRittWu?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |infRittWu?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |internalSubQuasiComponent?| ((|Union| (|Boolean|) "failed") |#5| |#5|)) (SIGNATURE |subQuasiComponent?| ((|Boolean|) |#5| |#5|)) (SIGNATURE |subQuasiComponent?| ((|Boolean|) |#5| (|List| |#5|))) (SIGNATURE |removeSuperfluousQuasiComponents| ((|List| |#5|) (|List| |#5|))) (SIGNATURE |subCase?| ((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) (SIGNATURE |removeSuperfluousCases| ((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) (SIGNATURE |prepareDecompose| ((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|))) (SIGNATURE |branchIfCan| ((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |SquareFreeQuasiComponentPackage|)) 
((|branchIfCan| (*1 *2 *3 *4 *3 *5 *5 *5 *5 *5) (|partial| AND (|isDomain| *5 (|Boolean|)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8)) (|isDomain| *2 (|Record| (|:| |eq| (|List| *9)) (|:| |tower| *4) (|:| |ineq| (|List| *9)))) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *6 *7 *8 *9 *4)) (|isDomain| *3 (|List| *9)) (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *9)))) (|prepareDecompose| (*1 *2 *3 *4 *5 *5) (AND (|isDomain| *4 (|List| *10)) (|isDomain| *5 (|Boolean|)) (|ofCategory| *10 (|RegularTriangularSetCategory| *6 *7 *8 *9)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8)) (|isDomain| *2 (|List| (|Record| (|:| |eq| (|List| *9)) (|:| |tower| *10) (|:| |ineq| (|List| *9))))) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *6 *7 *8 *9 *10)) (|isDomain| *3 (|List| *9)))) (|removeSuperfluousCases| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |val| (|List| *6)) (|:| |tower| *7)))) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *3 *4 *5 *6 *7)))) (|subCase?| (*1 *2 *3 *3) (AND (|isDomain| *3 (|Record| (|:| |val| (|List| *7)) (|:| |tower| *8))) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *8)))) (|removeSuperfluousQuasiComponents| (*1 *2 *2) (AND (|isDomain| *2 (|List| *7)) (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *3 *4 *5 *6 *7)))) (|subQuasiComponent?| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *5 *6 *7 *8 *3)))) (|subQuasiComponent?| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|internalSubQuasiComponent?| (*1 *2 *3 *3) (|partial| AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|infRittWu?| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|internalInfRittWu?| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|internalSubPolSet?| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|subPolSet?| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|subTriSet?| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|moreAlgebraic?| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|algebraicSort| (*1 *2 *2) (AND (|isDomain| *2 (|List| *7)) (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *3 *4 *5 *6 *7)))) (|supDimElseRittWu?| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|stopTable!| (*1 *2) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *3 *4 *5 *6 *7)) (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)))) (|startTable!| (*1 *2 *3 *3 *3) (AND (|isDomain| *3 (|String|)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))) 
(CATEGORY |package| (SIGNATURE |startTable!| ((|Void|) (|String|) (|String|) (|String|))) (SIGNATURE |stopTable!| ((|Void|))) (SIGNATURE |supDimElseRittWu?| ((|Boolean|) |#5| |#5|)) (SIGNATURE |algebraicSort| ((|List| |#5|) (|List| |#5|))) (SIGNATURE |moreAlgebraic?| ((|Boolean|) |#5| |#5|)) (SIGNATURE |subTriSet?| ((|Boolean|) |#5| |#5|)) (SIGNATURE |subPolSet?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |internalSubPolSet?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |internalInfRittWu?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |infRittWu?| ((|Boolean|) (|List| |#4|) (|List| |#4|))) (SIGNATURE |internalSubQuasiComponent?| ((|Union| (|Boolean|) "failed") |#5| |#5|)) (SIGNATURE |subQuasiComponent?| ((|Boolean|) |#5| |#5|)) (SIGNATURE |subQuasiComponent?| ((|Boolean|) |#5| (|List| |#5|))) (SIGNATURE |removeSuperfluousQuasiComponents| ((|List| |#5|) (|List| |#5|))) (SIGNATURE |subCase?| ((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) (SIGNATURE |removeSuperfluousCases| ((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) (SIGNATURE |prepareDecompose| ((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|))) (SIGNATURE |branchIfCan| ((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)))) 
((|stoseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) 94)) (|stosePrepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) 70)) (|stoseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) 88)) (|stoseInvertibleSetsqfreg| (((|List| |#5|) |#4| |#5|) 109)) (|stoseInvertibleSetreg| (((|List| |#5|) |#4| |#5|) 116)) (|stoseInvertibleSet| (((|List| |#5|) |#4| |#5|) 117)) (|stoseInvertible?sqfreg| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) 95)) (|stoseInvertible?reg| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) 115)) (|stoseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) 44) (((|Boolean|) |#4| |#5|) 52)) (|stoseInternalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) 82) (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) 49)) (|stoseIntegralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) 77)) (|stopTableInvSet!| (((|Void|)) 35)) (|stopTableGcd!| (((|Void|)) 25)) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) 31)) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) 20))) 
(((|SquareFreeRegularTriangularSetGcdPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |startTableGcd!| ((|Void|) (|String|) (|String|) (|String|))) (SIGNATURE |stopTableGcd!| ((|Void|))) (SIGNATURE |startTableInvSet!| ((|Void|) (|String|) (|String|) (|String|))) (SIGNATURE |stopTableInvSet!| ((|Void|))) (SIGNATURE |stosePrepareSubResAlgo| ((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|)) (SIGNATURE |stoseInternalLastSubResultant| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|))) (SIGNATURE |stoseInternalLastSubResultant| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|))) (SIGNATURE |stoseIntegralLastSubResultant| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|)) (SIGNATURE |stoseLastSubResultant| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|)) (SIGNATURE |stoseInvertible?| ((|Boolean|) |#4| |#5|)) (SIGNATURE |stoseInvertible?sqfreg| ((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|)) (SIGNATURE |stoseInvertibleSetsqfreg| ((|List| |#5|) |#4| |#5|)) (SIGNATURE |stoseInvertible?reg| ((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|)) (SIGNATURE |stoseInvertibleSetreg| ((|List| |#5|) |#4| |#5|)) (SIGNATURE |stoseInvertible?| ((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|)) (SIGNATURE |stoseInvertibleSet| ((|List| |#5|) |#4| |#5|)) (SIGNATURE |stoseSquareFreePart| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |SquareFreeRegularTriangularSetGcdPackage|)) 
((|stoseSquareFreePart| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4)))) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|stoseInvertibleSet| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|stoseInvertible?| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| *4)))) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|stoseInvertibleSetreg| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|stoseInvertible?reg| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| *4)))) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|stoseInvertibleSetsqfreg| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|stoseInvertible?sqfreg| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| *4)))) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|stoseInvertible?| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|stoseLastSubResultant| (*1 *2 *3 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4)))) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|stoseIntegralLastSubResultant| (*1 *2 *3 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4)))) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|stoseInternalLastSubResultant| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| (|Record| (|:| |val| (|List| *8)) (|:| |tower| *9)))) (|isDomain| *5 (|Boolean|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *6 *7 *4)) (|ofCategory| *9 (|RegularTriangularSetCategory| *6 *7 *4 *8)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|List| (|Record| (|:| |val| *8) (|:| |tower| *9)))) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *6 *7 *4 *8 *9)))) (|stoseInternalLastSubResultant| (*1 *2 *3 *3 *4 *5 *5) (AND (|isDomain| *5 (|Boolean|)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8)) (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4)))) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *6 *7 *8 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *3)))) (|stosePrepareSubResAlgo| (*1 *2 *3 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4)))) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|stopTableInvSet!| (*1 *2) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *3 *4 *5 *6 *7)) (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)))) (|startTableInvSet!| (*1 *2 *3 *3 *3) (AND (|isDomain| *3 (|String|)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|stopTableGcd!| (*1 *2) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *3 *4 *5 *6 *7)) (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)))) (|startTableGcd!| (*1 *2 *3 *3 *3) (AND (|isDomain| *3 (|String|)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))) 
(CATEGORY |package| (SIGNATURE |startTableGcd!| ((|Void|) (|String|) (|String|) (|String|))) (SIGNATURE |stopTableGcd!| ((|Void|))) (SIGNATURE |startTableInvSet!| ((|Void|) (|String|) (|String|) (|String|))) (SIGNATURE |stopTableInvSet!| ((|Void|))) (SIGNATURE |stosePrepareSubResAlgo| ((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|)) (SIGNATURE |stoseInternalLastSubResultant| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|))) (SIGNATURE |stoseInternalLastSubResultant| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|))) (SIGNATURE |stoseIntegralLastSubResultant| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|)) (SIGNATURE |stoseLastSubResultant| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|)) (SIGNATURE |stoseInvertible?| ((|Boolean|) |#4| |#5|)) (SIGNATURE |stoseInvertible?sqfreg| ((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|)) (SIGNATURE |stoseInvertibleSetsqfreg| ((|List| |#5|) |#4| |#5|)) (SIGNATURE |stoseInvertible?reg| ((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|)) (SIGNATURE |stoseInvertibleSetreg| ((|List| |#5|) |#4| |#5|)) (SIGNATURE |stoseInvertible?| ((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|)) (SIGNATURE |stoseInvertibleSet| ((|List| |#5|) |#4| |#5|)) (SIGNATURE |stoseSquareFreePart| ((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|))) 
((~= (((|Boolean|) $ $) 7)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 78)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 79) (((|List| $) (|List| |#4|) (|Boolean|)) 104)) (|variables| (((|List| |#3|) $) 32)) (|trivialIdeal?| (((|Boolean|) $) 25)) (|triangular?| (((|Boolean|) $) 16 (|has| |#1| (|IntegralDomain|)))) (|stronglyReduced?| (((|Boolean|) |#4| $) 94) (((|Boolean|) $) 90)) (|stronglyReduce| ((|#4| |#4| $) 85)) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) 119)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 26)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 43)) (|select| (($ (|Mapping| (|Boolean|) |#4|) $) 64 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| |#4| "failed") $ |#3|) 72)) (|sample| (($) 44 T CONST)) (|roughUnitIdeal?| (((|Boolean|) $) 21 (|has| |#1| (|IntegralDomain|)))) (|roughSubIdeal?| (((|Boolean|) $ $) 23 (|has| |#1| (|IntegralDomain|)))) (|roughEqualIdeals?| (((|Boolean|) $ $) 22 (|has| |#1| (|IntegralDomain|)))) (|roughBase?| (((|Boolean|) $) 24 (|has| |#1| (|IntegralDomain|)))) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 86)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) 17 (|has| |#1| (|IntegralDomain|)))) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) 18 (|has| |#1| (|IntegralDomain|)))) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 35)) (|retract| (($ (|List| |#4|)) 34)) (|rest| (((|Union| $ "failed") $) 75)) (|removeZero| ((|#4| |#4| $) 82)) (|removeDuplicates| (($ $) 67 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove| (($ |#4| $) 66 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#4|) $) 63 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 19 (|has| |#1| (|IntegralDomain|)))) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) 95)) (|reduceByQuasiMonic| ((|#4| |#4| $) 80)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 65 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 62 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 61 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 87)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 98)) (|purelyTranscendental?| (((|Boolean|) |#4| $) 129)) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) 126)) (|purelyAlgebraic?| (((|Boolean|) |#4| $) 130) (((|Boolean|) $) 127)) (|parts| (((|List| |#4|) $) 51 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|normalized?| (((|Boolean|) |#4| $) 97) (((|Boolean|) $) 96)) (|mvar| ((|#3| $) 33)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 42)) (|members| (((|List| |#4|) $) 52 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#4| $) 54 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#4| |#4|) $) 47 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#4| |#4|) $) 46)) (|mainVariables| (((|List| |#3|) $) 31)) (|mainVariable?| (((|Boolean|) |#3| $) 30)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 41)) (|latex| (((|String|) $) 9)) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) 121)) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) 120)) (|last| (((|Union| |#4| "failed") $) 76)) (|invertibleSet| (((|List| $) |#4| $) 122)) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) 125)) (|invertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) 124) (((|Boolean|) |#4| $) 123)) (|intersect| (((|List| $) |#4| $) 118) (((|List| $) (|List| |#4|) $) 117) (((|List| $) (|List| |#4|) (|List| $)) 116) (((|List| $) |#4| (|List| $)) 115)) (|internalAugment| (($ |#4| $) 110) (($ (|List| |#4|) $) 109)) (|initials| (((|List| |#4|) $) 100)) (|initiallyReduced?| (((|Boolean|) |#4| $) 92) (((|Boolean|) $) 88)) (|initiallyReduce| ((|#4| |#4| $) 83)) (|infRittWu?| (((|Boolean|) $ $) 103)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 20 (|has| |#1| (|IntegralDomain|)))) (|headReduced?| (((|Boolean|) |#4| $) 93) (((|Boolean|) $) 89)) (|headReduce| ((|#4| |#4| $) 84)) (|hash| (((|SingleInteger|) $) 10)) (|first| (((|Union| |#4| "failed") $) 77)) (|find| (((|Union| |#4| "failed") (|Mapping| (|Boolean|) |#4|) $) 60)) (|extendIfCan| (((|Union| $ "failed") $ |#4|) 71)) (|extend| (($ $ |#4|) 70) (((|List| $) |#4| $) 108) (((|List| $) |#4| (|List| $)) 107) (((|List| $) (|List| |#4|) $) 106) (((|List| $) (|List| |#4|) (|List| $)) 105)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) 49 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 58 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ |#4| |#4|) 57 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|Equation| |#4|)) 56 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|List| (|Equation| |#4|))) 55 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 37)) (|empty?| (((|Boolean|) $) 40)) (|empty| (($) 39)) (|degree| (((|NonNegativeInteger|) $) 99)) (|count| (((|NonNegativeInteger|) |#4| $) 53 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#4|) $) 50 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) 38)) (|convert| (((|InputForm|) $) 68 (|has| |#4| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#4|)) 59)) (|collectUpper| (($ $ |#3|) 27)) (|collectUnder| (($ $ |#3|) 29)) (|collectQuasiMonic| (($ $) 81)) (|collect| (($ $ |#3|) 28)) (|coerce| (((|OutputForm|) $) 11) (((|List| |#4|) $) 36)) (|coHeight| (((|NonNegativeInteger|) $) 69 (|has| |#3| (|Finite|)))) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 102) (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 101)) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) 91)) (|augment| (((|List| $) |#4| $) 114) (((|List| $) |#4| (|List| $)) 113) (((|List| $) (|List| |#4|) $) 112) (((|List| $) (|List| |#4|) (|List| $)) 111)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) 48 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|algebraicVariables| (((|List| |#3|) $) 74)) (|algebraicCoefficients?| (((|Boolean|) |#4| $) 128)) (|algebraic?| (((|Boolean|) |#3| $) 73)) (= (((|Boolean|) $ $) 6)) (|#| (((|NonNegativeInteger|) $) 45 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|SquareFreeRegularTriangularSetCategory| |#1| |#2| |#3| |#4|) (|Category|) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |t#1| |t#2| |t#3|)) (T |SquareFreeRegularTriangularSetCategory|)) 
NIL 
(|Join| (|RegularTriangularSetCategory| |t#1| |t#2| |t#3| |t#4|)) 
(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|TriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|Type|) . T)) 
((|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) 20)) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) 12)) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) 16)) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) 9)) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) 44) (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) 39)) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) 26)) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) 43)) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) 31)) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) 33)) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) 46)) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) 54))) 
(((|SymmetricGroupCombinatoricFunctions|) (CATEGORY |package| (SIGNATURE |coleman| ((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |inverseColeman| ((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|)))) (SIGNATURE |listYoungTableaus| ((|List| (|Matrix| (|Integer|))) (|List| (|Integer|)))) (SIGNATURE |makeYoungTableau| ((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |nextColeman| ((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|)))) (SIGNATURE |nextLatticePermutation| ((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|))) (SIGNATURE |nextPartition| ((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|))) (SIGNATURE |nextPartition| ((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|))) (SIGNATURE |numberOfImproperPartitions| ((|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |subSet| ((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |unrankImproperPartitions0| ((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |unrankImproperPartitions1| ((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|))))) (T |SymmetricGroupCombinatoricFunctions|)) 
((|unrankImproperPartitions1| (*1 *2 *3 *3 *3) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|)) (|isDomain| *3 (|Integer|)))) (|unrankImproperPartitions0| (*1 *2 *3 *3 *3) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|)) (|isDomain| *3 (|Integer|)))) (|subSet| (*1 *2 *3 *3 *3) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|)) (|isDomain| *3 (|Integer|)))) (|numberOfImproperPartitions| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|)))) (|nextPartition| (*1 *2 *3 *2 *4) (AND (|isDomain| *2 (|Vector| (|Integer|))) (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *4 (|Integer|)) (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|)))) (|nextPartition| (*1 *2 *2 *2 *3) (AND (|isDomain| *2 (|Vector| (|Integer|))) (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|)))) (|nextLatticePermutation| (*1 *2 *2 *2 *3) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *3 (|Boolean|)) (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|)))) (|nextColeman| (*1 *2 *3 *3 *2) (AND (|isDomain| *2 (|Matrix| (|Integer|))) (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|)))) (|makeYoungTableau| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|Matrix| (|Integer|))) (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|)))) (|listYoungTableaus| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|List| (|Matrix| (|Integer|)))) (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|)))) (|inverseColeman| (*1 *2 *2 *2 *3) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *3 (|Matrix| (|Integer|))) (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|)))) (|coleman| (*1 *2 *3 *3 *3) (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|Matrix| (|Integer|))) (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|))))) 
(CATEGORY |package| (SIGNATURE |coleman| ((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |inverseColeman| ((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|)))) (SIGNATURE |listYoungTableaus| ((|List| (|Matrix| (|Integer|))) (|List| (|Integer|)))) (SIGNATURE |makeYoungTableau| ((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |nextColeman| ((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|)))) (SIGNATURE |nextLatticePermutation| ((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|))) (SIGNATURE |nextPartition| ((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|))) (SIGNATURE |nextPartition| ((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|))) (SIGNATURE |numberOfImproperPartitions| ((|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |subSet| ((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |unrankImproperPartitions0| ((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |unrankImproperPartitions1| ((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)))) 
((^ (($ $ (|PositiveInteger|)) 12)) (** (($ $ (|PositiveInteger|)) 10))) 
(((|SemiGroup&| |#1|) (CATEGORY |domain| (SIGNATURE ^ (|#1| |#1| (|PositiveInteger|))) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|)))) (|SemiGroup|)) (T |SemiGroup&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE ^ (|#1| |#1| (|PositiveInteger|))) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|)))) 
((~= (((|Boolean|) $ $) 7)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (^ (($ $ (|PositiveInteger|)) 12)) (= (((|Boolean|) $ $) 6)) (** (($ $ (|PositiveInteger|)) 13)) (* (($ $ $) 14))) 
(((|SemiGroup|) (|Category|)) (T |SemiGroup|)) 
((* (*1 *1 *1 *1) (|ofCategory| *1 (|SemiGroup|))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|SemiGroup|)) (|isDomain| *2 (|PositiveInteger|)))) (^ (*1 *1 *1 *2) (AND (|ofCategory| *1 (|SemiGroup|)) (|isDomain| *2 (|PositiveInteger|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE * ($ $ $)) (SIGNATURE ** ($ $ (|PositiveInteger|))) (SIGNATURE ^ ($ $ (|PositiveInteger|))))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL (|has| |#3| (|SetCategory|)))) (|zero?| (((|Boolean|) $) NIL (|has| |#3| (|CancellationAbelianMonoid|)))) (|unitVector| (($ (|PositiveInteger|)) NIL (|has| |#3| (|Ring|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sup| (($ $ $) NIL (|has| |#3| (|OrderedAbelianMonoidSup|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL (|has| |#3| (|CancellationAbelianMonoid|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|size| (((|NonNegativeInteger|)) NIL (|has| |#3| (|Finite|)))) (|sign| (((|Integer|) $) NIL (|has| |#3| (|OrderedRing|)))) (|setelt| ((|#3| $ (|Integer|) |#3|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (AND (|has| |#3| (|RetractableTo| (|Integer|))) (|has| |#3| (|SetCategory|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (AND (|has| |#3| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#3| (|SetCategory|)))) (((|Union| |#3| "failed") $) NIL (|has| |#3| (|SetCategory|)))) (|retract| (((|Integer|) $) NIL (AND (|has| |#3| (|RetractableTo| (|Integer|))) (|has| |#3| (|SetCategory|)))) (((|Fraction| (|Integer|)) $) NIL (AND (|has| |#3| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#3| (|SetCategory|)))) ((|#3| $) NIL (|has| |#3| (|SetCategory|)))) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (AND (|has| |#3| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#3| (|Ring|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (AND (|has| |#3| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#3| (|Ring|)))) (((|Record| (|:| |mat| (|Matrix| |#3|)) (|:| |vec| (|Vector| |#3|))) (|Matrix| $) (|Vector| $)) NIL (|has| |#3| (|Ring|))) (((|Matrix| |#3|) (|Matrix| $)) NIL (|has| |#3| (|Ring|)))) (|recip| (((|Union| $ "failed") $) NIL (|has| |#3| (|Monoid|)))) (|random| (($) NIL (|has| |#3| (|Finite|)))) (|qsetelt!| ((|#3| $ (|Integer|) |#3|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#3| $ (|Integer|)) 12)) (|positive?| (((|Boolean|) $) NIL (|has| |#3| (|OrderedRing|)))) (|parts| (((|List| |#3|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|one?| (((|Boolean|) $) NIL (|has| |#3| (|Monoid|)))) (|negative?| (((|Boolean|) $) NIL (|has| |#3| (|OrderedRing|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL (OR (|has| |#3| (|OrderedAbelianMonoidSup|)) (|has| |#3| (|OrderedRing|))))) (|members| (((|List| |#3|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#3| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#3| (|SetCategory|))))) (|maxIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (OR (|has| |#3| (|OrderedAbelianMonoidSup|)) (|has| |#3| (|OrderedRing|))))) (|map!| (($ (|Mapping| |#3| |#3|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#3| |#3|) $) NIL)) (|lookup| (((|PositiveInteger|) $) NIL (|has| |#3| (|Finite|)))) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| |#3| (|SetCategory|)))) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|index| (($ (|PositiveInteger|)) NIL (|has| |#3| (|Finite|)))) (|hash| (((|SingleInteger|) $) NIL (|has| |#3| (|SetCategory|)))) (|first| ((|#3| $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|fill!| (($ $ |#3|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#3|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#3|))) NIL (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|)))) (($ $ (|Equation| |#3|)) NIL (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|)))) (($ $ |#3| |#3|) NIL (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|)))) (($ $ (|List| |#3|) (|List| |#3|)) NIL (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|enumerate| (((|List| $)) NIL (|has| |#3| (|Finite|)))) (|entry?| (((|Boolean|) |#3| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#3| (|SetCategory|))))) (|entries| (((|List| |#3|) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#3| $ (|Integer|) |#3|) NIL) ((|#3| $ (|Integer|)) NIL)) (|dot| ((|#3| $ $) NIL (|has| |#3| (|Ring|)))) (|directProduct| (($ (|Vector| |#3|)) NIL)) (|dimension| (((|CardinalNumber|)) NIL (|has| |#3| (|Field|)))) (|differentiate| (($ $) NIL (AND (|has| |#3| (|DifferentialRing|)) (|has| |#3| (|Ring|)))) (($ $ (|NonNegativeInteger|)) NIL (AND (|has| |#3| (|DifferentialRing|)) (|has| |#3| (|Ring|)))) (($ $ (|Symbol|)) NIL (AND (|has| |#3| (|PartialDifferentialRing| (|Symbol|))) (|has| |#3| (|Ring|)))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#3| 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(|Fraction| (|Integer|)))) (|has| |#3| (|SetCategory|)))) (($ |#3|) NIL (|has| |#3| (|SetCategory|)))) (|characteristic| (((|NonNegativeInteger|)) NIL (|has| |#3| (|Ring|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#3|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|abs| (($ $) NIL (|has| |#3| (|OrderedRing|)))) (^ (($ $ (|NonNegativeInteger|)) NIL (|has| |#3| (|Monoid|))) (($ $ (|PositiveInteger|)) NIL (|has| |#3| (|Monoid|)))) (|Zero| (($) NIL (|has| |#3| (|CancellationAbelianMonoid|)) CONST)) (|One| (($) NIL (|has| |#3| (|Monoid|)) CONST)) (D (($ $) NIL (AND (|has| |#3| (|DifferentialRing|)) (|has| |#3| (|Ring|)))) (($ $ (|NonNegativeInteger|)) NIL (AND (|has| |#3| (|DifferentialRing|)) (|has| |#3| (|Ring|)))) (($ $ (|Symbol|)) NIL (AND (|has| |#3| (|PartialDifferentialRing| (|Symbol|))) (|has| |#3| (|Ring|)))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#3| (|PartialDifferentialRing| (|Symbol|))) (|has| |#3| (|Ring|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| |#3| (|PartialDifferentialRing| (|Symbol|))) (|has| |#3| (|Ring|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| |#3| (|PartialDifferentialRing| (|Symbol|))) (|has| |#3| (|Ring|)))) (($ $ (|Mapping| |#3| |#3|) (|NonNegativeInteger|)) NIL (|has| |#3| (|Ring|))) (($ $ (|Mapping| |#3| |#3|)) NIL (|has| |#3| (|Ring|)))) (>= (((|Boolean|) $ $) NIL (OR (|has| |#3| (|OrderedAbelianMonoidSup|)) (|has| |#3| (|OrderedRing|))))) (> (((|Boolean|) $ $) NIL (OR (|has| |#3| (|OrderedAbelianMonoidSup|)) (|has| |#3| (|OrderedRing|))))) (= (((|Boolean|) $ $) NIL (|has| |#3| (|SetCategory|)))) (<= (((|Boolean|) $ $) NIL (OR (|has| |#3| (|OrderedAbelianMonoidSup|)) (|has| |#3| (|OrderedRing|))))) (< (((|Boolean|) $ $) 17 (OR (|has| |#3| (|OrderedAbelianMonoidSup|)) (|has| |#3| (|OrderedRing|))))) (/ (($ $ |#3|) NIL (|has| |#3| (|Field|)))) (- (($ $ $) NIL (|has| |#3| (|Ring|))) (($ $) NIL (|has| |#3| (|Ring|)))) (+ (($ $ $) NIL (|has| |#3| (|AbelianSemiGroup|)))) (** (($ $ (|NonNegativeInteger|)) NIL (|has| |#3| (|Monoid|))) (($ $ (|PositiveInteger|)) NIL (|has| |#3| (|Monoid|)))) (* (($ (|Integer|) $) NIL (|has| |#3| (|Ring|))) (($ $ $) NIL (|has| |#3| (|Monoid|))) (($ $ |#3|) NIL (|has| |#3| (|Monoid|))) (($ |#3| $) NIL (|has| |#3| (|Monoid|))) (($ (|NonNegativeInteger|) $) NIL (|has| |#3| (|CancellationAbelianMonoid|))) (($ (|PositiveInteger|) $) NIL (|has| |#3| (|AbelianSemiGroup|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|SplitHomogeneousDirectProduct| |#1| |#2| |#3|) (|DirectProductCategory| |#1| |#3|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|OrderedAbelianMonoidSup|)) (T |SplitHomogeneousDirectProduct|)) 
NIL 
(|DirectProductCategory| |#1| |#3|) 
((|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) 36)) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) 67 (|has| |#1| (|GcdDomain|)))) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) 53)) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) 44)) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) 55 (|has| |#1| (|GcdDomain|)))) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) 47)) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) 52))) 
(((|SturmHabichtPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |subresultantSequence| ((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|))) (SIGNATURE |SturmHabichtSequence| ((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|))) (SIGNATURE |SturmHabichtCoefficients| ((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|))) (SIGNATURE |SturmHabicht| ((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|))) (SIGNATURE |countRealRoots| ((|Integer|) (|UnivariatePolynomial| |#2| |#1|))) (IF (|has| |#1| (|GcdDomain|)) (PROGN (SIGNATURE |SturmHabichtMultiple| ((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|))) (SIGNATURE |countRealRootsMultiple| ((|Integer|) (|UnivariatePolynomial| |#2| |#1|)))) |noBranch|)) (|OrderedIntegralDomain|) (|Symbol|)) (T |SturmHabichtPackage|)) 
((|countRealRootsMultiple| (*1 *2 *3) (AND (|isDomain| *3 (|UnivariatePolynomial| *5 *4)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *4 (|OrderedIntegralDomain|)) (|ofType| *5 (|Symbol|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|SturmHabichtPackage| *4 *5)))) (|SturmHabichtMultiple| (*1 *2 *3 *3) (AND (|isDomain| *3 (|UnivariatePolynomial| *5 *4)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *4 (|OrderedIntegralDomain|)) (|ofType| *5 (|Symbol|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|SturmHabichtPackage| *4 *5)))) (|countRealRoots| (*1 *2 *3) (AND (|isDomain| *3 (|UnivariatePolynomial| *5 *4)) (|ofCategory| *4 (|OrderedIntegralDomain|)) (|ofType| *5 (|Symbol|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|SturmHabichtPackage| *4 *5)))) (|SturmHabicht| (*1 *2 *3 *3) (AND (|isDomain| *3 (|UnivariatePolynomial| *5 *4)) (|ofCategory| *4 (|OrderedIntegralDomain|)) (|ofType| *5 (|Symbol|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|SturmHabichtPackage| *4 *5)))) (|SturmHabichtCoefficients| (*1 *2 *3 *3) (AND (|isDomain| *3 (|UnivariatePolynomial| *5 *4)) (|ofCategory| *4 (|OrderedIntegralDomain|)) (|ofType| *5 (|Symbol|)) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|SturmHabichtPackage| *4 *5)))) (|SturmHabichtSequence| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|OrderedIntegralDomain|)) (|ofType| *5 (|Symbol|)) (|isDomain| *2 (|List| (|UnivariatePolynomial| *5 *4))) (|isDomain| *1 (|SturmHabichtPackage| *4 *5)) (|isDomain| *3 (|UnivariatePolynomial| *5 *4)))) (|subresultantSequence| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|OrderedIntegralDomain|)) (|ofType| *5 (|Symbol|)) (|isDomain| *2 (|List| (|UnivariatePolynomial| *5 *4))) (|isDomain| *1 (|SturmHabichtPackage| *4 *5)) (|isDomain| *3 (|UnivariatePolynomial| *5 *4))))) 
(CATEGORY |package| (SIGNATURE |subresultantSequence| ((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|))) (SIGNATURE |SturmHabichtSequence| ((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|))) (SIGNATURE |SturmHabichtCoefficients| ((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|))) (SIGNATURE |SturmHabicht| ((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|))) (SIGNATURE |countRealRoots| ((|Integer|) (|UnivariatePolynomial| |#2| |#1|))) (IF (|has| |#1| (|GcdDomain|)) (PROGN (SIGNATURE |SturmHabichtMultiple| ((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|))) (SIGNATURE |countRealRootsMultiple| ((|Integer|) (|UnivariatePolynomial| |#2| |#1|)))) |noBranch|)) 
((|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) 16) (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) 14) (((|Union| (|Integer|) "failed") |#2|) 51))) 
(((|ElementaryFunctionSign| |#1| |#2|) (CATEGORY |package| (SIGNATURE |sign| ((|Union| (|Integer|) "failed") |#2|)) (SIGNATURE |sign| ((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|))) (SIGNATURE |sign| ((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)))) (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|GcdDomain|)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |ElementaryFunctionSign|)) 
((|sign| (*1 *2 *3 *4 *3 *5) (|partial| AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|String|)) (|ofCategory| *6 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| *2) (|LinearlyExplicitRingOver| *2) (|GcdDomain|))) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|ElementaryFunctionSign| *6 *3)) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *6))))) (|sign| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|OrderedCompletion| *3)) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *6))) (|ofCategory| *6 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| *2) (|LinearlyExplicitRingOver| *2) (|GcdDomain|))) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|ElementaryFunctionSign| *6 *3)))) (|sign| (*1 *2 *3) (|partial| AND (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| *2) (|LinearlyExplicitRingOver| *2) (|GcdDomain|))) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|ElementaryFunctionSign| *4 *3)) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *4)))))) 
(CATEGORY |package| (SIGNATURE |sign| ((|Union| (|Integer|) "failed") |#2|)) (SIGNATURE |sign| ((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|))) (SIGNATURE |sign| ((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)))) 
((|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) 34) (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) 29) (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) 12))) 
(((|RationalFunctionSign| |#1|) (CATEGORY |package| (SIGNATURE |sign| ((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)))) (SIGNATURE |sign| ((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |sign| ((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)))) (|GcdDomain|)) (T |RationalFunctionSign|)) 
((|sign| (*1 *2 *3 *4 *3 *5) (|partial| AND (|isDomain| *3 (|Fraction| (|Polynomial| *6))) (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|String|)) (|ofCategory| *6 (|GcdDomain|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|RationalFunctionSign| *6)))) (|sign| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|OrderedCompletion| (|Fraction| (|Polynomial| *6)))) (|isDomain| *3 (|Fraction| (|Polynomial| *6))) (|ofCategory| *6 (|GcdDomain|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|RationalFunctionSign| *6)))) (|sign| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|Fraction| (|Polynomial| *4))) (|ofCategory| *4 (|GcdDomain|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|RationalFunctionSign| *4))))) 
(CATEGORY |package| (SIGNATURE |sign| ((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)))) (SIGNATURE |sign| ((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |sign| ((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)))) 
((|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) 11))) 
(((|SimplifyAlgebraicNumberConvertPackage|) (CATEGORY |package| (SIGNATURE |simplify| ((|Expression| (|Integer|)) (|AlgebraicNumber|))))) (T |SimplifyAlgebraicNumberConvertPackage|)) 
((|simplify| (*1 *2 *3) (AND (|isDomain| *3 (|AlgebraicNumber|)) (|isDomain| *2 (|Expression| (|Integer|))) (|isDomain| *1 (|SimplifyAlgebraicNumberConvertPackage|))))) 
(CATEGORY |package| (SIGNATURE |simplify| ((|Expression| (|Integer|)) (|AlgebraicNumber|)))) 
((~= (((|Boolean|) $ $) NIL)) (~ (($ $) 41)) (|zero?| (((|Boolean|) $) 65)) (|xor| (($ $ $) 48)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 84)) (|unitCanonical| (($ $) NIL)) (|unit?| (((|Boolean|) $) NIL)) (|symmetricRemainder| (($ $ $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|submod| (($ $ $ $) 74)) (|squareFreePart| (($ $) NIL)) (|squareFree| (((|Factored| $) $) NIL)) (|sizeLess?| (((|Boolean|) $ $) NIL)) (|sign| (((|Integer|) $) NIL)) (|shift| (($ $ $) 71)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL)) (|retract| (((|Integer|) $) NIL)) (|rem| (($ $ $) 59)) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) 78) (((|Matrix| (|Integer|)) (|Matrix| $)) 28)) (|recip| (((|Union| $ "failed") $) NIL)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL)) (|rational?| (((|Boolean|) $) NIL)) (|rational| (((|Fraction| (|Integer|)) $) NIL)) (|random| (($) 81) (($ $) 82)) (|quo| (($ $ $) 58)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL)) (|prime?| (((|Boolean|) $) NIL)) (|powmod| (($ $ $ $) NIL)) (|positiveRemainder| (($ $ $) 79)) (|positive?| (((|Boolean|) $) NIL)) (|permutation| (($ $ $) NIL)) (|patternMatch| (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL)) (|one?| (((|Boolean|) $) 66)) (|odd?| (((|Boolean|) $) 64)) (|not| (($ $) 42)) (|nextItem| (((|Union| $ "failed") $) NIL)) (|negative?| (((|Boolean|) $) 75)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|mulmod| (($ $ $ $) 72)) (|min| (($ $ $) 68) (($) 39)) (|max| (($ $ $) 67) (($) 38)) (|mask| (($ $) NIL)) (|length| (($ $) 70)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL)) (|lcm| (($ $ $) NIL) (($ (|List| $)) NIL)) (|latex| (((|String|) $) NIL)) (|invmod| (($ $ $) NIL)) (|init| (($) NIL T CONST)) (|inc| (($ $) 50)) (|hash| (((|SingleInteger|) $) NIL) (($ $) 69)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL)) (|gcd| (($ $ $) 62) (($ (|List| $)) NIL)) (|factorial| (($ $) NIL)) (|factor| (((|Factored| $) $) NIL)) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL)) (|even?| (((|Boolean|) $) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 61)) (|differentiate| (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (|dec| (($ $) 51)) (|copy| (($ $) NIL)) (|convert| (((|Integer|) $) 32) (((|InputForm|) $) NIL) (((|Pattern| (|Integer|)) $) NIL) (((|Float|) $) NIL) (((|DoubleFloat|) $) NIL)) (|coerce| (((|OutputForm|) $) 31) (($ (|Integer|)) 80) (($ $) NIL) (($ (|Integer|)) 80)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|bit?| (((|Boolean|) $ $) NIL)) (|binomial| (($ $ $) NIL)) (|base| (($) 37)) (|associates?| (((|Boolean|) $ $) NIL)) (|addmod| (($ $ $ $) 73)) (|abs| (($ $) 63)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|\\/| (($ $ $) 44)) (|Zero| (($) 35 T CONST)) (|Or| (($ $ $) 47)) (|One| (($) 36 T CONST)) (|OMwrite| (((|String|) $) 21) (((|String|) $ (|Boolean|)) 23) (((|Void|) (|OpenMathDevice|) $) 24) (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) 25)) (|Not| (($ $) 45)) (D (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (|And| (($ $ $) 46)) (>= (((|Boolean|) $ $) NIL)) (> (((|Boolean|) $ $) NIL)) (= (((|Boolean|) $ $) 40)) (<= (((|Boolean|) $ $) NIL)) (< (((|Boolean|) $ $) 49)) (|/\\| (($ $ $) 43)) (- (($ $) 52) (($ $ $) 54)) (+ (($ $ $) 53)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 57)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 34) (($ $ $) 55))) 
(((|SingleInteger|) (|Join| (|IntegerNumberSystem|) (|Logic|) (|OpenMath|) (CATEGORY |domain| (ATTRIBUTE |canonical|) (ATTRIBUTE |canonicalsClosed|) (ATTRIBUTE |noetherian|) (SIGNATURE |max| ($)) (SIGNATURE |min| ($)) (SIGNATURE |not| ($ $)) (SIGNATURE ~ ($ $)) (SIGNATURE |/\\| ($ $ $)) (SIGNATURE |\\/| ($ $ $)) (SIGNATURE |xor| ($ $ $)) (SIGNATURE |Not| ($ $)) (SIGNATURE |And| ($ $ $)) (SIGNATURE |Or| ($ $ $))))) (T |SingleInteger|)) 
((|\\/| (*1 *1 *1 *1) (|isDomain| *1 (|SingleInteger|))) (|/\\| (*1 *1 *1 *1) (|isDomain| *1 (|SingleInteger|))) (~ (*1 *1 *1) (|isDomain| *1 (|SingleInteger|))) (|max| (*1 *1) (|isDomain| *1 (|SingleInteger|))) (|min| (*1 *1) (|isDomain| *1 (|SingleInteger|))) (|not| (*1 *1 *1) (|isDomain| *1 (|SingleInteger|))) (|xor| (*1 *1 *1 *1) (|isDomain| *1 (|SingleInteger|))) (|Not| (*1 *1 *1) (|isDomain| *1 (|SingleInteger|))) (|And| (*1 *1 *1 *1) (|isDomain| *1 (|SingleInteger|))) (|Or| (*1 *1 *1 *1) (|isDomain| *1 (|SingleInteger|)))) 
(|Join| (|IntegerNumberSystem|) (|Logic|) (|OpenMath|) (CATEGORY |domain| (ATTRIBUTE |canonical|) (ATTRIBUTE |canonicalsClosed|) (ATTRIBUTE |noetherian|) (SIGNATURE |max| ($)) (SIGNATURE |min| ($)) (SIGNATURE |not| ($ $)) (SIGNATURE ~ ($ $)) (SIGNATURE |/\\| ($ $ $)) (SIGNATURE |\\/| ($ $ $)) (SIGNATURE |xor| ($ $ $)) (SIGNATURE |Not| ($ $)) (SIGNATURE |And| ($ $ $)) (SIGNATURE |Or| ($ $ $)))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|top| ((|#1| $) 41)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|sample| (($) 7 T CONST)) (|push!| ((|#1| |#1| $) 43)) (|pop!| ((|#1| $) 42)) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|inspect| ((|#1| $) 36)) (|insert!| (($ |#1| $) 37)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|extract!| ((|#1| $) 38)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|depth| (((|NonNegativeInteger|) $) 40)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|bag| (($ (|List| |#1|)) 39)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|StackAggregate| |#1|) (|Category|) (|Type|)) (T |StackAggregate|)) 
((|push!| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|StackAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|pop!| (*1 *2 *1) (AND (|ofCategory| *1 (|StackAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|top| (*1 *2 *1) (AND (|ofCategory| *1 (|StackAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|depth| (*1 *2 *1) (AND (|ofCategory| *1 (|StackAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|))))) 
(|Join| (|BagAggregate| |t#1|) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (SIGNATURE |push!| (|t#1| |t#1| $)) (SIGNATURE |pop!| (|t#1| $)) (SIGNATURE |top| (|t#1| $)) (SIGNATURE |depth| ((|NonNegativeInteger|) $)))) 
(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((|trace| ((|#3| $) 76)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL) (((|Union| |#3| "failed") $) 40)) (|retract| (((|Integer|) $) NIL) (((|Fraction| (|Integer|)) $) NIL) ((|#3| $) 37)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL) (((|Record| (|:| |mat| (|Matrix| |#3|)) (|:| |vec| (|Vector| |#3|))) (|Matrix| $) (|Vector| $)) 73) (((|Matrix| |#3|) (|Matrix| $)) 65)) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) 19) (($ $ (|Mapping| |#3| |#3|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|))) NIL) (($ $ (|Symbol|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL)) (|diagonalProduct| ((|#3| $) 78)) (|diagonal| ((|#4| $) 32)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ |#3|) 16)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 15) (($ $ (|Integer|)) 82))) 
(((|SquareMatrixCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |domain| (SIGNATURE ** (|#1| |#1| (|Integer|))) (SIGNATURE |diagonalProduct| (|#3| |#1|)) (SIGNATURE |trace| (|#3| |#1|)) (SIGNATURE |diagonal| (|#4| |#1|)) (SIGNATURE |reducedSystem| ((|Matrix| |#3|) (|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| |#3|)) (|:| |vec| (|Vector| |#3|))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Matrix| (|Integer|)) (|Matrix| |#1|))) (SIGNATURE |retract| (|#3| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#3| "failed") |#1|)) (SIGNATURE |coerce| (|#1| |#3|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#3| |#3|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#3| |#3|))) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|SquareMatrixCategory| |#2| |#3| |#4| |#5|) (|NonNegativeInteger|) (|Ring|) (|DirectProductCategory| |#2| |#3|) (|DirectProductCategory| |#2| |#3|)) (T |SquareMatrixCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE ** (|#1| |#1| (|Integer|))) (SIGNATURE |diagonalProduct| (|#3| |#1|)) (SIGNATURE |trace| (|#3| |#1|)) (SIGNATURE |diagonal| (|#4| |#1|)) (SIGNATURE |reducedSystem| ((|Matrix| |#3|) (|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| |#3|)) (|:| |vec| (|Vector| |#3|))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| |#1|) (|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Matrix| (|Integer|)) (|Matrix| |#1|))) (SIGNATURE |retract| (|#3| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#3| "failed") |#1|)) (SIGNATURE |coerce| (|#1| |#3|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#3| |#3|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#3| |#3|))) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|trace| ((|#2| $) 69)) (|symmetric?| (((|Boolean|) $) 109)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|square?| (((|Boolean|) $) 107)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 99)) (|scalarMatrix| (($ |#2|) 72)) (|sample| (($) 16 T CONST)) (|rowEchelon| (($ $) 126 (|has| |#2| (|EuclideanDomain|)))) (|row| ((|#3| $ (|Integer|)) 121)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) 83 (|has| |#2| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) 81 (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#2| "failed") $) 78)) (|retract| (((|Integer|) $) 84 (|has| |#2| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) 82 (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#2| $) 77)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) 76 (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) 75 (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| $) (|Vector| $)) 74) (((|Matrix| |#2|) (|Matrix| $)) 73)) (|recip| (((|Union| $ "failed") $) 33)) (|rank| (((|NonNegativeInteger|) $) 127 (|has| |#2| (|IntegralDomain|)))) (|qelt| ((|#2| $ (|Integer|) (|Integer|)) 119)) (|parts| (((|List| |#2|) $) 92 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|one?| (((|Boolean|) $) 30)) (|nullity| (((|NonNegativeInteger|) $) 128 (|has| |#2| (|IntegralDomain|)))) (|nullSpace| (((|List| |#4|) $) 129 (|has| |#2| (|IntegralDomain|)))) (|nrows| (((|NonNegativeInteger|) $) 115)) (|ncols| (((|NonNegativeInteger|) $) 116)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 100)) (|minordet| ((|#2| $) 64 (|has| |#2| (ATTRIBUTE (|commutative| "*"))))) (|minRowIndex| (((|Integer|) $) 111)) (|minColIndex| (((|Integer|) $) 113)) (|members| (((|List| |#2|) $) 91 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#2| $) 89 (AND (|has| |#2| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|maxRowIndex| (((|Integer|) $) 112)) (|maxColIndex| (((|Integer|) $) 114)) (|matrix| (($ (|List| (|List| |#2|))) 106)) (|map!| (($ (|Mapping| |#2| |#2|) $) 96 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) 123) (($ (|Mapping| |#2| |#2|) $) 97)) (|listOfLists| (((|List| (|List| |#2|)) $) 117)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 101)) (|latex| (((|String|) $) 9)) (|inverse| (((|Union| $ "failed") $) 63 (|has| |#2| (|Field|)))) (|hash| (((|SingleInteger|) $) 10)) (|exquo| (((|Union| $ "failed") $ |#2|) 124 (|has| |#2| (|IntegralDomain|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 94 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#2|))) 88 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|Equation| |#2|)) 87 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ |#2| |#2|) 86 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|List| |#2|) (|List| |#2|)) 85 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 105)) (|empty?| (((|Boolean|) $) 102)) (|empty| (($) 103)) (|elt| ((|#2| $ (|Integer|) (|Integer|) |#2|) 120) ((|#2| $ (|Integer|) (|Integer|)) 118)) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) 51) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) 50) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 43 (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 42 (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) 41 (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|)) 40 (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|NonNegativeInteger|)) 38 (|has| |#2| (|DifferentialRing|))) (($ $) 36 (|has| |#2| (|DifferentialRing|)))) (|diagonalProduct| ((|#2| $) 68)) (|diagonalMatrix| (($ (|List| |#2|)) 71)) (|diagonal?| (((|Boolean|) $) 108)) (|diagonal| ((|#3| $) 70)) (|determinant| ((|#2| $) 65 (|has| |#2| (ATTRIBUTE (|commutative| "*"))))) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) 93 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#2| $) 90 (AND (|has| |#2| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 104)) (|column| ((|#4| $ (|Integer|)) 122)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ (|Fraction| (|Integer|))) 80 (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|))))) (($ |#2|) 79)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 95 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|antisymmetric?| (((|Boolean|) $) 110)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $ 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(((|NonNegativeInteger|) $) 98 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|SquareMatrixCategory| |#1| |#2| |#3| |#4|) (|Category|) (|NonNegativeInteger|) (|Ring|) (|DirectProductCategory| |t#1| |t#2|) (|DirectProductCategory| |t#1| |t#2|)) (T |SquareMatrixCategory|)) 
((|scalarMatrix| (*1 *1 *2) (AND (|ofCategory| *2 (|Ring|)) (|ofCategory| *1 (|SquareMatrixCategory| *3 *2 *4 *5)) (|ofCategory| *4 (|DirectProductCategory| *3 *2)) (|ofCategory| *5 (|DirectProductCategory| *3 *2)))) (|diagonalMatrix| (*1 *1 *2) (AND (|isDomain| *2 (|List| *4)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *1 (|SquareMatrixCategory| *3 *4 *5 *6)) (|ofCategory| *5 (|DirectProductCategory| *3 *4)) (|ofCategory| *6 (|DirectProductCategory| *3 *4)))) (|diagonal| (*1 *2 *1) (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *4 *2 *5)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *3 *4)) (|ofCategory| *2 (|DirectProductCategory| *3 *4)))) (|trace| (*1 *2 *1) (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *2 *4 *5)) (|ofCategory| *4 (|DirectProductCategory| *3 *2)) (|ofCategory| *5 (|DirectProductCategory| *3 *2)) (|ofCategory| *2 (|Ring|)))) (|diagonalProduct| (*1 *2 *1) (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *2 *4 *5)) (|ofCategory| *4 (|DirectProductCategory| *3 *2)) (|ofCategory| *5 (|DirectProductCategory| *3 *2)) (|ofCategory| *2 (|Ring|)))) (* (*1 *2 *1 *2) (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *4 *5 *2)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *3 *4)) (|ofCategory| *2 (|DirectProductCategory| *3 *4)))) (* (*1 *2 *2 *1) (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *4 *2 *5)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|DirectProductCategory| *3 *4)) (|ofCategory| *5 (|DirectProductCategory| *3 *4)))) (|determinant| (*1 *2 *1) (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *2 *4 *5)) (|ofCategory| *4 (|DirectProductCategory| *3 *2)) (|ofCategory| *5 (|DirectProductCategory| *3 *2)) (|has| *2 (ATTRIBUTE (|commutative| "*"))) (|ofCategory| *2 (|Ring|)))) (|minordet| (*1 *2 *1) (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *2 *4 *5)) (|ofCategory| *4 (|DirectProductCategory| *3 *2)) (|ofCategory| *5 (|DirectProductCategory| *3 *2)) (|has| *2 (ATTRIBUTE (|commutative| "*"))) (|ofCategory| *2 (|Ring|)))) (|inverse| (*1 *1 *1) (|partial| AND (|ofCategory| *1 (|SquareMatrixCategory| *2 *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|DirectProductCategory| *2 *3)) (|ofCategory| *5 (|DirectProductCategory| *2 *3)) (|ofCategory| *3 (|Field|)))) (** (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|SquareMatrixCategory| *3 *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *3 *4)) (|ofCategory| *6 (|DirectProductCategory| *3 *4)) (|ofCategory| *4 (|Field|))))) 
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(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Aggregate|) . T) ((|Algebra| |#2|) |has| |#2| (ATTRIBUTE (|commutative| "*"))) ((|BasicType|) . T) ((|BiModule| |#2| |#2|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|DifferentialExtension| |#2|) . T) ((|DifferentialRing|) |has| |#2| (|DifferentialRing|)) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|FullyLinearlyExplicitRingOver| |#2|) . T) ((|FullyRetractableTo| |#2|) . T) ((|HomogeneousAggregate| |#2|) . T) ((|InnerEvalable| |#2| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|LeftModule| |#2|) . T) ((|LeftModule| $) . T) ((|LinearlyExplicitRingOver| (|Integer|)) |has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#2|) . T) ((|Module| |#2|) OR (|has| |#2| (|CommutativeRing|)) (|has| |#2| (ATTRIBUTE (|commutative| "*")))) ((|Monoid|) . T) ((|PartialDifferentialRing| (|Symbol|)) |has| |#2| (|PartialDifferentialRing| (|Symbol|))) ((|RectangularMatrixCategory| |#1| |#1| |#2| |#3| |#4|) . T) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#2| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#2|) . T) ((|RightModule| |#2|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|smith| ((|#4| |#4|) 67)) (|hermite| ((|#4| |#4|) 62)) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) 75)) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) 66)) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) 64))) 
(((|SmithNormalForm| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |hermite| (|#4| |#4|)) (SIGNATURE |completeHermite| ((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|)) (SIGNATURE |smith| (|#4| |#4|)) (SIGNATURE |completeSmith| ((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|)) (SIGNATURE |diophantineSystem| ((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|))) (|EuclideanDomain|) (|FiniteLinearAggregate| |#1|) (|FiniteLinearAggregate| |#1|) (|MatrixCategory| |#1| |#2| |#3|)) (T |SmithNormalForm|)) 
((|diophantineSystem| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|EuclideanDomain|)) (|ofCategory| *6 (|FiniteLinearAggregate| *5)) (|ofCategory| *4 (|FiniteLinearAggregate| *5)) (|isDomain| *2 (|Record| (|:| |particular| (|Union| *4 "failed")) (|:| |basis| (|List| *4)))) (|isDomain| *1 (|SmithNormalForm| *5 *6 *4 *3)) (|ofCategory| *3 (|MatrixCategory| *5 *6 *4)))) (|completeSmith| (*1 *2 *3) (AND (|ofCategory| *4 (|EuclideanDomain|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *2 (|Record| (|:| |Smith| *3) (|:| |leftEqMat| *3) (|:| |rightEqMat| *3))) (|isDomain| *1 (|SmithNormalForm| *4 *5 *6 *3)) (|ofCategory| *3 (|MatrixCategory| *4 *5 *6)))) (|smith| (*1 *2 *2) (AND (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *1 (|SmithNormalForm| *3 *4 *5 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *4 *5)))) (|completeHermite| (*1 *2 *3) (AND (|ofCategory| *4 (|EuclideanDomain|)) (|ofCategory| *5 (|FiniteLinearAggregate| *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *4)) (|isDomain| *2 (|Record| (|:| |Hermite| *3) (|:| |eqMat| *3))) (|isDomain| *1 (|SmithNormalForm| *4 *5 *6 *3)) (|ofCategory| *3 (|MatrixCategory| *4 *5 *6)))) (|hermite| (*1 *2 *2) (AND (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *1 (|SmithNormalForm| *3 *4 *5 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *4 *5))))) 
(CATEGORY |package| (SIGNATURE |hermite| (|#4| |#4|)) (SIGNATURE |completeHermite| ((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|)) (SIGNATURE |smith| (|#4| |#4|)) (SIGNATURE |completeSmith| ((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|)) (SIGNATURE |diophantineSystem| ((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 17)) (|variables| (((|List| |#2|) $) 160)) (|univariate| (((|SparseUnivariatePolynomial| $) $ |#2|) 54) (((|SparseUnivariatePolynomial| |#1|) $) 43)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 110 (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) 112 (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) 114 (|has| |#1| (|IntegralDomain|)))) (|totalDegree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|List| |#2|)) 193)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL (|has| |#1| (|GcdDomain|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#1| (|GcdDomain|)))) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 157) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| |#2| "failed") $) NIL)) (|retract| ((|#1| $) 155) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) ((|#2| $) NIL)) (|resultant| (($ $ $ |#2|) NIL (|has| |#1| (|CommutativeRing|)))) (|reductum| (($ $) 197)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| 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(|SparseUnivariatePolynomial| |#1|) |#2|) 48) (($ (|SparseUnivariatePolynomial| $) |#2|) 64)) (|monomials| (((|List| $) $) NIL)) (|monomial?| (((|Boolean|) $) 31)) (|monomial| (($ |#1| (|IndexedExponents| |#2|)) 71) (($ $ |#2| (|NonNegativeInteger|)) 52) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) NIL)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#2|) NIL)) (|minimumDegree| (((|IndexedExponents| |#2|) $) 187) (((|NonNegativeInteger|) $ |#2|) 188) (((|List| (|NonNegativeInteger|)) $ (|List| |#2|)) 189)) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|mapExponents| (($ (|Mapping| (|IndexedExponents| |#2|) (|IndexedExponents| |#2|)) $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) 122)) (|mainVariable| (((|Union| |#2| "failed") $) 162)) (|leadingMonomial| (($ $) 196)) (|leadingCoefficient| ((|#1| $) 37)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| |#1| (|GcdDomain|)))) (|lcm| (($ (|List| $)) NIL (|has| |#1| (|GcdDomain|))) (($ $ $) NIL (|has| |#1| (|GcdDomain|)))) (|latex| (((|String|) $) NIL)) (|isTimes| (((|Union| (|List| $) "failed") $) NIL)) (|isPlus| (((|Union| (|List| $) "failed") $) NIL)) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|ground?| (((|Boolean|) $) 32)) (|ground| ((|#1| $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 140 (|has| |#1| (|GcdDomain|)))) (|gcd| (($ (|List| $)) 145 (|has| |#1| (|GcdDomain|))) (($ $ $) 132 (|has| |#1| (|GcdDomain|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|exquo| (((|Union| $ "failed") $ |#1|) NIL (|has| |#1| (|IntegralDomain|))) (((|Union| $ "failed") $ $) 120 (|has| |#1| (|IntegralDomain|)))) (|eval| (($ $ (|List| (|Equation| $))) NIL) (($ $ (|Equation| $)) NIL) (($ $ $ $) NIL) (($ $ (|List| $) (|List| $)) NIL) (($ $ |#2| |#1|) 165) (($ $ (|List| |#2|) (|List| |#1|)) 178) (($ $ |#2| $) 164) (($ $ (|List| |#2|) (|List| $)) 177)) (|discriminant| (($ $ |#2|) NIL (|has| |#1| (|CommutativeRing|)))) (|differentiate| (($ $ |#2|) 195) (($ $ (|List| |#2|)) NIL) (($ $ |#2| (|NonNegativeInteger|)) NIL) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) NIL)) (|degree| (((|IndexedExponents| |#2|) $) 183) (((|NonNegativeInteger|) $ |#2|) 179) (((|List| (|NonNegativeInteger|)) $ (|List| |#2|)) 181)) (|convert| (((|Pattern| (|Float|)) $) NIL (AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Float|)))))) (((|Pattern| (|Integer|)) $) NIL (AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Integer|)))))) (((|InputForm|) $) NIL (AND (|has| |#1| (|ConvertibleTo| (|InputForm|))) (|has| |#2| (|ConvertibleTo| (|InputForm|)))))) (|content| ((|#1| $) 128 (|has| |#1| (|GcdDomain|))) (($ $ |#2|) 131 (|has| |#1| (|GcdDomain|)))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))))) (|coerce| (((|OutputForm|) $) 151) (($ (|Integer|)) 76) (($ |#1|) 77) (($ |#2|) 28) (($ $) NIL (|has| |#1| (|IntegralDomain|))) (($ (|Fraction| (|Integer|))) NIL (OR (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))))) (|coefficients| (((|List| |#1|) $) 154)) (|coefficient| ((|#1| $ (|IndexedExponents| |#2|)) 73) (($ $ |#2| (|NonNegativeInteger|)) NIL) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) NIL)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) 79)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|CommutativeRing|)))) (|associates?| (((|Boolean|) $ $) 117 (|has| |#1| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) 102) (($ $ (|NonNegativeInteger|)) 104)) (|Zero| (($) 12 T CONST)) (|One| (($) 14 T CONST)) (D (($ $ |#2|) NIL) (($ $ (|List| |#2|)) NIL) (($ $ |#2| (|NonNegativeInteger|)) NIL) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) NIL)) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) 97)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (/ (($ $ |#1|) 126 (|has| |#1| (|Field|)))) (- (($ $) 85) (($ $ $) 95)) (+ (($ $ $) 49)) (** (($ $ (|PositiveInteger|)) 103) (($ $ (|NonNegativeInteger|)) 100)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 88) (($ $ $) 65) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ |#1| $) 90) (($ $ |#1|) NIL))) 
(((|SparseMultivariatePolynomial| |#1| |#2|) (|PolynomialCategory| |#1| (|IndexedExponents| |#2|) |#2|) (|Ring|) (|OrderedSet|)) (T |SparseMultivariatePolynomial|)) 
NIL 
(|PolynomialCategory| |#1| (|IndexedExponents| |#2|) |#2|) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|variables| (((|List| |#2|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|tanh| (($ $) 155 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|tan| (($ $) 131 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sqrt| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sinh| (($ $) 151 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sin| (($ $) 127 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|series| (($ (|Stream| |#3|)) 11)) (|sech| (($ $) 159 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sec| (($ $) 135 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sample| (($) NIL T CONST)) (|reductum| (($ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) NIL) (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) NIL)) (|pole?| (((|Boolean|) $) NIL)) (|pi| (($) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|order| (((|NonNegativeInteger|) $ |#2|) NIL) (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) NIL)) (|one?| (((|Boolean|) $) NIL)) (|nthRoot| (($ $ (|Integer|)) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|monomial?| (((|Boolean|) $) NIL)) (|monomial| (($ $ (|List| |#2|) (|List| (|IndexedExponents| |#2|))) NIL) (($ $ |#2| (|IndexedExponents| |#2|)) NIL) (($ |#1| (|IndexedExponents| |#2|)) NIL) (($ $ |#2| (|NonNegativeInteger|)) 72) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|log| (($ $) 125 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|leadingMonomial| (($ $) NIL)) (|leadingCoefficient| ((|#1| $) NIL)) (|latex| (((|String|) $) NIL)) (|integrate| (($ $ |#2|) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ |#2| |#1|) 178 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|hash| (((|SingleInteger|) $) NIL)) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) 177 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|extend| (($ $ (|NonNegativeInteger|)) 17)) (|exquo| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|exp| (($ $) 123 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|eval| (($ $ |#2| $) 110) (($ $ (|List| |#2|) (|List| $)) 103) (($ $ (|List| (|Equation| $))) NIL) (($ $ (|Equation| $)) NIL) (($ $ $ $) NIL) (($ $ (|List| $) (|List| $)) NIL)) (|differentiate| (($ $ |#2|) 112) (($ $ (|List| |#2|)) NIL) (($ $ |#2| (|NonNegativeInteger|)) NIL) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) NIL)) (|degree| (((|IndexedExponents| |#2|) $) NIL)) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) 93)) (|csch| (($ $) 161 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|csc| (($ $) 137 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|coth| (($ $) 157 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cot| (($ $) 133 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cosh| (($ $) 153 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cos| (($ $) 129 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|complete| (($ $) 19)) (|coerce| (((|OutputForm|) $) 193) (($ (|Integer|)) NIL) (($ |#1|) 60 (|has| |#1| (|CommutativeRing|))) (($ $) NIL (|has| |#1| (|IntegralDomain|))) (($ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ |#2|) 79) (($ |#3|) 77)) (|coefficients| (((|Stream| |#3|) $) NIL)) (|coefficient| ((|#1| $ (|IndexedExponents| |#2|)) 58) (($ $ |#2| (|NonNegativeInteger|)) NIL) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) 51) ((|#3| $ (|NonNegativeInteger|)) 43)) (|charthRoot| (((|Union| $ "failed") $) NIL (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|atanh| (($ $) 167 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|atan| (($ $) 143 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|associates?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|asinh| (($ $) 163 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asin| (($ $) 139 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asech| (($ $) 171 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asec| (($ $) 147 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acsch| (($ $) 173 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acsc| (($ $) 149 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acoth| (($ $) 169 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acot| (($ $) 145 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acosh| (($ $) 165 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acos| (($ $) 141 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 20 T CONST)) (|One| (($) 12 T CONST)) (D (($ $ |#2|) NIL) (($ $ (|List| |#2|)) NIL) (($ $ |#2| (|NonNegativeInteger|)) NIL) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) NIL)) (= (((|Boolean|) $ $) NIL)) (/ (($ $ |#1|) 195 (|has| |#1| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) 75)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 84) (($ $ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) 115 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 74) (($ $ (|Fraction| (|Integer|))) 120 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ (|Fraction| (|Integer|)) $) 118 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ |#1| $) 63) (($ $ |#1|) 64) (($ |#3| $) 62))) 
(((|SparseMultivariateTaylorSeries| |#1| |#2| |#3|) (|Join| (|MultivariateTaylorSeriesCategory| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |coefficient| (|#3| $ (|NonNegativeInteger|))) (SIGNATURE |coefficients| ((|Stream| |#3|) $)) (SIGNATURE |series| ($ (|Stream| |#3|))) (SIGNATURE |coerce| ($ |#2|)) (SIGNATURE |coerce| ($ |#3|)) (SIGNATURE * ($ |#3| $)) (SIGNATURE |csubst| ((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|)))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |integrate| ($ $ |#2| |#1|)) (SIGNATURE |fintegrate| ($ (|Mapping| $) |#2| |#1|))) |noBranch|))) (|Ring|) (|OrderedSet|) (|PolynomialCategory| |#1| (|IndexedExponents| |#2|) |#2|)) (T |SparseMultivariateTaylorSeries|)) 
((|coefficient| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *2 (|PolynomialCategory| *4 (|IndexedExponents| *5) *5)) (|isDomain| *1 (|SparseMultivariateTaylorSeries| *4 *5 *2)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedSet|)))) (|coefficients| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|Stream| *5)) (|isDomain| *1 (|SparseMultivariateTaylorSeries| *3 *4 *5)) (|ofCategory| *5 (|PolynomialCategory| *3 (|IndexedExponents| *4) *4)))) (|series| (*1 *1 *2) (AND (|isDomain| *2 (|Stream| *5)) (|ofCategory| *5 (|PolynomialCategory| *3 (|IndexedExponents| *4) *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|SparseMultivariateTaylorSeries| *3 *4 *5)))) (|coerce| (*1 *1 *2) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedSet|)) (|isDomain| *1 (|SparseMultivariateTaylorSeries| *3 *2 *4)) (|ofCategory| *4 (|PolynomialCategory| *3 (|IndexedExponents| *2) *2)))) (|coerce| (*1 *1 *2) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|SparseMultivariateTaylorSeries| *3 *4 *2)) (|ofCategory| *2 (|PolynomialCategory| *3 (|IndexedExponents| *4) *4)))) (* (*1 *1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|SparseMultivariateTaylorSeries| *3 *4 *2)) (|ofCategory| *2 (|PolynomialCategory| *3 (|IndexedExponents| *4) *4)))) (|csubst| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|List| (|Stream| *7))) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|PolynomialCategory| *5 (|IndexedExponents| *6) *6)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Mapping| (|Stream| *7) *7)) (|isDomain| *1 (|SparseMultivariateTaylorSeries| *5 *6 *7)))) (|integrate| (*1 *1 *1 *2 *3) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedSet|)) (|isDomain| *1 (|SparseMultivariateTaylorSeries| *3 *2 *4)) (|ofCategory| *4 (|PolynomialCategory| *3 (|IndexedExponents| *2) *2)))) (|fintegrate| (*1 *1 *2 *3 *4) (AND (|isDomain| *2 (|Mapping| (|SparseMultivariateTaylorSeries| *4 *3 *5))) (|ofCategory| *4 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|SparseMultivariateTaylorSeries| *4 *3 *5)) (|ofCategory| *5 (|PolynomialCategory| *4 (|IndexedExponents| *3) *3))))) 
(|Join| (|MultivariateTaylorSeriesCategory| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |coefficient| (|#3| $ (|NonNegativeInteger|))) (SIGNATURE |coefficients| ((|Stream| |#3|) $)) (SIGNATURE |series| ($ (|Stream| |#3|))) (SIGNATURE |coerce| ($ |#2|)) (SIGNATURE |coerce| ($ |#3|)) (SIGNATURE * ($ |#3| $)) (SIGNATURE |csubst| ((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|)))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |integrate| ($ $ |#2| |#1|)) (SIGNATURE |fintegrate| ($ (|Mapping| $) |#2| |#1|))) |noBranch|))) 
((~= (((|Boolean|) $ $) 7)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 78)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 79) (((|List| $) (|List| |#4|) (|Boolean|)) 104)) (|variables| (((|List| |#3|) $) 32)) (|trivialIdeal?| (((|Boolean|) $) 25)) (|triangular?| (((|Boolean|) $) 16 (|has| |#1| (|IntegralDomain|)))) (|stronglyReduced?| (((|Boolean|) |#4| $) 94) (((|Boolean|) $) 90)) (|stronglyReduce| ((|#4| |#4| $) 85)) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) 119)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 26)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 43)) (|select| (($ (|Mapping| (|Boolean|) |#4|) $) 64 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| |#4| "failed") $ |#3|) 72)) (|sample| (($) 44 T CONST)) (|roughUnitIdeal?| (((|Boolean|) $) 21 (|has| |#1| (|IntegralDomain|)))) (|roughSubIdeal?| (((|Boolean|) $ $) 23 (|has| |#1| (|IntegralDomain|)))) (|roughEqualIdeals?| (((|Boolean|) $ $) 22 (|has| |#1| (|IntegralDomain|)))) (|roughBase?| (((|Boolean|) $) 24 (|has| |#1| (|IntegralDomain|)))) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 86)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) 17 (|has| |#1| (|IntegralDomain|)))) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) 18 (|has| |#1| (|IntegralDomain|)))) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 35)) (|retract| (($ (|List| |#4|)) 34)) (|rest| (((|Union| $ "failed") $) 75)) (|removeZero| ((|#4| |#4| $) 82)) (|removeDuplicates| (($ $) 67 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove| (($ |#4| $) 66 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#4|) $) 63 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 19 (|has| |#1| (|IntegralDomain|)))) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) 95)) (|reduceByQuasiMonic| ((|#4| |#4| $) 80)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 65 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 62 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 61 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 87)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 98)) (|purelyTranscendental?| (((|Boolean|) |#4| $) 129)) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) 126)) (|purelyAlgebraic?| (((|Boolean|) |#4| $) 130) (((|Boolean|) $) 127)) (|parts| (((|List| |#4|) $) 51 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|normalized?| (((|Boolean|) |#4| $) 97) (((|Boolean|) $) 96)) (|mvar| ((|#3| $) 33)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 42)) (|members| (((|List| |#4|) $) 52 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#4| $) 54 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#4| |#4|) $) 47 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#4| |#4|) $) 46)) (|mainVariables| (((|List| |#3|) $) 31)) (|mainVariable?| (((|Boolean|) |#3| $) 30)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 41)) (|latex| (((|String|) $) 9)) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) 121)) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) 120)) (|last| (((|Union| |#4| "failed") $) 76)) (|invertibleSet| (((|List| $) |#4| $) 122)) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) 125)) (|invertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) 124) (((|Boolean|) |#4| $) 123)) (|intersect| (((|List| $) |#4| $) 118) (((|List| $) (|List| |#4|) $) 117) (((|List| $) (|List| |#4|) (|List| $)) 116) (((|List| $) |#4| (|List| $)) 115)) (|internalAugment| (($ |#4| $) 110) (($ (|List| |#4|) $) 109)) (|initials| (((|List| |#4|) $) 100)) (|initiallyReduced?| (((|Boolean|) |#4| $) 92) (((|Boolean|) $) 88)) (|initiallyReduce| ((|#4| |#4| $) 83)) (|infRittWu?| (((|Boolean|) $ $) 103)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 20 (|has| |#1| (|IntegralDomain|)))) (|headReduced?| (((|Boolean|) |#4| $) 93) (((|Boolean|) $) 89)) (|headReduce| ((|#4| |#4| $) 84)) (|hash| (((|SingleInteger|) $) 10)) (|first| (((|Union| |#4| "failed") $) 77)) (|find| (((|Union| |#4| "failed") (|Mapping| (|Boolean|) |#4|) $) 60)) (|extendIfCan| (((|Union| $ "failed") $ |#4|) 71)) (|extend| (($ $ |#4|) 70) (((|List| $) |#4| $) 108) (((|List| $) |#4| (|List| $)) 107) (((|List| $) (|List| |#4|) $) 106) (((|List| $) (|List| |#4|) (|List| $)) 105)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) 49 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 58 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ |#4| |#4|) 57 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|Equation| |#4|)) 56 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|List| (|Equation| |#4|))) 55 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 37)) (|empty?| (((|Boolean|) $) 40)) (|empty| (($) 39)) (|degree| (((|NonNegativeInteger|) $) 99)) (|count| (((|NonNegativeInteger|) |#4| $) 53 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#4|) $) 50 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) 38)) (|convert| (((|InputForm|) $) 68 (|has| |#4| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#4|)) 59)) (|collectUpper| (($ $ |#3|) 27)) (|collectUnder| (($ $ |#3|) 29)) (|collectQuasiMonic| (($ $) 81)) (|collect| (($ $ |#3|) 28)) (|coerce| (((|OutputForm|) $) 11) (((|List| |#4|) $) 36)) (|coHeight| (((|NonNegativeInteger|) $) 69 (|has| |#3| (|Finite|)))) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 102) (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 101)) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) 91)) (|augment| (((|List| $) |#4| $) 114) (((|List| $) |#4| (|List| $)) 113) (((|List| $) (|List| |#4|) $) 112) (((|List| $) (|List| |#4|) (|List| $)) 111)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) 48 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|algebraicVariables| (((|List| |#3|) $) 74)) (|algebraicCoefficients?| (((|Boolean|) |#4| $) 128)) (|algebraic?| (((|Boolean|) |#3| $) 73)) (= (((|Boolean|) $ $) 6)) (|#| (((|NonNegativeInteger|) $) 45 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|SquareFreeNormalizedTriangularSetCategory| |#1| |#2| |#3| |#4|) (|Category|) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |t#1| |t#2| |t#3|)) (T |SquareFreeNormalizedTriangularSetCategory|)) 
NIL 
(|Join| (|SquareFreeRegularTriangularSetCategory| |t#1| |t#2| |t#3| |t#4|) (|NormalizedTriangularSetCategory| |t#1| |t#2| |t#3| |t#4|)) 
(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|NormalizedTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|SquareFreeRegularTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|TriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|Type|) . T)) 
((|solve| (((|List| |#2|) |#1|) 12)) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) 37) (((|List| |#2|) |#1|) 47)) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) 35) (((|List| |#2|) |#1|) 45)) (|particularSolution| ((|#2| |#1|) 42)) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) 16)) (|linear| (((|List| |#2|) |#2| |#2|) 34) (((|List| |#2|) |#1|) 44)) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) 36) (((|List| |#2|) |#1|) 46)) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) 41)) (|aQuadratic| ((|#2| |#2| |#2| |#2|) 39)) (|aLinear| ((|#2| |#2| |#2|) 38)) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) 40))) 
(((|PolynomialSolveByFormulas| |#1| |#2|) (CATEGORY |package| (SIGNATURE |solve| ((|List| |#2|) |#1|)) (SIGNATURE |particularSolution| (|#2| |#1|)) (SIGNATURE |mapSolve| ((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|))) (SIGNATURE |linear| ((|List| |#2|) |#1|)) (SIGNATURE |quadratic| ((|List| |#2|) |#1|)) (SIGNATURE |cubic| ((|List| |#2|) |#1|)) (SIGNATURE |quartic| ((|List| |#2|) |#1|)) (SIGNATURE |linear| ((|List| |#2|) |#2| |#2|)) (SIGNATURE |quadratic| ((|List| |#2|) |#2| |#2| |#2|)) (SIGNATURE |cubic| ((|List| |#2|) |#2| |#2| |#2| |#2|)) (SIGNATURE |quartic| ((|List| |#2|) |#2| |#2| |#2| |#2| |#2|)) (SIGNATURE |aLinear| (|#2| |#2| |#2|)) (SIGNATURE |aQuadratic| (|#2| |#2| |#2| |#2|)) (SIGNATURE |aCubic| (|#2| |#2| |#2| |#2| |#2|)) (SIGNATURE |aQuartic| (|#2| |#2| |#2| |#2| |#2| |#2|))) (|UnivariatePolynomialCategory| |#2|) (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (T |PolynomialSolveByFormulas|)) 
((|aQuartic| (*1 *2 *2 *2 *2 *2 *2) (AND (|ofCategory| *2 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *2)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|aCubic| (*1 *2 *2 *2 *2 *2) (AND (|ofCategory| *2 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *2)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|aQuadratic| (*1 *2 *2 *2 *2) (AND (|ofCategory| *2 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *2)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|aLinear| (*1 *2 *2 *2) (AND (|ofCategory| *2 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *2)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|quartic| (*1 *2 *3 *3 *3 *3 *3) (AND (|ofCategory| *3 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PolynomialSolveByFormulas| *4 *3)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|cubic| (*1 *2 *3 *3 *3 *3) (AND (|ofCategory| *3 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PolynomialSolveByFormulas| *4 *3)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|quadratic| (*1 *2 *3 *3 *3) (AND (|ofCategory| *3 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PolynomialSolveByFormulas| *4 *3)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|linear| (*1 *2 *3 *3) (AND (|ofCategory| *3 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PolynomialSolveByFormulas| *4 *3)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|quartic| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *4)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|cubic| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *4)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|quadratic| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *4)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|linear| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *4)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|mapSolve| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| *5 *5)) (|ofCategory| *5 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (|isDomain| *2 (|Record| (|:| |solns| (|List| *5)) (|:| |maps| (|List| (|Record| (|:| |arg| *5) (|:| |res| *5)))))) (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *5)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|particularSolution| (*1 *2 *3) (AND (|ofCategory| *2 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *2)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|solve| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *4)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |solve| ((|List| |#2|) |#1|)) (SIGNATURE |particularSolution| (|#2| |#1|)) (SIGNATURE |mapSolve| ((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|))) (SIGNATURE |linear| ((|List| |#2|) |#1|)) (SIGNATURE |quadratic| ((|List| |#2|) |#1|)) (SIGNATURE |cubic| ((|List| |#2|) |#1|)) (SIGNATURE |quartic| ((|List| |#2|) |#1|)) (SIGNATURE |linear| ((|List| |#2|) |#2| |#2|)) (SIGNATURE |quadratic| ((|List| |#2|) |#2| |#2| |#2|)) (SIGNATURE |cubic| ((|List| |#2|) |#2| |#2| |#2| |#2|)) (SIGNATURE |quartic| ((|List| |#2|) |#2| |#2| |#2| |#2| |#2|)) (SIGNATURE |aLinear| (|#2| |#2| |#2|)) (SIGNATURE |aQuadratic| (|#2| |#2| |#2| |#2|)) (SIGNATURE |aCubic| (|#2| |#2| |#2| |#2| |#2|)) (SIGNATURE |aQuartic| (|#2| |#2| |#2| |#2| |#2| |#2|))) 
((|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) 94) (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) 93) (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) 91) (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) 89) (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) 75) (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) 76) (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) 70) (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) 59)) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) 87) (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) 43)) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) 97) (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) 96))) 
(((|RadicalSolvePackage| |#1|) (CATEGORY |package| (SIGNATURE |radicalSolve| ((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |radicalSolve| ((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)))) (SIGNATURE |radicalSolve| ((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|))) (SIGNATURE |radicalSolve| ((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |radicalSolve| ((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|)))) (SIGNATURE |radicalSolve| ((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |radicalSolve| ((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)))) (SIGNATURE |radicalSolve| ((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))))) (SIGNATURE |radicalRoots| ((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |radicalRoots| ((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|)))) (SIGNATURE |contractSolve| ((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|))) (SIGNATURE |contractSolve| ((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)))) (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|))) (T |RadicalSolvePackage|)) 
((|contractSolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5))) (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|))) (|isDomain| *2 (|SuchThat| (|List| (|Expression| *5)) (|List| (|Equation| (|Expression| *5))))) (|isDomain| *1 (|RadicalSolvePackage| *5)))) (|contractSolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Equation| (|Fraction| (|Polynomial| *5)))) (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|))) (|isDomain| *2 (|SuchThat| (|List| (|Expression| *5)) (|List| (|Equation| (|Expression| *5))))) (|isDomain| *1 (|RadicalSolvePackage| *5)))) (|radicalRoots| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| *5)))) (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|List| (|Expression| *5)))) (|isDomain| *1 (|RadicalSolvePackage| *5)))) (|radicalRoots| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5))) (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|Expression| *5))) (|isDomain| *1 (|RadicalSolvePackage| *5)))) (|radicalSolve| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Equation| (|Fraction| (|Polynomial| *4))))) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|List| (|Equation| (|Expression| *4))))) (|isDomain| *1 (|RadicalSolvePackage| *4)))) (|radicalSolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Equation| (|Fraction| (|Polynomial| *5))))) (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|List| (|Equation| (|Expression| *5))))) (|isDomain| *1 (|RadicalSolvePackage| *5)))) (|radicalSolve| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| *4)))) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|List| (|Equation| (|Expression| *4))))) (|isDomain| *1 (|RadicalSolvePackage| *4)))) (|radicalSolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| *5)))) (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|List| (|Equation| (|Expression| *5))))) (|isDomain| *1 (|RadicalSolvePackage| *5)))) (|radicalSolve| (*1 *2 *3) (AND (|isDomain| *3 (|Equation| (|Fraction| (|Polynomial| *4)))) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|Equation| (|Expression| *4)))) (|isDomain| *1 (|RadicalSolvePackage| *4)))) (|radicalSolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Equation| (|Fraction| (|Polynomial| *5)))) (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|Equation| (|Expression| *5)))) (|isDomain| *1 (|RadicalSolvePackage| *5)))) (|radicalSolve| (*1 *2 *3) (AND (|isDomain| *3 (|Fraction| (|Polynomial| *4))) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|Equation| (|Expression| *4)))) (|isDomain| *1 (|RadicalSolvePackage| *4)))) (|radicalSolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5))) (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|OrderedSet|) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|Equation| (|Expression| *5)))) (|isDomain| *1 (|RadicalSolvePackage| *5))))) 
(CATEGORY |package| (SIGNATURE |radicalSolve| ((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |radicalSolve| ((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)))) (SIGNATURE |radicalSolve| ((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|))) (SIGNATURE |radicalSolve| ((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |radicalSolve| ((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|)))) (SIGNATURE |radicalSolve| ((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))))) (SIGNATURE |radicalSolve| ((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)))) (SIGNATURE |radicalSolve| ((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))))) (SIGNATURE |radicalRoots| ((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |radicalRoots| ((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|)))) (SIGNATURE |contractSolve| ((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|))) (SIGNATURE |contractSolve| ((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)))) 
((|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) 27)) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) 39))) 
(((|TransSolvePackageService| |#1|) (CATEGORY |package| (SIGNATURE |decomposeFunc| ((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))))) (SIGNATURE |unvectorise| ((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)))) (|Join| (|IntegralDomain|) (|OrderedSet|))) (T |TransSolvePackageService|)) 
((|unvectorise| (*1 *2 *3 *2 *4) (AND (|isDomain| *2 (|Fraction| (|SparseUnivariatePolynomial| (|Expression| *5)))) (|isDomain| *3 (|Vector| (|Expression| *5))) (|isDomain| *4 (|Integer|)) (|ofCategory| *5 (|Join| (|IntegralDomain|) (|OrderedSet|))) (|isDomain| *1 (|TransSolvePackageService| *5)))) (|decomposeFunc| (*1 *2 *2 *2 *2) (AND (|isDomain| *2 (|Fraction| (|SparseUnivariatePolynomial| (|Expression| *3)))) (|ofCategory| *3 (|Join| (|IntegralDomain|) (|OrderedSet|))) (|isDomain| *1 (|TransSolvePackageService| *3))))) 
(CATEGORY |package| (SIGNATURE |decomposeFunc| ((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))))) (SIGNATURE |unvectorise| ((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)))) 
((|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) 216) (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) 20) (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) 26) (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) 25) (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) 21))) 
(((|TransSolvePackage| |#1|) (CATEGORY |package| (SIGNATURE |solve| ((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|))) (SIGNATURE |solve| ((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)))) (SIGNATURE |solve| ((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|))) (SIGNATURE |solve| ((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|))) (SIGNATURE |solve| ((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))))) (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (T |TransSolvePackage|)) 
((|solve| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|List| (|Equation| (|Expression| *5))))) (|isDomain| *1 (|TransSolvePackage| *5)) (|isDomain| *3 (|List| (|Equation| (|Expression| *5)))))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|Equation| (|Expression| *5)))) (|isDomain| *1 (|TransSolvePackage| *5)) (|isDomain| *3 (|Expression| *5)))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|Equation| (|Expression| *5)))) (|isDomain| *1 (|TransSolvePackage| *5)) (|isDomain| *3 (|Equation| (|Expression| *5))))) (|solve| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|Equation| (|Expression| *4)))) (|isDomain| *1 (|TransSolvePackage| *4)) (|isDomain| *3 (|Equation| (|Expression| *4))))) (|solve| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|OrderedSet|) (|EuclideanDomain|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|Equation| (|Expression| *4)))) (|isDomain| *1 (|TransSolvePackage| *4)) (|isDomain| *3 (|Expression| *4))))) 
(CATEGORY |package| (SIGNATURE |solve| ((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|))) (SIGNATURE |solve| ((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)))) (SIGNATURE |solve| ((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|))) (SIGNATURE |solve| ((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|))) (SIGNATURE |solve| ((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))))) 
((|insertionSort!| ((|#2| |#2|) 20 (|has| |#1| (|OrderedSet|))) ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) 16)) (|bubbleSort!| ((|#2| |#2|) 19 (|has| |#1| (|OrderedSet|))) ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) 15))) 
(((|SortPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |bubbleSort!| (|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|))) (SIGNATURE |insertionSort!| (|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|))) (IF (|has| |#1| (|OrderedSet|)) (PROGN (SIGNATURE |bubbleSort!| (|#2| |#2|)) (SIGNATURE |insertionSort!| (|#2| |#2|))) |noBranch|)) (|Type|) (|Join| (|IndexedAggregate| (|Integer|) |#1|) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|) (ATTRIBUTE |shallowlyMutable|)))) (T |SortPackage|)) 
((|insertionSort!| (*1 *2 *2) (AND (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|SortPackage| *3 *2)) (|ofCategory| *2 (|Join| (|IndexedAggregate| (|Integer|) *3) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|) (ATTRIBUTE |shallowlyMutable|)))))) (|bubbleSort!| (*1 *2 *2) (AND (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|SortPackage| *3 *2)) (|ofCategory| *2 (|Join| (|IndexedAggregate| (|Integer|) *3) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|) (ATTRIBUTE |shallowlyMutable|)))))) (|insertionSort!| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *1 (|SortPackage| *4 *2)) (|ofCategory| *2 (|Join| (|IndexedAggregate| (|Integer|) *4) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|) (ATTRIBUTE |shallowlyMutable|)))))) (|bubbleSort!| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *1 (|SortPackage| *4 *2)) (|ofCategory| *2 (|Join| (|IndexedAggregate| (|Integer|) *4) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|) (ATTRIBUTE |shallowlyMutable|))))))) 
(CATEGORY |package| (SIGNATURE |bubbleSort!| (|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|))) (SIGNATURE |insertionSort!| (|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|))) (IF (|has| |#1| (|OrderedSet|)) (PROGN (SIGNATURE |bubbleSort!| (|#2| |#2|)) (SIGNATURE |insertionSort!| (|#2| |#2|))) |noBranch|)) 
((~= (((|Boolean|) $ $) NIL)) (|subspace| (((|SubSpace| 3 |#1|) $) 105)) (|polygon?| (((|Boolean|) $) 72)) (|polygon| (($ $ (|List| (|Point| |#1|))) 20) (($ $ (|List| (|List| |#1|))) 75) (($ (|List| (|Point| |#1|))) 74) (((|List| (|Point| |#1|)) $) 73)) (|point?| (((|Boolean|) $) 41)) (|point| (($ $ (|Point| |#1|)) 46) (($ $ (|List| |#1|)) 51) (($ $ (|NonNegativeInteger|)) 53) (($ (|Point| |#1|)) 47) (((|Point| |#1|) $) 45)) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) 103)) (|numberOfComposites| (((|NonNegativeInteger|) $) 26)) (|numberOfComponents| (((|NonNegativeInteger|) $) 25)) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) 39)) (|mesh?| (((|Boolean|) $) 82)) (|mesh| (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) 89) (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) 91) (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) 85) (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) 93) (($ (|List| (|List| (|Point| |#1|)))) 86) (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) 87) (((|List| (|List| (|Point| |#1|))) $) 84)) (|merge| (($ (|List| $)) 28) (($ $ $) 29)) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) 101)) (|lp| (((|List| (|Point| |#1|)) $) 96)) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) 100)) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) NIL)) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) 98)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) 37)) (|curve?| (((|Boolean|) $) 54)) (|curve| (($ $ (|List| (|Point| |#1|))) 56) (($ $ (|List| (|List| |#1|))) 62) (($ (|List| (|Point| |#1|))) 57) (((|List| (|Point| |#1|)) $) 55)) (|create3Space| (($) 23) (($ (|SubSpace| 3 |#1|)) 24)) (|copy| (($ $) 35)) (|composites| (((|List| $) $) 34)) (|composite| (($ (|List| $)) 31)) (|components| (((|List| $) $) 33)) (|coerce| (((|OutputForm|) $) 109)) (|closedCurve?| (((|Boolean|) $) 64)) (|closedCurve| (($ $ (|List| (|Point| |#1|))) 66) (($ $ (|List| (|List| |#1|))) 69) (($ (|List| (|Point| |#1|))) 67) (((|List| (|Point| |#1|)) $) 65)) (|check| (($ $) 104)) (= (((|Boolean|) $ $) NIL))) 
(((|ThreeSpace| |#1|) (|ThreeSpaceCategory| |#1|) (|Ring|)) (T |ThreeSpace|)) 
NIL 
(|ThreeSpaceCategory| |#1|) 
((~= (((|Boolean|) $ $) 7)) (|subspace| (((|SubSpace| 3 |#1|) $) 12)) (|polygon?| (((|Boolean|) $) 28)) (|polygon| (($ $ (|List| (|Point| |#1|))) 32) (($ $ (|List| (|List| |#1|))) 31) (($ (|List| (|Point| |#1|))) 30) (((|List| (|Point| |#1|)) $) 29)) (|point?| (((|Boolean|) $) 43)) (|point| (($ $ (|Point| |#1|)) 48) (($ $ (|List| |#1|)) 47) (($ $ (|NonNegativeInteger|)) 46) (($ (|Point| |#1|)) 45) (((|Point| |#1|) $) 44)) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) 14)) (|numberOfComposites| (((|NonNegativeInteger|) $) 57)) (|numberOfComponents| (((|NonNegativeInteger|) $) 58)) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) 49)) (|mesh?| (((|Boolean|) $) 20)) (|mesh| (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) 27) (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) 26) (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) 25) (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) 24) (($ (|List| (|List| (|Point| |#1|)))) 23) (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) 22) (((|List| (|List| (|Point| |#1|))) $) 21)) (|merge| (($ (|List| $)) 56) (($ $ $) 55)) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) 15)) (|lp| (((|List| (|Point| |#1|)) $) 19)) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) 16)) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) 17)) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) 18)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) 50)) (|curve?| (((|Boolean|) $) 38)) (|curve| (($ $ (|List| (|Point| |#1|))) 42) (($ $ (|List| (|List| |#1|))) 41) (($ (|List| (|Point| |#1|))) 40) (((|List| (|Point| |#1|)) $) 39)) (|create3Space| (($) 60) (($ (|SubSpace| 3 |#1|)) 59)) (|copy| (($ $) 51)) (|composites| (((|List| $) $) 52)) (|composite| (($ (|List| $)) 54)) (|components| (((|List| $) $) 53)) (|coerce| (((|OutputForm|) $) 11)) (|closedCurve?| (((|Boolean|) $) 33)) (|closedCurve| (($ $ (|List| (|Point| |#1|))) 37) (($ $ (|List| (|List| |#1|))) 36) (($ (|List| (|Point| |#1|))) 35) (((|List| (|Point| |#1|)) $) 34)) (|check| (($ $) 13)) (= (((|Boolean|) $ $) 6))) 
(((|ThreeSpaceCategory| |#1|) (|Category|) (|Ring|)) (T |ThreeSpaceCategory|)) 
((|coerce| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|OutputForm|)))) (|create3Space| (*1 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|create3Space| (*1 *1 *2) (AND (|isDomain| *2 (|SubSpace| 3 *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|ThreeSpaceCategory| *3)))) (|numberOfComponents| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|numberOfComposites| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|merge| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|merge| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|composite| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|components| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|ThreeSpaceCategory| *3)))) (|composites| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|ThreeSpaceCategory| *3)))) (|copy| (*1 *1 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|enterPointData| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| (|Point| *4))) (|ofCategory| *1 (|ThreeSpaceCategory| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|modifyPointData| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *3 (|Point| *4)) (|ofCategory| *1 (|ThreeSpaceCategory| *4)) (|ofCategory| *4 (|Ring|)))) (|point| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Point| *3)) (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|point| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|point| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|point| (*1 *1 *2) (AND (|isDomain| *2 (|Point| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|ThreeSpaceCategory| *3)))) (|point| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Point| *3)))) (|point?| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Boolean|)))) (|curve| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Point| *3))) (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|curve| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|curve| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Point| *3))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|ThreeSpaceCategory| *3)))) (|curve| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|List| (|Point| *3))))) (|curve?| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Boolean|)))) (|closedCurve| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Point| *3))) (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|closedCurve| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|closedCurve| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Point| *3))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|ThreeSpaceCategory| *3)))) (|closedCurve| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|List| (|Point| *3))))) (|closedCurve?| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Boolean|)))) (|polygon| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Point| *3))) (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|polygon| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|polygon| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Point| *3))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|ThreeSpaceCategory| *3)))) (|polygon| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|List| (|Point| *3))))) (|polygon?| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Boolean|)))) (|mesh| (*1 *1 *1 *2 *3 *4) (AND (|isDomain| *2 (|List| (|List| (|Point| *5)))) (|isDomain| *3 (|List| (|SubSpaceComponentProperty|))) (|isDomain| *4 (|SubSpaceComponentProperty|)) (|ofCategory| *1 (|ThreeSpaceCategory| *5)) (|ofCategory| *5 (|Ring|)))) (|mesh| (*1 *1 *1 *2 *3 *4) (AND (|isDomain| *2 (|List| (|List| (|List| *5)))) (|isDomain| *3 (|List| (|SubSpaceComponentProperty|))) (|isDomain| *4 (|SubSpaceComponentProperty|)) (|ofCategory| *1 (|ThreeSpaceCategory| *5)) (|ofCategory| *5 (|Ring|)))) (|mesh| (*1 *1 *1 *2 *3 *3) (AND (|isDomain| *2 (|List| (|List| (|Point| *4)))) (|isDomain| *3 (|Boolean|)) (|ofCategory| *1 (|ThreeSpaceCategory| *4)) (|ofCategory| *4 (|Ring|)))) (|mesh| (*1 *1 *1 *2 *3 *3) (AND (|isDomain| *2 (|List| (|List| (|List| *4)))) (|isDomain| *3 (|Boolean|)) (|ofCategory| *1 (|ThreeSpaceCategory| *4)) (|ofCategory| *4 (|Ring|)))) (|mesh| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|List| (|Point| *3)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|ThreeSpaceCategory| *3)))) (|mesh| (*1 *1 *2 *3 *3) (AND (|isDomain| *2 (|List| (|List| (|Point| *4)))) (|isDomain| *3 (|Boolean|)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *1 (|ThreeSpaceCategory| *4)))) (|mesh| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|List| (|List| (|Point| *3)))))) (|mesh?| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Boolean|)))) (|lp| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|List| (|Point| *3))))) (|lllip| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|List| (|List| (|List| (|NonNegativeInteger|))))))) (|lllp| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|List| (|List| (|List| (|Point| *3))))))) (|llprop| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|List| (|List| (|SubSpaceComponentProperty|)))))) (|lprop| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|List| (|SubSpaceComponentProperty|))))) (|objects| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|)))))) (|check| (*1 *1 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|subspace| (*1 *2 *1) (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|SubSpace| 3 *3))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |create3Space| ($)) (SIGNATURE |create3Space| ($ (|SubSpace| 3 |t#1|))) (SIGNATURE |numberOfComponents| ((|NonNegativeInteger|) $)) (SIGNATURE |numberOfComposites| ((|NonNegativeInteger|) $)) (SIGNATURE |merge| ($ (|List| $))) (SIGNATURE |merge| ($ $ $)) (SIGNATURE |composite| ($ (|List| $))) (SIGNATURE |components| ((|List| $) $)) (SIGNATURE |composites| ((|List| $) $)) (SIGNATURE |copy| ($ $)) (SIGNATURE |enterPointData| ((|NonNegativeInteger|) $ (|List| (|Point| |t#1|)))) (SIGNATURE |modifyPointData| ($ $ (|NonNegativeInteger|) (|Point| |t#1|))) (SIGNATURE |point| ($ $ (|Point| |t#1|))) (SIGNATURE |point| ($ $ (|List| |t#1|))) (SIGNATURE |point| ($ $ (|NonNegativeInteger|))) (SIGNATURE |point| ($ (|Point| |t#1|))) (SIGNATURE |point| ((|Point| |t#1|) $)) (SIGNATURE |point?| ((|Boolean|) $)) (SIGNATURE |curve| ($ $ (|List| (|Point| |t#1|)))) (SIGNATURE |curve| ($ $ (|List| (|List| |t#1|)))) (SIGNATURE |curve| ($ (|List| (|Point| |t#1|)))) (SIGNATURE |curve| ((|List| (|Point| |t#1|)) $)) (SIGNATURE |curve?| ((|Boolean|) $)) (SIGNATURE |closedCurve| ($ $ (|List| (|Point| |t#1|)))) (SIGNATURE |closedCurve| ($ $ (|List| (|List| |t#1|)))) (SIGNATURE |closedCurve| ($ (|List| (|Point| |t#1|)))) (SIGNATURE |closedCurve| ((|List| (|Point| |t#1|)) $)) (SIGNATURE |closedCurve?| ((|Boolean|) $)) (SIGNATURE |polygon| ($ $ (|List| (|Point| |t#1|)))) (SIGNATURE |polygon| ($ $ (|List| (|List| |t#1|)))) (SIGNATURE |polygon| ($ (|List| (|Point| |t#1|)))) (SIGNATURE |polygon| ((|List| (|Point| |t#1|)) $)) (SIGNATURE |polygon?| ((|Boolean|) $)) (SIGNATURE |mesh| ($ $ (|List| (|List| (|Point| |t#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|))) (SIGNATURE |mesh| ($ $ (|List| (|List| (|List| |t#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|))) (SIGNATURE |mesh| ($ $ (|List| (|List| (|Point| |t#1|))) (|Boolean|) (|Boolean|))) (SIGNATURE |mesh| ($ $ (|List| (|List| (|List| |t#1|))) (|Boolean|) (|Boolean|))) (SIGNATURE |mesh| ($ (|List| (|List| (|Point| |t#1|))))) (SIGNATURE |mesh| ($ (|List| (|List| (|Point| |t#1|))) (|Boolean|) (|Boolean|))) (SIGNATURE |mesh| ((|List| (|List| (|Point| |t#1|))) $)) (SIGNATURE |mesh?| ((|Boolean|) $)) (SIGNATURE |lp| ((|List| (|Point| |t#1|)) $)) (SIGNATURE |lllip| ((|List| (|List| (|List| (|NonNegativeInteger|)))) $)) (SIGNATURE |lllp| ((|List| (|List| (|List| (|Point| |t#1|)))) $)) (SIGNATURE |llprop| ((|List| (|List| (|SubSpaceComponentProperty|))) $)) (SIGNATURE |lprop| ((|List| (|SubSpaceComponentProperty|)) $)) (SIGNATURE |objects| ((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $)) (SIGNATURE |check| ($ $)) (SIGNATURE |subspace| ((|SubSpace| 3 |t#1|) $)) (SIGNATURE |coerce| ((|OutputForm|) $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((|outputAsTex| (((|Void|) (|List| (|OutputForm|))) 23) (((|Void|) (|OutputForm|)) 22)) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) 21) (((|Void|) (|OutputForm|)) 20)) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) 19) (((|Void|) (|OutputForm|)) 11) (((|Void|) (|String|) (|OutputForm|)) 17))) 
(((|SpecialOutputPackage|) (CATEGORY |package| (SIGNATURE |outputAsFortran| ((|Void|) (|String|) (|OutputForm|))) (SIGNATURE |outputAsFortran| ((|Void|) (|OutputForm|))) (SIGNATURE |outputAsScript| ((|Void|) (|OutputForm|))) (SIGNATURE |outputAsTex| ((|Void|) (|OutputForm|))) (SIGNATURE |outputAsFortran| ((|Void|) (|List| (|OutputForm|)))) (SIGNATURE |outputAsScript| ((|Void|) (|List| (|OutputForm|)))) (SIGNATURE |outputAsTex| ((|Void|) (|List| (|OutputForm|)))))) (T |SpecialOutputPackage|)) 
((|outputAsTex| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|OutputForm|))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SpecialOutputPackage|)))) (|outputAsScript| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|OutputForm|))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SpecialOutputPackage|)))) (|outputAsFortran| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|OutputForm|))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SpecialOutputPackage|)))) (|outputAsTex| (*1 *2 *3) (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SpecialOutputPackage|)))) (|outputAsScript| (*1 *2 *3) (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SpecialOutputPackage|)))) (|outputAsFortran| (*1 *2 *3) (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SpecialOutputPackage|)))) (|outputAsFortran| (*1 *2 *3 *4) (AND (|isDomain| *3 (|String|)) (|isDomain| *4 (|OutputForm|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SpecialOutputPackage|))))) 
(CATEGORY |package| (SIGNATURE |outputAsFortran| ((|Void|) (|String|) (|OutputForm|))) (SIGNATURE |outputAsFortran| ((|Void|) (|OutputForm|))) (SIGNATURE |outputAsScript| ((|Void|) (|OutputForm|))) (SIGNATURE |outputAsTex| ((|Void|) (|OutputForm|))) (SIGNATURE |outputAsFortran| ((|Void|) (|List| (|OutputForm|)))) (SIGNATURE |outputAsScript| ((|Void|) (|List| (|OutputForm|)))) (SIGNATURE |outputAsTex| ((|Void|) (|List| (|OutputForm|))))) 
((|polygamma| (($ $ $) 10)) (|digamma| (($ $) 9)) (|besselY| (($ $ $) 13)) (|besselK| (($ $ $) 15)) (|besselJ| (($ $ $) 12)) (|besselI| (($ $ $) 14)) (|airyBi| (($ $) 17)) (|airyAi| (($ $) 16)) (|abs| (($ $) 6)) (|Gamma| (($ $ $) 11) (($ $) 7)) (|Beta| (($ $ $) 8))) 
(((|SpecialFunctionCategory|) (|Category|)) (T |SpecialFunctionCategory|)) 
((|airyBi| (*1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|))) (|airyAi| (*1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|))) (|besselK| (*1 *1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|))) (|besselI| (*1 *1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|))) (|besselY| (*1 *1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|))) (|besselJ| (*1 *1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|))) (|Gamma| (*1 *1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|))) (|polygamma| (*1 *1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|))) (|digamma| (*1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|))) (|Beta| (*1 *1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|))) (|Gamma| (*1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|))) (|abs| (*1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|)))) 
(|Join| (CATEGORY |domain| (SIGNATURE |abs| ($ $)) (SIGNATURE |Gamma| ($ $)) (SIGNATURE |Beta| ($ $ $)) (SIGNATURE |digamma| ($ $)) (SIGNATURE |polygamma| ($ $ $)) (SIGNATURE |Gamma| ($ $ $)) (SIGNATURE |besselJ| ($ $ $)) (SIGNATURE |besselY| ($ $ $)) (SIGNATURE |besselI| ($ $ $)) (SIGNATURE |besselK| ($ $ $)) (SIGNATURE |airyAi| ($ $)) (SIGNATURE |airyBi| ($ $)))) 
((~= (((|Boolean|) $ $) 41)) (|value| ((|#1| $) 15)) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) 36)) (|status| (((|Boolean|) $) 17)) (|setValue!| (($ $ |#1|) 28)) (|setStatus!| (($ $ (|Boolean|)) 30)) (|setEmpty!| (($ $) 31)) (|setCondition!| (($ $ |#2|) 29)) (|latex| (((|String|) $) NIL)) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) 35)) (|hash| (((|SingleInteger|) $) NIL)) (|empty?| (((|Boolean|) $) 14)) (|empty| (($) 10)) (|copy| (($ $) 27)) (|construct| (($ |#1| |#2| (|Boolean|)) 18) (($ |#1| |#2|) 19) (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) 21) (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) 24) (((|List| $) |#1| (|List| |#2|)) 26)) (|condition| ((|#2| $) 16)) (|coerce| (((|OutputForm|) $) 50)) (= (((|Boolean|) $ $) 39))) 
(((|SplittingNode| |#1| |#2|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |empty| ($)) (SIGNATURE |empty?| ((|Boolean|) $)) (SIGNATURE |value| (|#1| $)) (SIGNATURE |condition| (|#2| $)) (SIGNATURE |status| ((|Boolean|) $)) (SIGNATURE |construct| ($ |#1| |#2| (|Boolean|))) (SIGNATURE |construct| ($ |#1| |#2|)) (SIGNATURE |construct| ($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) (SIGNATURE |construct| ((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))))) (SIGNATURE |construct| ((|List| $) |#1| (|List| |#2|))) (SIGNATURE |copy| ($ $)) (SIGNATURE |setValue!| ($ $ |#1|)) (SIGNATURE |setCondition!| ($ $ |#2|)) (SIGNATURE |setStatus!| ($ $ (|Boolean|))) (SIGNATURE |setEmpty!| ($ $)) (SIGNATURE |infLex?| ((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|))) (SIGNATURE |subNode?| ((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|))))) (|Join| (|SetCategory|) (|Aggregate|)) (|Join| (|SetCategory|) (|Aggregate|))) (T |SplittingNode|)) 
((|empty| (*1 *1) (AND (|isDomain| *1 (|SplittingNode| *2 *3)) (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))))) (|empty?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SplittingNode| *3 *4)) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|))))) (|value| (*1 *2 *1) (AND (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|))) (|isDomain| *1 (|SplittingNode| *2 *3)) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))))) (|condition| (*1 *2 *1) (AND (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|))) (|isDomain| *1 (|SplittingNode| *3 *2)) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))))) (|status| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SplittingNode| *3 *4)) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|))))) (|construct| (*1 *1 *2 *3 *4) (AND (|isDomain| *4 (|Boolean|)) (|isDomain| *1 (|SplittingNode| *2 *3)) (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))))) (|construct| (*1 *1 *2 *3) (AND (|isDomain| *1 (|SplittingNode| *2 *3)) (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))))) (|construct| (*1 *1 *2) (AND (|isDomain| *2 (|Record| (|:| |val| *3) (|:| |tower| *4))) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|))) (|isDomain| *1 (|SplittingNode| *3 *4)))) (|construct| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Record| (|:| |val| *4) (|:| |tower| *5)))) (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *5 (|Join| (|SetCategory|) (|Aggregate|))) (|isDomain| *2 (|List| (|SplittingNode| *4 *5))) (|isDomain| *1 (|SplittingNode| *4 *5)))) (|construct| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *5)) (|ofCategory| *5 (|Join| (|SetCategory|) (|Aggregate|))) (|isDomain| *2 (|List| (|SplittingNode| *3 *5))) (|isDomain| *1 (|SplittingNode| *3 *5)) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))))) (|copy| (*1 *1 *1) (AND (|isDomain| *1 (|SplittingNode| *2 *3)) (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))))) (|setValue!| (*1 *1 *1 *2) (AND (|isDomain| *1 (|SplittingNode| *2 *3)) (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))))) (|setCondition!| (*1 *1 *1 *2) (AND (|isDomain| *1 (|SplittingNode| *3 *2)) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|))))) (|setStatus!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SplittingNode| *3 *4)) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|))))) (|setEmpty!| (*1 *1 *1) (AND (|isDomain| *1 (|SplittingNode| *2 *3)) (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))))) (|infLex?| (*1 *2 *1 *1 *3 *4) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *5 *5)) (|isDomain| *4 (|Mapping| (|Boolean|) *6 *6)) (|ofCategory| *5 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *6 (|Join| (|SetCategory|) (|Aggregate|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SplittingNode| *5 *6)))) (|subNode?| (*1 *2 *1 *1 *3) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *5 *5)) (|ofCategory| *5 (|Join| (|SetCategory|) (|Aggregate|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SplittingNode| *4 *5)) (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|)))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |empty| ($)) (SIGNATURE |empty?| ((|Boolean|) $)) (SIGNATURE |value| (|#1| $)) (SIGNATURE |condition| (|#2| $)) (SIGNATURE |status| ((|Boolean|) $)) (SIGNATURE |construct| ($ |#1| |#2| (|Boolean|))) (SIGNATURE |construct| ($ |#1| |#2|)) (SIGNATURE |construct| ($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) (SIGNATURE |construct| ((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))))) (SIGNATURE |construct| ((|List| $) |#1| (|List| |#2|))) (SIGNATURE |copy| ($ $)) (SIGNATURE |setValue!| ($ $ |#1|)) (SIGNATURE |setCondition!| ($ $ |#2|)) (SIGNATURE |setStatus!| ($ $ (|Boolean|))) (SIGNATURE |setEmpty!| ($ $)) (SIGNATURE |infLex?| ((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|))) (SIGNATURE |subNode?| ((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|))))) 
((~= (((|Boolean|) $ $) NIL (|has| (|SplittingNode| |#1| |#2|) (|SetCategory|)))) (|value| (((|SplittingNode| |#1| |#2|) $) 25)) (|updateStatus!| (($ $) 75)) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) 84)) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) 89) (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) 90)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setvalue!| (((|SplittingNode| |#1| |#2|) $ (|SplittingNode| |#1| |#2|)) 42 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| (((|SplittingNode| |#1| |#2|) $ "value" (|SplittingNode| |#1| |#2|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) 40 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) NIL T CONST)) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) 79)) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) 38)) (|remove| (($ (|SplittingNode| |#1| |#2|) $) 30)) (|parts| (((|List| (|SplittingNode| |#1| |#2|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) 50)) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) 81)) (|node?| (((|Boolean|) $ $) NIL (|has| (|SplittingNode| |#1| |#2|) (|SetCategory|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| (|SplittingNode| |#1| |#2|)) $) 54 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|SplittingNode| |#1| |#2|) (|SetCategory|))))) (|map!| (($ (|Mapping| (|SplittingNode| |#1| |#2|) (|SplittingNode| |#1| |#2|)) $) 46 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| (|SplittingNode| |#1| |#2|) (|SplittingNode| |#1| |#2|)) $) 45)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|leaves| (((|List| (|SplittingNode| |#1| |#2|)) $) 52)) (|leaf?| (((|Boolean|) $) 41)) (|latex| (((|String|) $) NIL (|has| (|SplittingNode| |#1| |#2|) (|SetCategory|)))) (|hash| (((|SingleInteger|) $) NIL (|has| (|SplittingNode| |#1| |#2|) (|SetCategory|)))) (|extractSplittingLeaf| (((|Union| $ "failed") $) 74)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) (|SplittingNode| |#1| |#2|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| (|SplittingNode| |#1| |#2|)))) NIL (AND (|has| (|SplittingNode| |#1| |#2|) (|Evalable| (|SplittingNode| |#1| |#2|))) (|has| (|SplittingNode| |#1| |#2|) (|SetCategory|)))) (($ $ (|Equation| (|SplittingNode| |#1| |#2|))) NIL (AND (|has| (|SplittingNode| |#1| |#2|) (|Evalable| (|SplittingNode| |#1| |#2|))) (|has| (|SplittingNode| |#1| |#2|) (|SetCategory|)))) (($ $ (|SplittingNode| |#1| |#2|) (|SplittingNode| |#1| |#2|)) NIL (AND (|has| (|SplittingNode| |#1| |#2|) (|Evalable| (|SplittingNode| |#1| |#2|))) (|has| (|SplittingNode| |#1| |#2|) (|SetCategory|)))) (($ $ (|List| (|SplittingNode| |#1| |#2|)) (|List| (|SplittingNode| |#1| |#2|))) NIL (AND (|has| (|SplittingNode| |#1| |#2|) (|Evalable| (|SplittingNode| |#1| |#2|))) (|has| (|SplittingNode| |#1| |#2|) (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 49)) (|empty?| (((|Boolean|) $) 22)) (|empty| (($) 24)) (|elt| (((|SplittingNode| |#1| |#2|) $ "value") NIL)) (|distance| (((|Integer|) $ $) NIL)) (|cyclic?| (((|Boolean|) $) 43)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|SplittingNode| |#1| |#2|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) (|SplittingNode| |#1| |#2|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|SplittingNode| |#1| |#2|) (|SetCategory|))))) (|copy| (($ $) 48)) (|construct| (($ (|SplittingNode| |#1| |#2|)) 9) (($ |#1| |#2| (|List| $)) 12) (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) 14) (($ |#1| |#2| |#1| (|List| |#2|)) 17)) (|conditions| (((|List| |#2|) $) 80)) (|coerce| (((|OutputForm|) $) 72 (|has| (|SplittingNode| |#1| |#2|) (|SetCategory|)))) (|children| (((|List| $) $) 28)) (|child?| (((|Boolean|) $ $) NIL (|has| (|SplittingNode| |#1| |#2|) (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|SplittingNode| |#1| |#2|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 63 (|has| (|SplittingNode| |#1| |#2|) (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 57 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|SplittingTree| |#1| |#2|) (|Join| (|RecursiveAggregate| (|SplittingNode| |#1| |#2|)) (CATEGORY |domain| (ATTRIBUTE |shallowlyMutable|) (ATTRIBUTE |finiteAggregate|) (SIGNATURE |extractSplittingLeaf| ((|Union| $ "failed") $)) (SIGNATURE |updateStatus!| ($ $)) (SIGNATURE |construct| ($ (|SplittingNode| |#1| |#2|))) (SIGNATURE |construct| ($ |#1| |#2| (|List| $))) (SIGNATURE |construct| ($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|)))) (SIGNATURE |construct| ($ |#1| |#2| |#1| (|List| |#2|))) (SIGNATURE |conditions| ((|List| |#2|) $)) (SIGNATURE |result| ((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $)) (SIGNATURE |nodeOf?| ((|Boolean|) (|SplittingNode| |#1| |#2|) $)) (SIGNATURE |subNodeOf?| ((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|))) (SIGNATURE |remove| ($ (|SplittingNode| |#1| |#2|) $)) (SIGNATURE |remove!| ($ (|SplittingNode| |#1| |#2|) $)) (SIGNATURE |splitNodeOf!| ($ $ $ (|List| (|SplittingNode| |#1| |#2|)))) (SIGNATURE |splitNodeOf!| ($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|))))) (|Join| (|SetCategory|) (|Aggregate|)) (|Join| (|SetCategory|) (|Aggregate|))) (T |SplittingTree|)) 
((|extractSplittingLeaf| (*1 *1 *1) (|partial| AND (|isDomain| *1 (|SplittingTree| *2 *3)) (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))))) (|updateStatus!| (*1 *1 *1) (AND (|isDomain| *1 (|SplittingTree| *2 *3)) (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))))) (|construct| (*1 *1 *2) (AND (|isDomain| *2 (|SplittingNode| *3 *4)) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|))) (|isDomain| *1 (|SplittingTree| *3 *4)))) (|construct| (*1 *1 *2 *3 *4) (AND (|isDomain| *4 (|List| (|SplittingTree| *2 *3))) (|isDomain| *1 (|SplittingTree| *2 *3)) (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))))) (|construct| (*1 *1 *2 *3 *4) (AND (|isDomain| *4 (|List| (|SplittingNode| *2 *3))) (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))) (|isDomain| *1 (|SplittingTree| *2 *3)))) (|construct| (*1 *1 *2 *3 *2 *4) (AND (|isDomain| *4 (|List| *3)) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))) (|isDomain| *1 (|SplittingTree| *2 *3)) (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|))))) (|conditions| (*1 *2 *1) (AND (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|SplittingTree| *3 *4)) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|))))) (|result| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4)))) (|isDomain| *1 (|SplittingTree| *3 *4)) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|))))) (|nodeOf?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|SplittingNode| *4 *5)) (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *5 (|Join| (|SetCategory|) (|Aggregate|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SplittingTree| *4 *5)))) (|subNodeOf?| (*1 *2 *3 *1 *4) (AND (|isDomain| *3 (|SplittingNode| *5 *6)) (|isDomain| *4 (|Mapping| (|Boolean|) *6 *6)) (|ofCategory| *5 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *6 (|Join| (|SetCategory|) (|Aggregate|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SplittingTree| *5 *6)))) (|remove| (*1 *1 *2 *1) (AND (|isDomain| *2 (|SplittingNode| *3 *4)) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|))) (|isDomain| *1 (|SplittingTree| *3 *4)))) (|remove!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|SplittingNode| *3 *4)) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|))) (|isDomain| *1 (|SplittingTree| *3 *4)))) (|splitNodeOf!| (*1 *1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|SplittingNode| *3 *4))) (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|))) (|isDomain| *1 (|SplittingTree| *3 *4)))) (|splitNodeOf!| (*1 *1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| (|SplittingNode| *4 *5))) (|isDomain| *3 (|Mapping| (|Boolean|) *5 *5)) (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|))) (|ofCategory| *5 (|Join| (|SetCategory|) (|Aggregate|))) (|isDomain| *1 (|SplittingTree| *4 *5))))) 
(|Join| (|RecursiveAggregate| (|SplittingNode| |#1| |#2|)) (CATEGORY |domain| (ATTRIBUTE |shallowlyMutable|) (ATTRIBUTE |finiteAggregate|) (SIGNATURE |extractSplittingLeaf| ((|Union| $ "failed") $)) (SIGNATURE |updateStatus!| ($ $)) (SIGNATURE |construct| ($ (|SplittingNode| |#1| |#2|))) (SIGNATURE |construct| ($ |#1| |#2| (|List| $))) (SIGNATURE |construct| ($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|)))) (SIGNATURE |construct| ($ |#1| |#2| |#1| (|List| |#2|))) (SIGNATURE |conditions| ((|List| |#2|) $)) (SIGNATURE |result| ((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $)) (SIGNATURE |nodeOf?| ((|Boolean|) (|SplittingNode| |#1| |#2|) $)) (SIGNATURE |subNodeOf?| ((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|))) (SIGNATURE |remove| ($ (|SplittingNode| |#1| |#2|) $)) (SIGNATURE |remove!| ($ (|SplittingNode| |#1| |#2|) $)) (SIGNATURE |splitNodeOf!| ($ $ $ (|List| (|SplittingNode| |#1| |#2|)))) (SIGNATURE |splitNodeOf!| ($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|transpose| (($ $) NIL)) (|trace| ((|#2| $) NIL)) (|symmetric?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareMatrix| (($ (|Matrix| |#2|)) 45)) (|square?| (((|Boolean|) $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|scalarMatrix| (($ |#2|) 9)) (|sample| (($) NIL T CONST)) (|rowEchelon| (($ $) 58 (|has| |#2| (|EuclideanDomain|)))) (|row| (((|DirectProduct| |#1| |#2|) $ (|Integer|)) 31)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (|has| |#2| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#2| "failed") $) NIL)) (|retract| (((|Integer|) $) NIL (|has| |#2| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) NIL (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#2| $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| |#2|) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) 72)) (|rank| (((|NonNegativeInteger|) $) 60 (|has| |#2| (|IntegralDomain|)))) (|qelt| ((|#2| $ (|Integer|) (|Integer|)) NIL)) (|parts| (((|List| |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|one?| (((|Boolean|) $) NIL)) (|nullity| (((|NonNegativeInteger|) $) 62 (|has| |#2| (|IntegralDomain|)))) (|nullSpace| (((|List| (|DirectProduct| |#1| |#2|)) $) 66 (|has| |#2| (|IntegralDomain|)))) (|nrows| (((|NonNegativeInteger|) $) NIL)) (|ncols| (((|NonNegativeInteger|) $) NIL)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minordet| ((|#2| $) 56 (|has| |#2| (ATTRIBUTE (|commutative| "*"))))) (|minRowIndex| (((|Integer|) $) NIL)) (|minColIndex| (((|Integer|) $) NIL)) (|members| (((|List| |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|maxRowIndex| (((|Integer|) $) NIL)) (|maxColIndex| (((|Integer|) $) NIL)) (|matrix| (($ (|List| (|List| |#2|))) 26)) (|map!| (($ (|Mapping| |#2| |#2|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) NIL) (($ (|Mapping| |#2| |#2|) $) NIL)) (|listOfLists| (((|List| (|List| |#2|)) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL)) (|inverse| (((|Union| $ "failed") $) 69 (|has| |#2| (|Field|)))) (|hash| (((|SingleInteger|) $) NIL)) (|exquo| (((|Union| $ "failed") $ |#2|) NIL (|has| |#2| (|IntegralDomain|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#2|))) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|Equation| |#2|)) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ |#2| |#2|) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|List| |#2|) (|List| |#2|)) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) NIL)) (|elt| ((|#2| $ (|Integer|) (|Integer|) |#2|) NIL) ((|#2| $ (|Integer|) (|Integer|)) NIL)) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) NIL) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|)) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|DifferentialRing|))) (($ $) NIL (|has| |#2| (|DifferentialRing|)))) (|diagonalProduct| ((|#2| $) NIL)) (|diagonalMatrix| (($ (|List| |#2|)) 40)) (|diagonal?| (((|Boolean|) $) NIL)) (|diagonal| (((|DirectProduct| |#1| |#2|) $) NIL)) (|determinant| ((|#2| $) 54 (|has| |#2| (ATTRIBUTE (|commutative| "*"))))) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#2| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) 81 (|has| |#2| (|ConvertibleTo| (|InputForm|))))) (|column| (((|DirectProduct| |#1| |#2|) $ (|Integer|)) 33)) (|coerce| (((|OutputForm|) $) 36) (($ (|Integer|)) NIL) (($ (|Fraction| (|Integer|))) NIL (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|))))) (($ |#2|) NIL) (((|Matrix| |#2|) $) 42)) (|characteristic| (((|NonNegativeInteger|)) 17)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|antisymmetric?| (((|Boolean|) $) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 11 T CONST)) (|One| (($) 14 T CONST)) (D (($ $ (|Mapping| |#2| |#2|)) NIL) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|)) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|DifferentialRing|))) (($ $) NIL (|has| |#2| (|DifferentialRing|)))) (= (((|Boolean|) $ $) NIL)) (/ (($ $ |#2|) NIL (|has| |#2| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 52) (($ $ (|Integer|)) 71 (|has| |#2| (|Field|)))) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ |#2|) NIL) (($ |#2| $) NIL) (((|DirectProduct| |#1| |#2|) $ (|DirectProduct| |#1| |#2|)) 48) (((|DirectProduct| |#1| |#2|) (|DirectProduct| |#1| |#2|) $) 50)) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|SquareMatrix| |#1| |#2|) (|Join| (|SquareMatrixCategory| |#1| |#2| (|DirectProduct| |#1| |#2|) (|DirectProduct| |#1| |#2|)) (|CoercibleTo| (|Matrix| |#2|)) (CATEGORY |domain| (SIGNATURE |transpose| ($ $)) (SIGNATURE |squareMatrix| ($ (|Matrix| |#2|))) (SIGNATURE |coerce| ((|Matrix| |#2|) $)) (IF (|has| |#2| (ATTRIBUTE (|commutative| "*"))) (ATTRIBUTE |central|) |noBranch|) (IF (|has| |#2| (ATTRIBUTE (|commutative| "*"))) (IF (|has| |#2| (ATTRIBUTE |unitsKnown|)) (ATTRIBUTE |unitsKnown|) |noBranch|) |noBranch|) (IF (|has| |#2| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |noBranch|))) (|NonNegativeInteger|) (|Ring|)) (T |SquareMatrix|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|SquareMatrix| *3 *4)) (|ofType| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Ring|)))) (|transpose| (*1 *1 *1) (AND (|isDomain| *1 (|SquareMatrix| *2 *3)) (|ofType| *2 (|NonNegativeInteger|)) (|ofCategory| *3 (|Ring|)))) (|squareMatrix| (*1 *1 *2) (AND (|isDomain| *2 (|Matrix| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|SquareMatrix| *3 *4)) (|ofType| *3 (|NonNegativeInteger|))))) 
(|Join| (|SquareMatrixCategory| |#1| |#2| (|DirectProduct| |#1| |#2|) (|DirectProduct| |#1| |#2|)) (|CoercibleTo| (|Matrix| |#2|)) (CATEGORY |domain| (SIGNATURE |transpose| ($ $)) (SIGNATURE |squareMatrix| ($ (|Matrix| |#2|))) (SIGNATURE |coerce| ((|Matrix| |#2|) $)) (IF (|has| |#2| (ATTRIBUTE (|commutative| "*"))) (ATTRIBUTE |central|) |noBranch|) (IF (|has| |#2| (ATTRIBUTE (|commutative| "*"))) (IF (|has| |#2| (ATTRIBUTE |unitsKnown|)) (ATTRIBUTE |unitsKnown|) |noBranch|) |noBranch|) (IF (|has| |#2| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |noBranch|))) 
((|upperCase| (($ $) 19)) (|trim| (($ $ (|Character|)) 10) (($ $ (|CharacterClass|)) 14)) (|prefix?| (((|Boolean|) $ $) 24)) (|lowerCase| (($ $) 17)) (|elt| (((|Character|) $ (|Integer|) (|Character|)) NIL) (((|Character|) $ (|Integer|)) NIL) (($ $ (|UniversalSegment| (|Integer|))) NIL) (($ $ $) 29)) (|coerce| (($ (|Character|)) 27) (((|OutputForm|) $) NIL))) 
(((|StringAggregate&| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |elt| (|#1| |#1| |#1|)) (SIGNATURE |trim| (|#1| |#1| (|CharacterClass|))) (SIGNATURE |trim| (|#1| |#1| (|Character|))) (SIGNATURE |coerce| (|#1| (|Character|))) (SIGNATURE |prefix?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |upperCase| (|#1| |#1|)) (SIGNATURE |lowerCase| (|#1| |#1|)) (SIGNATURE |elt| (|#1| |#1| (|UniversalSegment| (|Integer|)))) (SIGNATURE |elt| ((|Character|) |#1| (|Integer|))) (SIGNATURE |elt| ((|Character|) |#1| (|Integer|) (|Character|)))) (|StringAggregate|)) (T |StringAggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |elt| (|#1| |#1| |#1|)) (SIGNATURE |trim| (|#1| |#1| (|CharacterClass|))) (SIGNATURE |trim| (|#1| |#1| (|Character|))) (SIGNATURE |coerce| (|#1| (|Character|))) (SIGNATURE |prefix?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |upperCase| (|#1| |#1|)) (SIGNATURE |lowerCase| (|#1| |#1|)) (SIGNATURE |elt| (|#1| |#1| (|UniversalSegment| (|Integer|)))) (SIGNATURE |elt| ((|Character|) |#1| (|Integer|))) (SIGNATURE |elt| ((|Character|) |#1| (|Integer|) (|Character|)))) 
((~= (((|Boolean|) $ $) 18 (|has| (|Character|) (|SetCategory|)))) (|upperCase!| (($ $) 113)) (|upperCase| (($ $) 114)) (|trim| (($ $ (|Character|)) 101) (($ $ (|CharacterClass|)) 100)) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|suffix?| (((|Boolean|) $ $) 111)) (|substring?| (((|Boolean|) $ $ (|Integer|)) 110)) (|split| (((|List| $) $ (|Character|)) 103) (((|List| $) $ (|CharacterClass|)) 102)) (|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) (|Character|) (|Character|)) $) 91) (((|Boolean|) $) 85 (|has| (|Character|) (|OrderedSet|)))) (|sort!| (($ (|Mapping| (|Boolean|) (|Character|) (|Character|)) $) 82 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $) 81 (AND (|has| (|Character|) (|OrderedSet|)) (|has| $ (ATTRIBUTE |shallowlyMutable|))))) (|sort| (($ (|Mapping| (|Boolean|) (|Character|) (|Character|)) $) 92) (($ $) 86 (|has| (|Character|) (|OrderedSet|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setelt| (((|Character|) $ (|Integer|) (|Character|)) 49 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Character|) $ (|UniversalSegment| (|Integer|)) (|Character|)) 53 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select| (($ (|Mapping| (|Boolean|) (|Character|)) $) 70 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) 7 T CONST)) (|rightTrim| (($ $ (|Character|)) 97) (($ $ (|CharacterClass|)) 96)) (|reverse!| (($ $) 83 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) 93)) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) 107)) (|removeDuplicates| (($ $) 73 (AND (|has| (|Character|) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove| (($ (|Character|) $) 72 (AND (|has| (|Character|) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) (|Character|)) $) 69 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| (((|Character|) (|Mapping| (|Character|) (|Character|) (|Character|)) $ (|Character|) (|Character|)) 71 (AND (|has| (|Character|) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|Character|) (|Mapping| (|Character|) (|Character|) (|Character|)) $ (|Character|)) 68 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Character|) (|Mapping| (|Character|) (|Character|) (|Character|)) $) 67 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| (((|Character|) $ (|Integer|) (|Character|)) 50 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| (((|Character|) $ (|Integer|)) 48)) (|prefix?| (((|Boolean|) $ $) 112)) (|position| (((|Integer|) (|Mapping| (|Boolean|) (|Character|)) $) 90) (((|Integer|) (|Character|) $) 89 (|has| (|Character|) (|SetCategory|))) (((|Integer|) (|Character|) $ (|Integer|)) 88 (|has| (|Character|) (|SetCategory|))) (((|Integer|) $ $ (|Integer|)) 106) (((|Integer|) (|CharacterClass|) $ (|Integer|)) 105)) (|parts| (((|List| (|Character|)) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|new| (($ (|NonNegativeInteger|) (|Character|)) 64)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|minIndex| (((|Integer|) $) 40 (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) 80 (|has| (|Character|) (|OrderedSet|)))) (|merge| (($ (|Mapping| (|Boolean|) (|Character|) (|Character|)) $ $) 94) (($ $ $) 87 (|has| (|Character|) (|OrderedSet|)))) (|members| (((|List| (|Character|)) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|Character|) $) 27 (AND (|has| (|Character|) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|maxIndex| (((|Integer|) $) 41 (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) 79 (|has| (|Character|) (|OrderedSet|)))) (|match?| (((|Boolean|) $ $ (|Character|)) 108)) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) 109)) (|map!| (($ (|Mapping| (|Character|) (|Character|)) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| (|Character|) (|Character|)) $) 35) (($ (|Mapping| (|Character|) (|Character|) (|Character|)) $ $) 59)) (|lowerCase!| (($ $) 115)) (|lowerCase| (($ $) 116)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|leftTrim| (($ $ (|Character|)) 99) (($ $ (|CharacterClass|)) 98)) (|latex| (((|String|) $) 22 (|has| (|Character|) (|SetCategory|)))) (|insert| (($ (|Character|) $ (|Integer|)) 55) (($ $ $ (|Integer|)) 54)) (|indices| (((|List| (|Integer|)) $) 43)) (|index?| (((|Boolean|) (|Integer|) $) 44)) (|hash| (((|SingleInteger|) $) 21 (|has| (|Character|) (|SetCategory|)))) (|first| (((|Character|) $) 39 (|has| (|Integer|) (|OrderedSet|)))) (|find| (((|Union| (|Character|) "failed") (|Mapping| (|Boolean|) (|Character|)) $) 66)) (|fill!| (($ $ (|Character|)) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) (|Character|)) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| (|Character|)))) 26 (AND (|has| (|Character|) (|Evalable| (|Character|))) (|has| (|Character|) (|SetCategory|)))) (($ $ (|Equation| (|Character|))) 25 (AND (|has| (|Character|) (|Evalable| (|Character|))) (|has| (|Character|) (|SetCategory|)))) (($ $ (|Character|) (|Character|)) 24 (AND (|has| (|Character|) (|Evalable| (|Character|))) (|has| (|Character|) (|SetCategory|)))) (($ $ (|List| (|Character|)) (|List| (|Character|))) 23 (AND (|has| (|Character|) (|Evalable| (|Character|))) (|has| (|Character|) (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|entry?| (((|Boolean|) (|Character|) $) 42 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Character|) (|SetCategory|))))) (|entries| (((|List| (|Character|)) $) 45)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| (((|Character|) $ (|Integer|) (|Character|)) 47) (((|Character|) $ (|Integer|)) 46) (($ $ (|UniversalSegment| (|Integer|))) 58) (($ $ $) 95)) (|delete| (($ $ (|Integer|)) 57) (($ $ (|UniversalSegment| (|Integer|))) 56)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|Character|)) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) (|Character|) $) 28 (AND (|has| (|Character|) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copyInto!| (($ $ $ (|Integer|)) 84 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) 13)) (|convert| (((|InputForm|) $) 74 (|has| (|Character|) (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| (|Character|))) 65)) (|concat| (($ $ (|Character|)) 63) (($ (|Character|) $) 62) (($ $ $) 61) (($ (|List| $)) 60)) (|coerce| (($ (|Character|)) 104) (((|OutputForm|) $) 20 (|has| (|Character|) (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|Character|)) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (>= (((|Boolean|) $ $) 77 (|has| (|Character|) (|OrderedSet|)))) (> (((|Boolean|) $ $) 76 (|has| (|Character|) (|OrderedSet|)))) (= (((|Boolean|) $ $) 19 (|has| (|Character|) (|SetCategory|)))) (<= (((|Boolean|) $ $) 78 (|has| (|Character|) (|OrderedSet|)))) (< (((|Boolean|) $ $) 75 (|has| (|Character|) (|OrderedSet|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|StringAggregate|) (|Category|)) (T |StringAggregate|)) 
((|lowerCase| (*1 *1 *1) (|ofCategory| *1 (|StringAggregate|))) (|lowerCase!| (*1 *1 *1) (|ofCategory| *1 (|StringAggregate|))) (|upperCase| (*1 *1 *1) (|ofCategory| *1 (|StringAggregate|))) (|upperCase!| (*1 *1 *1) (|ofCategory| *1 (|StringAggregate|))) (|prefix?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|Boolean|)))) (|suffix?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|Boolean|)))) (|substring?| (*1 *2 *1 *1 *3) (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Boolean|)))) (|match| (*1 *2 *1 *1 *3) (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *3 (|Character|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|match?| (*1 *2 *1 *1 *3) (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *3 (|Character|)) (|isDomain| *2 (|Boolean|)))) (|replace| (*1 *1 *1 *2 *1) (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|UniversalSegment| (|Integer|))))) (|position| (*1 *2 *1 *1 *2) (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|Integer|)))) (|position| (*1 *2 *3 *1 *2) (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|Integer|)) (|isDomain| *3 (|CharacterClass|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Character|)) (|ofCategory| *1 (|StringAggregate|)))) (|split| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Character|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|StringAggregate|)))) (|split| (*1 *2 *1 *3) (AND (|isDomain| *3 (|CharacterClass|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|StringAggregate|)))) (|trim| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|Character|)))) (|trim| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|CharacterClass|)))) (|leftTrim| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|Character|)))) (|leftTrim| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|CharacterClass|)))) (|rightTrim| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|Character|)))) (|rightTrim| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|CharacterClass|)))) (|elt| (*1 *1 *1 *1) (|ofCategory| *1 (|StringAggregate|)))) 
(|Join| (|OneDimensionalArrayAggregate| (|Character|)) (CATEGORY |domain| (SIGNATURE |lowerCase| ($ $)) (SIGNATURE |lowerCase!| ($ $)) (SIGNATURE |upperCase| ($ $)) (SIGNATURE |upperCase!| ($ $)) (SIGNATURE |prefix?| ((|Boolean|) $ $)) (SIGNATURE |suffix?| ((|Boolean|) $ $)) (SIGNATURE |substring?| ((|Boolean|) $ $ (|Integer|))) (SIGNATURE |match| ((|NonNegativeInteger|) $ $ (|Character|))) (SIGNATURE |match?| ((|Boolean|) $ $ (|Character|))) (SIGNATURE |replace| ($ $ (|UniversalSegment| (|Integer|)) $)) (SIGNATURE |position| ((|Integer|) $ $ (|Integer|))) (SIGNATURE |position| ((|Integer|) (|CharacterClass|) $ (|Integer|))) (SIGNATURE |coerce| ($ (|Character|))) (SIGNATURE |split| ((|List| $) $ (|Character|))) (SIGNATURE |split| ((|List| $) $ (|CharacterClass|))) (SIGNATURE |trim| ($ $ (|Character|))) (SIGNATURE |trim| ($ $ (|CharacterClass|))) (SIGNATURE |leftTrim| ($ $ (|Character|))) (SIGNATURE |leftTrim| ($ $ (|CharacterClass|))) (SIGNATURE |rightTrim| ($ $ (|Character|))) (SIGNATURE |rightTrim| ($ $ (|CharacterClass|))) (SIGNATURE |elt| ($ $ $)))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| (|Character|) (|SetCategory|)) (|has| (|Character|) (|OrderedSet|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| (|Character|) (|SetCategory|)) (|has| (|Character|) (|OrderedSet|))) ((|Collection| (|Character|)) . T) ((|ConvertibleTo| (|InputForm|)) |has| (|Character|) (|ConvertibleTo| (|InputForm|))) ((|Eltable| (|Integer|) (|Character|)) . T) ((|EltableAggregate| (|Integer|) (|Character|)) . T) ((|Evalable| (|Character|)) AND (|has| (|Character|) (|Evalable| (|Character|))) (|has| (|Character|) (|SetCategory|))) ((|FiniteLinearAggregate| (|Character|)) . T) ((|HomogeneousAggregate| (|Character|)) . T) ((|IndexedAggregate| (|Integer|) (|Character|)) . T) ((|InnerEvalable| (|Character|) (|Character|)) AND (|has| (|Character|) (|Evalable| (|Character|))) (|has| (|Character|) (|SetCategory|))) ((|LinearAggregate| (|Character|)) . T) ((|OneDimensionalArrayAggregate| (|Character|)) . T) ((|OrderedSet|) |has| (|Character|) (|OrderedSet|)) ((|SetCategory|) OR (|has| (|Character|) (|SetCategory|)) (|has| (|Character|) (|OrderedSet|))) ((|Type|) . T)) 
((|upDateBranches| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| |#4|) (|List| |#5|) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) (|NonNegativeInteger|)) 93)) (|transcendentalDecompose| (((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5|) 54) (((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|)) 53)) (|printInfo| (((|Void|) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|NonNegativeInteger|)) 85)) (|numberOfVariables| (((|NonNegativeInteger|) (|List| |#4|) (|List| |#5|)) 27)) (|internalDecompose| (((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5|) 56) (((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|)) 55) (((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|) (|Boolean|)) 57)) (|decompose| (((|List| |#5|) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) 76) (((|List| |#5|) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) 77)) (|convert| (((|String|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) 80)) (|algebraicDecompose| (((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5|) 52)) (|KrullNumber| (((|NonNegativeInteger|) (|List| |#4|) (|List| |#5|)) 19))) 
(((|SquareFreeRegularSetDecompositionPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |KrullNumber| ((|NonNegativeInteger|) (|List| |#4|) (|List| |#5|))) (SIGNATURE |numberOfVariables| ((|NonNegativeInteger|) (|List| |#4|) (|List| |#5|))) (SIGNATURE |algebraicDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5|)) (SIGNATURE |transcendentalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|))) (SIGNATURE |transcendentalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5|)) (SIGNATURE |internalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|) (|Boolean|))) (SIGNATURE |internalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|))) (SIGNATURE |internalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5|)) (SIGNATURE |decompose| ((|List| |#5|) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|))) (SIGNATURE |decompose| ((|List| |#5|) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |upDateBranches| ((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| |#4|) (|List| |#5|) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) (|NonNegativeInteger|))) (SIGNATURE |convert| ((|String|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) (SIGNATURE |printInfo| ((|Void|) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|NonNegativeInteger|)))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|SquareFreeRegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |SquareFreeRegularSetDecompositionPackage|)) 
((|printInfo| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Record| (|:| |val| (|List| *8)) (|:| |tower| *9)))) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *9 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SquareFreeRegularSetDecompositionPackage| *5 *6 *7 *8 *9)))) (|convert| (*1 *2 *3) (AND (|isDomain| *3 (|Record| (|:| |val| (|List| *7)) (|:| |tower| *8))) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *8 (|SquareFreeRegularTriangularSetCategory| *4 *5 *6 *7)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|String|)) (|isDomain| *1 (|SquareFreeRegularSetDecompositionPackage| *4 *5 *6 *7 *8)))) (|upDateBranches| (*1 *2 *3 *4 *2 *5 *6) (AND (|isDomain| *5 (|Record| (|:| |done| (|List| *11)) (|:| |todo| (|List| (|Record| (|:| |val| *3) (|:| |tower| *11)))))) (|isDomain| *6 (|NonNegativeInteger|)) (|isDomain| *2 (|List| (|Record| (|:| |val| (|List| *10)) (|:| |tower| *11)))) (|isDomain| *3 (|List| *10)) (|isDomain| *4 (|List| *11)) (|ofCategory| *10 (|RecursivePolynomialCategory| *7 *8 *9)) (|ofCategory| *11 (|SquareFreeRegularTriangularSetCategory| *7 *8 *9 *10)) (|ofCategory| *7 (|GcdDomain|)) (|ofCategory| *8 (|OrderedAbelianMonoidSup|)) (|ofCategory| *9 (|OrderedSet|)) (|isDomain| *1 (|SquareFreeRegularSetDecompositionPackage| *7 *8 *9 *10 *11)))) (|decompose| (*1 *2 *3 *2 *4 *4 *4 *4 *4) (AND (|isDomain| *2 (|List| *9)) (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *9 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *1 (|SquareFreeRegularSetDecompositionPackage| *5 *6 *7 *8 *9)))) (|decompose| (*1 *2 *3 *2 *4 *4) (AND (|isDomain| *2 (|List| *9)) (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *9 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *1 (|SquareFreeRegularSetDecompositionPackage| *5 *6 *7 *8 *9)))) (|internalDecompose| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Record| (|:| |done| (|List| *4)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4)))))) (|isDomain| *1 (|SquareFreeRegularSetDecompositionPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *3)))) (|internalDecompose| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|NonNegativeInteger|)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8)) (|isDomain| *2 (|Record| (|:| |done| (|List| *4)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4)))))) (|isDomain| *1 (|SquareFreeRegularSetDecompositionPackage| *6 *7 *8 *3 *4)) (|ofCategory| *4 (|SquareFreeRegularTriangularSetCategory| *6 *7 *8 *3)))) (|internalDecompose| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *5 (|NonNegativeInteger|)) (|isDomain| *6 (|Boolean|)) (|ofCategory| *7 (|GcdDomain|)) (|ofCategory| *8 (|OrderedAbelianMonoidSup|)) (|ofCategory| *9 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *7 *8 *9)) (|isDomain| *2 (|Record| (|:| |done| (|List| *4)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4)))))) (|isDomain| *1 (|SquareFreeRegularSetDecompositionPackage| *7 *8 *9 *3 *4)) (|ofCategory| *4 (|SquareFreeRegularTriangularSetCategory| *7 *8 *9 *3)))) (|transcendentalDecompose| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Record| (|:| |done| (|List| *4)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4)))))) (|isDomain| *1 (|SquareFreeRegularSetDecompositionPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *3)))) (|transcendentalDecompose| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|NonNegativeInteger|)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8)) (|isDomain| *2 (|Record| (|:| |done| (|List| *4)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4)))))) (|isDomain| *1 (|SquareFreeRegularSetDecompositionPackage| *6 *7 *8 *3 *4)) (|ofCategory| *4 (|SquareFreeRegularTriangularSetCategory| *6 *7 *8 *3)))) (|algebraicDecompose| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Record| (|:| |done| (|List| *4)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4)))))) (|isDomain| *1 (|SquareFreeRegularSetDecompositionPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *3)))) (|numberOfVariables| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|List| *9)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *9 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|SquareFreeRegularSetDecompositionPackage| *5 *6 *7 *8 *9)))) (|KrullNumber| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|List| *9)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *9 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|SquareFreeRegularSetDecompositionPackage| *5 *6 *7 *8 *9))))) 
(CATEGORY |package| (SIGNATURE |KrullNumber| ((|NonNegativeInteger|) (|List| |#4|) (|List| |#5|))) (SIGNATURE |numberOfVariables| ((|NonNegativeInteger|) (|List| |#4|) (|List| |#5|))) (SIGNATURE |algebraicDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5|)) (SIGNATURE |transcendentalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|))) (SIGNATURE |transcendentalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5|)) (SIGNATURE |internalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|) (|Boolean|))) (SIGNATURE |internalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5| (|NonNegativeInteger|))) (SIGNATURE |internalDecompose| ((|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) |#4| |#5|)) (SIGNATURE |decompose| ((|List| |#5|) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|))) (SIGNATURE |decompose| ((|List| |#5|) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |upDateBranches| ((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| |#4|) (|List| |#5|) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|Record| (|:| |done| (|List| |#5|)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))))) (|NonNegativeInteger|))) (SIGNATURE |convert| ((|String|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) (SIGNATURE |printInfo| ((|Void|) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|NonNegativeInteger|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) NIL)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 109) (((|List| $) (|List| |#4|) (|Boolean|)) 110) (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) 108) (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) 111)) (|variables| (((|List| |#3|) $) NIL)) (|trivialIdeal?| (((|Boolean|) $) NIL)) (|triangular?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|stronglyReduced?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|stronglyReduce| ((|#4| |#4| $) NIL)) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) 83)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|select| (($ (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| |#4| "failed") $ |#3|) 61)) (|sample| (($) NIL T CONST)) (|roughUnitIdeal?| (((|Boolean|) $) 26 (|has| |#1| (|IntegralDomain|)))) (|roughSubIdeal?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|roughEqualIdeals?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|roughBase?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) NIL)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) NIL)) (|retract| (($ (|List| |#4|)) NIL)) (|rest| (((|Union| $ "failed") $) 39)) (|removeZero| ((|#4| |#4| $) 64)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|))))) (|remove| (($ |#4| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|)))) (($ (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 77 (|has| |#1| (|IntegralDomain|)))) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) NIL)) (|reduceByQuasiMonic| ((|#4| |#4| $) NIL)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|)))) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| (|Mapping| |#4| |#4| |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) NIL)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) NIL)) (|purelyTranscendental?| (((|Boolean|) |#4| $) NIL)) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) NIL)) (|purelyAlgebraic?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) 123)) (|parts| (((|List| |#4|) $) 16 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|normalized?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|mvar| ((|#3| $) 33)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#4|) $) 17 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#4| $) 25 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|))))) (|map!| (($ (|Mapping| |#4| |#4|) $) 23 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#4| |#4|) $) 21)) (|mainVariables| (((|List| |#3|) $) NIL)) (|mainVariable?| (((|Boolean|) |#3| $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL)) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) NIL)) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) 102)) (|last| (((|Union| |#4| "failed") $) 37)) (|invertibleSet| (((|List| $) |#4| $) 87)) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) NIL)) (|invertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) 97) (((|Boolean|) |#4| $) 52)) (|intersect| (((|List| $) |#4| $) 106) (((|List| $) (|List| |#4|) $) NIL) (((|List| $) (|List| |#4|) (|List| $)) 107) (((|List| $) |#4| (|List| $)) NIL)) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) 118)) (|internalAugment| (($ |#4| $) 74) (($ (|List| |#4|) $) 75) (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) 73)) (|initials| (((|List| |#4|) $) NIL)) (|initiallyReduced?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|initiallyReduce| ((|#4| |#4| $) NIL)) (|infRittWu?| (((|Boolean|) $ $) NIL)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) NIL (|has| |#1| (|IntegralDomain|)))) (|headReduced?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|headReduce| ((|#4| |#4| $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|first| (((|Union| |#4| "failed") $) 35)) (|find| (((|Union| |#4| "failed") (|Mapping| (|Boolean|) |#4|) $) NIL)) (|extendIfCan| (((|Union| $ "failed") $ |#4|) 47)) (|extend| (($ $ |#4|) NIL) (((|List| $) |#4| $) 89) (((|List| $) |#4| (|List| $)) NIL) (((|List| $) (|List| |#4|) $) NIL) (((|List| $) (|List| |#4|) (|List| $)) 85)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ |#4| |#4|) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|Equation| |#4|)) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|List| (|Equation| |#4|))) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) 15)) (|empty| (($) 13)) (|degree| (((|NonNegativeInteger|) $) NIL)) (|count| (((|NonNegativeInteger|) |#4| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) 12)) (|convert| (((|InputForm|) $) NIL (|has| |#4| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#4|)) 20)) (|collectUpper| (($ $ |#3|) 42)) (|collectUnder| (($ $ |#3|) 43)) (|collectQuasiMonic| (($ $) NIL)) (|collect| (($ $ |#3|) NIL)) (|coerce| (((|OutputForm|) $) 31) (((|List| |#4|) $) 40)) (|coHeight| (((|NonNegativeInteger|) $) NIL (|has| |#3| (|Finite|)))) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) NIL) (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) NIL)) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) NIL)) (|augment| (((|List| $) |#4| $) 53) (((|List| $) |#4| (|List| $)) NIL) (((|List| $) (|List| |#4|) $) NIL) (((|List| $) (|List| |#4|) (|List| $)) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|algebraicVariables| (((|List| |#3|) $) NIL)) (|algebraicCoefficients?| (((|Boolean|) |#4| $) NIL)) (|algebraic?| (((|Boolean|) |#3| $) 60)) (= (((|Boolean|) $ $) NIL)) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|SquareFreeRegularTriangularSet| |#1| |#2| |#3| |#4|) (|Join| (|SquareFreeRegularTriangularSetCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |internalAugment| ((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |zeroSetSplit| ((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|))) (SIGNATURE |zeroSetSplit| ((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |internalZeroSetSplit| ((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |preprocess| ((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|))))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|)) (T |SquareFreeRegularTriangularSet|)) 
((|internalAugment| (*1 *2 *3 *1 *4 *4 *4 *4 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|List| (|SquareFreeRegularTriangularSet| *5 *6 *7 *3))) (|isDomain| *1 (|SquareFreeRegularTriangularSet| *5 *6 *7 *3)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)))) (|zeroSetSplit| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|List| (|SquareFreeRegularTriangularSet| *5 *6 *7 *8))) (|isDomain| *1 (|SquareFreeRegularTriangularSet| *5 *6 *7 *8)))) (|zeroSetSplit| (*1 *2 *3 *4 *4 *4 *4) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|List| (|SquareFreeRegularTriangularSet| *5 *6 *7 *8))) (|isDomain| *1 (|SquareFreeRegularTriangularSet| *5 *6 *7 *8)))) (|internalZeroSetSplit| (*1 *2 *3 *4 *4 *4) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|List| (|SquareFreeRegularTriangularSet| *5 *6 *7 *8))) (|isDomain| *1 (|SquareFreeRegularTriangularSet| *5 *6 *7 *8)))) (|preprocess| (*1 *2 *3 *4 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Record| (|:| |val| (|List| *8)) (|:| |towers| (|List| (|SquareFreeRegularTriangularSet| *5 *6 *7 *8))))) (|isDomain| *1 (|SquareFreeRegularTriangularSet| *5 *6 *7 *8)) (|isDomain| *3 (|List| *8))))) 
(|Join| (|SquareFreeRegularTriangularSetCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |internalAugment| ((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |zeroSetSplit| ((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|))) (SIGNATURE |zeroSetSplit| ((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |internalZeroSetSplit| ((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |preprocess| ((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|))))) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|top| ((|#1| $) 28)) (|stack| (($ (|List| |#1|)) 33)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|sample| (($) NIL T CONST)) (|push!| ((|#1| |#1| $) 30)) (|pop!| ((|#1| $) 26)) (|parts| (((|List| |#1|) $) 34 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 37)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|inspect| ((|#1| $) 29)) (|insert!| (($ |#1| $) 31)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|extract!| ((|#1| $) 27)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) 24)) (|empty| (($) 32)) (|depth| (((|NonNegativeInteger|) $) 22)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) 20)) (|coerce| (((|OutputForm|) $) 17 (|has| |#1| (|SetCategory|)))) (|bag| (($ (|List| |#1|)) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 12 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 23 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|Stack| |#1|) (|Join| (|StackAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |stack| ($ (|List| |#1|))) (SIGNATURE |pop!| (|#1| $)) (SIGNATURE |extract!| (|#1| $)) (SIGNATURE |push!| (|#1| |#1| $)) (SIGNATURE |insert!| ($ |#1| $)) (SIGNATURE |inspect| (|#1| $)) (SIGNATURE |top| (|#1| $)) (SIGNATURE |depth| ((|NonNegativeInteger|) $)) (SIGNATURE |less?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |size?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |bag| ($ (|List| |#1|))) (SIGNATURE |empty?| ((|Boolean|) $)) (SIGNATURE |empty| ($)) (SIGNATURE |sample| ($)) (SIGNATURE |copy| ($ $)) (SIGNATURE |eq?| ((|Boolean|) $ $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (IF (|has| $ (ATTRIBUTE |shallowlyMutable|)) (SIGNATURE |map!| ($ (|Mapping| |#1| |#1|) $)) |noBranch|) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |latex| ((|String|) $)) (SIGNATURE |hash| ((|SingleInteger|) $)) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE = ((|Boolean|) $ $)) (SIGNATURE ~= ((|Boolean|) $ $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (PROGN (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |#| ((|NonNegativeInteger|) $)) (SIGNATURE |parts| ((|List| |#1|) $)) (SIGNATURE |members| ((|List| |#1|) $))) |noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |member?| ((|Boolean|) |#1| $)) (SIGNATURE |count| ((|NonNegativeInteger|) |#1| $))) |noBranch|) |noBranch|))) (|SetCategory|)) (T |Stack|)) 
((|eq?| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Stack| *3)) (|ofCategory| *3 (|SetCategory|)))) (|copy| (*1 *1 *1) (AND (|isDomain| *1 (|Stack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|empty| (*1 *1) (AND (|isDomain| *1 (|Stack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|empty?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Stack| *3)) (|ofCategory| *3 (|SetCategory|)))) (|less?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Stack| *4)) (|ofCategory| *4 (|SetCategory|)))) (|more?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Stack| *4)) (|ofCategory| *4 (|SetCategory|)))) (|size?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Stack| *4)) (|ofCategory| *4 (|SetCategory|)))) (|sample| (*1 *1) (AND (|isDomain| *1 (|Stack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|#| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Stack| *3)) (|ofCategory| *3 (|SetCategory|)))) (|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Stack| *3)))) (|map!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Stack| *3)))) (|any?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Stack| *4)))) (|every?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Stack| *4)))) (|count| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Stack| *4)))) (|parts| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|Stack| *3)) (|ofCategory| *3 (|SetCategory|)))) (|members| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|Stack| *3)) (|ofCategory| *3 (|SetCategory|)))) (|count| (*1 *2 *3 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Stack| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|member?| (*1 *2 *3 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Stack| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|latex| (*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|Stack| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|hash| (*1 *2 *1) (AND (|isDomain| *2 (|SingleInteger|)) (|isDomain| *1 (|Stack| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|Stack| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (= (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Stack| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (~= (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Stack| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|bag| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Stack| *3)))) (|extract!| (*1 *2 *1) (AND (|isDomain| *1 (|Stack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|insert!| (*1 *1 *2 *1) (AND (|isDomain| *1 (|Stack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|inspect| (*1 *2 *1) (AND (|isDomain| *1 (|Stack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|push!| (*1 *2 *2 *1) (AND (|isDomain| *1 (|Stack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|pop!| (*1 *2 *1) (AND (|isDomain| *1 (|Stack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|top| (*1 *2 *1) (AND (|isDomain| *1 (|Stack| *2)) (|ofCategory| *2 (|SetCategory|)))) (|depth| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Stack| *3)) (|ofCategory| *3 (|SetCategory|)))) (|stack| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Stack| *3))))) 
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((|setelt| ((|#2| $ "value" |#2|) NIL) ((|#2| $ "first" |#2|) NIL) (($ $ "rest" $) NIL) ((|#2| $ "last" |#2|) NIL) ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) 43) ((|#2| $ (|Integer|) |#2|) 40)) (|possiblyInfinite?| (((|Boolean|) $) 11)) (|map!| (($ (|Mapping| |#2| |#2|) $) 38)) (|first| ((|#2| $) NIL) (($ $ (|NonNegativeInteger|)) 16)) (|fill!| (($ $ |#2|) 39)) (|explicitlyFinite?| (((|Boolean|) $) 10)) (|elt| ((|#2| $ "value") NIL) ((|#2| $ "first") NIL) (($ $ "rest") NIL) ((|#2| $ "last") NIL) (($ $ (|UniversalSegment| (|Integer|))) 30) ((|#2| $ (|Integer|)) 22) ((|#2| $ (|Integer|) |#2|) NIL)) (|concat!| (($ $ $) 46) (($ $ |#2|) NIL)) (|concat| (($ $ $) 32) (($ |#2| $) NIL) (($ (|List| $)) 35) (($ $ |#2|) NIL))) 
(((|StreamAggregate&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |possiblyInfinite?| ((|Boolean|) |#1|)) (SIGNATURE |explicitlyFinite?| ((|Boolean|) |#1|)) (SIGNATURE |setelt| (|#2| |#1| (|Integer|) |#2|)) (SIGNATURE |elt| (|#2| |#1| (|Integer|) |#2|)) (SIGNATURE |elt| (|#2| |#1| (|Integer|))) (SIGNATURE |fill!| (|#1| |#1| |#2|)) (SIGNATURE |concat| (|#1| |#1| |#2|)) (SIGNATURE |concat| (|#1| (|List| |#1|))) (SIGNATURE |elt| (|#1| |#1| (|UniversalSegment| (|Integer|)))) (SIGNATURE |setelt| (|#2| |#1| (|UniversalSegment| (|Integer|)) |#2|)) (SIGNATURE |setelt| (|#2| |#1| "last" |#2|)) (SIGNATURE |setelt| (|#1| |#1| "rest" |#1|)) (SIGNATURE |setelt| (|#2| |#1| "first" |#2|)) (SIGNATURE |concat!| (|#1| |#1| |#2|)) (SIGNATURE |concat!| (|#1| |#1| |#1|)) (SIGNATURE |elt| (|#2| |#1| "last")) (SIGNATURE |elt| (|#1| |#1| "rest")) (SIGNATURE |first| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |elt| (|#2| |#1| "first")) (SIGNATURE |first| (|#2| |#1|)) (SIGNATURE |concat| (|#1| |#2| |#1|)) (SIGNATURE |concat| (|#1| |#1| |#1|)) (SIGNATURE |setelt| (|#2| |#1| "value" |#2|)) (SIGNATURE |elt| (|#2| |#1| "value")) (SIGNATURE |map!| (|#1| (|Mapping| |#2| |#2|) |#1|))) (|StreamAggregate| |#2|) (|Type|)) (T |StreamAggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |possiblyInfinite?| ((|Boolean|) |#1|)) (SIGNATURE |explicitlyFinite?| ((|Boolean|) |#1|)) (SIGNATURE |setelt| (|#2| |#1| (|Integer|) |#2|)) (SIGNATURE |elt| (|#2| |#1| (|Integer|) |#2|)) (SIGNATURE |elt| (|#2| |#1| (|Integer|))) (SIGNATURE |fill!| (|#1| |#1| |#2|)) (SIGNATURE |concat| (|#1| |#1| |#2|)) (SIGNATURE |concat| (|#1| (|List| |#1|))) (SIGNATURE |elt| (|#1| |#1| (|UniversalSegment| (|Integer|)))) (SIGNATURE |setelt| (|#2| |#1| (|UniversalSegment| (|Integer|)) |#2|)) (SIGNATURE |setelt| (|#2| |#1| "last" |#2|)) (SIGNATURE |setelt| (|#1| |#1| "rest" |#1|)) (SIGNATURE |setelt| (|#2| |#1| "first" |#2|)) (SIGNATURE |concat!| (|#1| |#1| |#2|)) (SIGNATURE |concat!| (|#1| |#1| |#1|)) (SIGNATURE |elt| (|#2| |#1| "last")) (SIGNATURE |elt| (|#1| |#1| "rest")) (SIGNATURE |first| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |elt| (|#2| |#1| "first")) (SIGNATURE |first| (|#2| |#1|)) (SIGNATURE |concat| (|#1| |#2| |#1|)) (SIGNATURE |concat| (|#1| |#1| |#1|)) (SIGNATURE |setelt| (|#2| |#1| "value" |#2|)) (SIGNATURE |elt| (|#2| |#1| "value")) (SIGNATURE |map!| (|#1| (|Mapping| |#2| |#2|) |#1|))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) 45)) (|third| ((|#1| $) 62)) (|tail| (($ $) 64)) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) 94 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|split!| (($ $ (|Integer|)) 49 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setvalue!| ((|#1| $ |#1|) 36 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setrest!| (($ $ $) 53 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setlast!| ((|#1| $ |#1|) 51 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setfirst!| ((|#1| $ |#1|) 55 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ "first" |#1|) 54 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "rest" $) 52 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ "last" |#1|) 50 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) 114 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ (|Integer|) |#1|) 83 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 99 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|second| ((|#1| $) 63)) (|sample| (($) 7 T CONST)) (|rest| (($ $) 70) (($ $ (|NonNegativeInteger|)) 68)) (|removeDuplicates| (($ $) 96 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) 100 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ |#1| $) 97 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $) 102 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 101 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 98 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|qsetelt!| ((|#1| $ (|Integer|) 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(((|StreamAggregate| |#1|) (|Category|) (|Type|)) (T |StreamAggregate|)) 
((|explicitlyFinite?| (*1 *2 *1) (AND (|ofCategory| *1 (|StreamAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|possiblyInfinite?| (*1 *2 *1) (AND (|ofCategory| *1 (|StreamAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|Boolean|))))) 
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(((|SparseTable| |#1| |#2| |#3|) (|TableAggregate| |#1| |#2|) (|SetCategory|) (|SetCategory|) |#2|) (T |SparseTable|)) 
NIL 
(|TableAggregate| |#1| |#2|) 
((~= (((|Boolean|) $ $) 7)) (|nextItem| (((|Union| $ "failed") $) 12)) (|latex| (((|String|) $) 9)) (|init| (($) 13 T CONST)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11)) (= (((|Boolean|) $ $) 6))) 
(((|StepThrough|) (|Category|)) (T |StepThrough|)) 
((|init| (*1 *1) (|ofCategory| *1 (|StepThrough|))) (|nextItem| (*1 *1 *1) (|partial| |ofCategory| *1 (|StepThrough|)))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |init| ($) |constant|) (SIGNATURE |nextItem| ((|Union| $ "failed") $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T)) 
((|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) 17)) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) 13)) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) 20)) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) 15))) 
(((|StreamInfiniteProduct| |#1|) (CATEGORY |package| (SIGNATURE |infiniteProduct| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |evenInfiniteProduct| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |oddInfiniteProduct| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |generalInfiniteProduct| ((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)))) (|Join| (|IntegralDomain|) (|CharacteristicZero|))) (T |StreamInfiniteProduct|)) 
((|generalInfiniteProduct| (*1 *2 *2 *3 *3) (AND (|isDomain| *2 (|Stream| *4)) (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *1 (|StreamInfiniteProduct| *4)))) (|oddInfiniteProduct| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *1 (|StreamInfiniteProduct| *3)))) (|evenInfiniteProduct| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *1 (|StreamInfiniteProduct| *3)))) (|infiniteProduct| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *1 (|StreamInfiniteProduct| *3))))) 
(CATEGORY |package| (SIGNATURE |infiniteProduct| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |evenInfiniteProduct| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |oddInfiniteProduct| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |generalInfiniteProduct| ((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)))) 
((|tensorMap| (((|Stream| |#1|) (|Stream| |#1|) (|Mapping| (|List| |#1|) |#1|)) 16))) 
(((|StreamTensor| |#1|) (CATEGORY |package| (SIGNATURE |tensorMap| ((|Stream| |#1|) (|Stream| |#1|) (|Mapping| (|List| |#1|) |#1|)))) (|Type|)) (T |StreamTensor|)) 
((|tensorMap| (*1 *2 *2 *3) (AND (|isDomain| *2 (|Stream| *4)) (|isDomain| *3 (|Mapping| (|List| *4) *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *1 (|StreamTensor| *4))))) 
(CATEGORY |package| (SIGNATURE |tensorMap| ((|Stream| |#1|) (|Stream| |#1|) (|Mapping| (|List| |#1|) |#1|)))) 
((|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) 15))) 
(((|StreamFunctions1| |#1|) (CATEGORY |package| (SIGNATURE |concat| ((|Stream| |#1|) (|Stream| (|Stream| |#1|))))) (|Type|)) (T |StreamFunctions1|)) 
((|concat| (*1 *2 *3) (AND (|isDomain| *3 (|Stream| (|Stream| *4))) (|isDomain| *2 (|Stream| *4)) (|isDomain| *1 (|StreamFunctions1| *4)) (|ofCategory| *4 (|Type|))))) 
(CATEGORY |package| (SIGNATURE |concat| ((|Stream| |#1|) (|Stream| (|Stream| |#1|))))) 
((|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) 25)) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) 26)) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) 16))) 
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(CATEGORY |package| (SIGNATURE |map| ((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|))) (SIGNATURE |scan| ((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|))) (SIGNATURE |reduce| (|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)))) 
((|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) 21))) 
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((|map| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *8 *6 *7)) (|isDomain| *4 (|Stream| *6)) (|isDomain| *5 (|Stream| *7)) (|ofCategory| *6 (|Type|)) (|ofCategory| *7 (|Type|)) (|ofCategory| *8 (|Type|)) (|isDomain| *2 (|Stream| *8)) (|isDomain| *1 (|StreamFunctions3| *6 *7 *8))))) 
(CATEGORY |package| (SIGNATURE |map| ((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)))) 
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|#1| (|SetCategory|))))) (|copy| (($ $) 41)) (|convert| (((|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#1|)) 50)) (|cons| (($ |#1| $) 94)) (|concat!| (($ $ $) 97 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ |#1|) 98 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|concat| (($ $ $) 75) (($ |#1| $) 42) (($ (|List| $)) 80) (($ $ |#1|) 74)) (|complete| (($ $) 47)) (|coerce| (((|OutputForm|) $) 39 (|has| |#1| (|SetCategory|))) (($ (|List| |#1|)) 108)) (|children| (((|List| $) $) NIL)) (|child?| (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 111 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|Stream| |#1|) (|Join| (|LazyStreamAggregate| |#1|) (CATEGORY |domain| (ATTRIBUTE |shallowlyMutable|) (SIGNATURE |coerce| ($ (|List| |#1|))) (SIGNATURE |repeating| ($ (|List| |#1|))) (IF (|has| |#1| (|SetCategory|)) (SIGNATURE |repeating?| ((|Boolean|) (|List| |#1|) $)) |noBranch|) (SIGNATURE |findCycle| ((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $)) (SIGNATURE |delay| ($ (|Mapping| $))) (SIGNATURE |cons| ($ |#1| $)) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |output| ((|Void|) (|Integer|) $)) (SIGNATURE |showAllElements| ((|OutputForm|) $)) (SIGNATURE |showAll?| ((|Boolean|)))) |noBranch|) (SIGNATURE |setrest!| ($ $ (|Integer|) $)) (SIGNATURE |generate| ($ (|Mapping| |#1|))) (SIGNATURE |generate| ($ (|Mapping| |#1| |#1|) |#1|)) (SIGNATURE |filterWhile| ($ (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |filterUntil| ($ (|Mapping| (|Boolean|) |#1|) $)))) (|Type|)) (T |Stream|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|Stream| *3)))) (|repeating| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|Stream| *3)))) (|repeating?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Stream| *4)))) (|findCycle| (*1 *2 *3 *1) (AND (|isDomain| *2 (|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|)))) (|isDomain| *1 (|Stream| *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *3 (|NonNegativeInteger|)))) (|delay| (*1 *1 *2) (AND (|isDomain| *2 (|Mapping| (|Stream| *3))) (|isDomain| *1 (|Stream| *3)) (|ofCategory| *3 (|Type|)))) (|cons| (*1 *1 *2 *1) (AND (|isDomain| *1 (|Stream| *2)) (|ofCategory| *2 (|Type|)))) (|output| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Stream| *4)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *4 (|Type|)))) (|showAllElements| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|Stream| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|Type|)))) (|showAll?| (*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Stream| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|Type|)))) (|setrest!| (*1 *1 *1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Stream| *3)) (|ofCategory| *3 (|Type|)))) (|generate| (*1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|Stream| *3)))) (|generate| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|Stream| *3)))) (|filterWhile| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|Stream| *3)))) (|filterUntil| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|Stream| *3))))) 
(|Join| (|LazyStreamAggregate| |#1|) (CATEGORY |domain| (ATTRIBUTE |shallowlyMutable|) (SIGNATURE |coerce| ($ (|List| |#1|))) (SIGNATURE |repeating| ($ (|List| |#1|))) (IF (|has| |#1| (|SetCategory|)) (SIGNATURE |repeating?| ((|Boolean|) (|List| |#1|) $)) |noBranch|) (SIGNATURE |findCycle| ((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $)) (SIGNATURE |delay| ($ (|Mapping| $))) (SIGNATURE |cons| ($ |#1| $)) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |output| ((|Void|) (|Integer|) $)) (SIGNATURE |showAllElements| ((|OutputForm|) $)) (SIGNATURE |showAll?| ((|Boolean|)))) |noBranch|) (SIGNATURE |setrest!| ($ $ (|Integer|) $)) (SIGNATURE |generate| ($ (|Mapping| |#1|))) (SIGNATURE |generate| ($ (|Mapping| |#1| |#1|) |#1|)) (SIGNATURE |filterWhile| ($ (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |filterUntil| ($ (|Mapping| (|Boolean|) |#1|) $)))) 
((~= (((|Boolean|) $ $) 18)) (|upperCase!| (($ $) 113)) (|upperCase| (($ $) 114)) (|trim| (($ $ (|Character|)) 101) (($ $ (|CharacterClass|)) 100)) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|suffix?| (((|Boolean|) $ $) 111)) (|substring?| (((|Boolean|) $ $ (|Integer|)) 110)) (|string| (($ (|Integer|)) 118)) (|split| (((|List| $) $ (|Character|)) 103) (((|List| $) $ (|CharacterClass|)) 102)) (|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) (|Character|) (|Character|)) $) 91) (((|Boolean|) $) 85 (|has| (|Character|) (|OrderedSet|)))) (|sort!| (($ (|Mapping| (|Boolean|) (|Character|) (|Character|)) $) 82 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $) 81 (AND (|has| (|Character|) (|OrderedSet|)) (|has| $ (ATTRIBUTE |shallowlyMutable|))))) (|sort| (($ (|Mapping| (|Boolean|) (|Character|) (|Character|)) $) 92) (($ $) 86 (|has| (|Character|) (|OrderedSet|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setelt| (((|Character|) $ 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(|isDomain| *1 (|StreamTaylorSeriesOperations| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *3 (|Integer|)))) (|integers| (*1 *2 *3) (AND (|isDomain| *2 (|Stream| (|Integer|))) (|isDomain| *1 (|StreamTaylorSeriesOperations| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *3 (|Integer|)))) (|monom| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Stream| *3)) (|isDomain| *1 (|StreamTaylorSeriesOperations| *3)) (|ofCategory| *3 (|Ring|)))) (|recip| (*1 *2 *2) (|partial| AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|StreamTaylorSeriesOperations| *3)))) (/ (*1 *2 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|StreamTaylorSeriesOperations| *3)))) (|exquo| (*1 *2 *2 *2) (|partial| AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|StreamTaylorSeriesOperations| *3)))) (* (*1 *2 *2 *3) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|StreamTaylorSeriesOperations| *3)))) (* (*1 *2 *3 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|StreamTaylorSeriesOperations| *3)))) (* (*1 *2 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|StreamTaylorSeriesOperations| *3)))) (- (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|StreamTaylorSeriesOperations| *3)))) (- (*1 *2 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|StreamTaylorSeriesOperations| *3)))) (+ (*1 *2 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))) 
(CATEGORY |package| (SIGNATURE + ((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE - ((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE - ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE * ((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE * ((|Stream| |#1|) |#1| (|Stream| |#1|))) (SIGNATURE * ((|Stream| |#1|) (|Stream| |#1|) |#1|)) (SIGNATURE |exquo| ((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE / ((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |recip| ((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|))) (SIGNATURE |monom| ((|Stream| |#1|) |#1| (|Integer|))) (SIGNATURE |integers| ((|Stream| (|Integer|)) (|Integer|))) (SIGNATURE |oddintegers| ((|Stream| (|Integer|)) (|Integer|))) (SIGNATURE |int| ((|Stream| |#1|) |#1|)) (SIGNATURE |mapmult| ((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |deriv| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |gderiv| ((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|))) (SIGNATURE |coerce| ((|Stream| |#1|) |#1|)) (SIGNATURE |eval| ((|Stream| |#1|) (|Stream| |#1|) |#1|)) (SIGNATURE |compose| ((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |lagrange| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |revert| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |addiag| ((|Stream| |#1|) (|Stream| (|Stream| |#1|)))) (SIGNATURE |lambert| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |oddlambert| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |evenlambert| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |generalLambert| ((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|))) (SIGNATURE |multisect| ((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|))) (SIGNATURE |invmultisect| ((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |integrate| ((|Stream| |#1|) |#1| (|Stream| |#1|))) (SIGNATURE |lazyIntegrate| ((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|)))) (SIGNATURE |nlde| ((|Stream| |#1|) (|Stream| (|Stream| |#1|)))) (SIGNATURE |powern| ((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)))) |noBranch|) (IF (|has| |#1| (|Field|)) (PROGN (SIGNATURE |mapdiv| ((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |lazyGintegrate| ((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|)))) (SIGNATURE |power| ((|Stream| |#1|) |#1| (|Stream| |#1|)))) |noBranch|)) 
((|tanh| (((|Stream| |#1|) (|Stream| |#1|)) 57)) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) 39)) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) 53)) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) 35)) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) 60)) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) 42)) (|log| (((|Stream| |#1|) (|Stream| |#1|)) 31)) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) 27)) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) 61)) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) 43)) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) 58)) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) 40)) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) 55)) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) 37)) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) 65)) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) 47)) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) 63)) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) 45)) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) 68)) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) 50)) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) 69)) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) 51)) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) 67)) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) 49)) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) 66)) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) 48)) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) 33))) 
(((|StreamTranscendentalFunctionsNonCommutative| |#1|) (CATEGORY |package| (SIGNATURE |exp| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |log| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE ** ((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |sin| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |cos| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |tan| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |cot| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |sec| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |csc| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |asin| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acos| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |atan| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acot| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |asec| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acsc| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |sinh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |cosh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |tanh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |coth| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |sech| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |csch| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |asinh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acosh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |atanh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acoth| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |asech| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acsch| ((|Stream| |#1|) (|Stream| |#1|)))) (|Algebra| (|Fraction| (|Integer|)))) (T |StreamTranscendentalFunctionsNonCommutative|)) 
((|acsch| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|asech| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|acoth| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|atanh| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|acosh| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|asinh| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|csch| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|sech| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|coth| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|tanh| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|cosh| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|sinh| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|acsc| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|asec| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|acot| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|atan| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|acos| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|asin| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|csc| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|sec| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|cot| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|tan| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|cos| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|sin| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (** (*1 *2 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|log| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|exp| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3))))) 
(CATEGORY |package| (SIGNATURE |exp| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |log| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE ** ((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |sin| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |cos| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |tan| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |cot| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |sec| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |csc| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |asin| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acos| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |atan| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acot| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |asec| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acsc| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |sinh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |cosh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |tanh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |coth| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |sech| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |csch| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |asinh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acosh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |atanh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acoth| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |asech| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acsch| ((|Stream| |#1|) (|Stream| |#1|)))) 
((|tanh| (((|Stream| |#1|) (|Stream| |#1|)) 100)) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) 64)) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) 96)) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) 97)) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) 53)) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) 54)) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) 102)) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) 71)) (|log| (((|Stream| |#1|) (|Stream| |#1|)) 39)) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) 36)) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) 103)) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) 72)) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) 101)) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) 67)) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) 98)) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) 55)) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) 111)) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) 86)) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) 105)) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) 82)) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) 115)) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) 90)) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) 117)) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) 92)) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) 113)) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) 88)) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) 107)) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) 84)) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) 40))) 
(((|StreamTranscendentalFunctions| |#1|) (CATEGORY |package| (SIGNATURE |exp| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |log| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE ** ((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |sincos| ((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|))) (SIGNATURE |sin| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |cos| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |tan| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |cot| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |sec| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |csc| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |asin| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acos| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |atan| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acot| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |asec| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acsc| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |sinhcosh| ((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|))) (SIGNATURE |sinh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |cosh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |tanh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |coth| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |sech| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |csch| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |asinh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acosh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |atanh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acoth| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |asech| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acsch| ((|Stream| |#1|) (|Stream| |#1|)))) (|Algebra| (|Fraction| (|Integer|)))) (T |StreamTranscendentalFunctions|)) 
((|acsch| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|asech| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|acoth| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|atanh| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|acosh| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|asinh| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|csch| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|sech| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|coth| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|tanh| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|cosh| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|sinh| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|sinhcosh| (*1 *2 *3) (AND (|ofCategory| *4 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |sinh| (|Stream| *4)) (|:| |cosh| (|Stream| *4)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *4)) (|isDomain| *3 (|Stream| *4)))) (|acsc| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|asec| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|acot| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|atan| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|acos| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|asin| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|csc| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|sec| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|cot| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|tan| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|cos| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|sin| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|sincos| (*1 *2 *3) (AND (|ofCategory| *4 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |sin| (|Stream| *4)) (|:| |cos| (|Stream| *4)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *4)) (|isDomain| *3 (|Stream| *4)))) (** (*1 *2 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|log| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|exp| (*1 *2 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3))))) 
(CATEGORY |package| (SIGNATURE |exp| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |log| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE ** ((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |sincos| ((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|))) (SIGNATURE |sin| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |cos| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |tan| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |cot| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |sec| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |csc| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |asin| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acos| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |atan| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acot| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |asec| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acsc| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |sinhcosh| ((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|))) (SIGNATURE |sinh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |cosh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |tanh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |coth| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |sech| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |csch| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |asinh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acosh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |atanh| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acoth| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |asech| ((|Stream| |#1|) (|Stream| |#1|))) (SIGNATURE |acsch| ((|Stream| |#1|) (|Stream| |#1|)))) 
((|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) 35)) (|primitivePart| ((|#2| |#2| |#1|) 19 (|has| |#1| (|EuclideanDomain|))))) 
(((|SubResultantPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |subresultantVector| ((|PrimitiveArray| |#2|) |#2| |#2|)) (IF (|has| |#1| (|EuclideanDomain|)) (SIGNATURE |primitivePart| (|#2| |#2| |#1|)) |noBranch|)) (|IntegralDomain|) (|UnivariatePolynomialCategory| |#1|)) (T |SubResultantPackage|)) 
((|primitivePart| (*1 *2 *2 *3) (AND (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|SubResultantPackage| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|subresultantVector| (*1 *2 *3 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|PrimitiveArray| *3)) (|isDomain| *1 (|SubResultantPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |subresultantVector| ((|PrimitiveArray| |#2|) |#2| |#2|)) (IF (|has| |#1| (|EuclideanDomain|)) (SIGNATURE |primitivePart| (|#2| |#2| |#1|)) |noBranch|)) 
((~= (((|Boolean|) $ $) NIL)) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) 66)) (|subspace| (($) 25)) (|shallowCopy| (($ $) 41)) (|separate| (((|List| $) $) 50)) (|root?| (((|Boolean|) $) 16)) (|pointData| (((|List| (|Point| |#2|)) $) 73)) (|parent| (($ $) 67)) (|numberOfChildren| (((|NonNegativeInteger|) $) 36)) (|new| (($) 24)) (|modifyPoint| (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) 59) (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) 60) (($ $ (|NonNegativeInteger|) (|Point| |#2|)) 62)) (|merge| (($ $ $) 47) (($ (|List| $)) 49)) (|level| (((|NonNegativeInteger|) $) 74)) (|leaf?| (((|Boolean|) $) 15)) (|latex| (((|String|) $) NIL)) (|internal?| (((|Boolean|) $) 17)) (|hash| (((|SingleInteger|) $) NIL)) (|extractProperty| (((|SubSpaceComponentProperty|) $) 72)) (|extractPoint| (((|Point| |#2|) $) 68)) (|extractIndex| (((|NonNegativeInteger|) $) 69)) (|extractClosed| (((|Boolean|) $) 71)) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) 65)) (|deepCopy| (($ $) 42)) (|coerce| (((|OutputForm|) $) 84)) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) 64)) (|children| (((|List| $) $) 11)) (|child| (($ $ (|NonNegativeInteger|)) 35)) (|birth| (($ $) 31)) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) 55)) (|addPoint2| (($ $ (|Point| |#2|)) 54)) (|addPoint| (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) 53) (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) 57) (((|NonNegativeInteger|) $ (|Point| |#2|)) 58)) (= (((|Boolean|) $ $) 78))) 
(((|SubSpace| |#1| |#2|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |leaf?| ((|Boolean|) $)) (SIGNATURE |root?| ((|Boolean|) $)) (SIGNATURE |internal?| ((|Boolean|) $)) (SIGNATURE |new| ($)) (SIGNATURE |subspace| ($)) (SIGNATURE |birth| ($ $)) (SIGNATURE |child| ($ $ (|NonNegativeInteger|))) (SIGNATURE |children| ((|List| $) $)) (SIGNATURE |numberOfChildren| ((|NonNegativeInteger|) $)) (SIGNATURE |shallowCopy| ($ $)) (SIGNATURE |deepCopy| ($ $)) (SIGNATURE |merge| ($ $ $)) (SIGNATURE |merge| ($ (|List| $))) (SIGNATURE |separate| ((|List| $) $)) (SIGNATURE |addPoint| ($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|))) (SIGNATURE |addPoint2| ($ $ (|Point| |#2|))) (SIGNATURE |addPointLast| ($ $ $ (|Point| |#2|) (|NonNegativeInteger|))) (SIGNATURE |modifyPoint| ($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|))) (SIGNATURE |addPoint| ($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|))) (SIGNATURE |modifyPoint| ($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|))) (SIGNATURE |addPoint| ((|NonNegativeInteger|) $ (|Point| |#2|))) (SIGNATURE |modifyPoint| ($ $ (|NonNegativeInteger|) (|Point| |#2|))) (SIGNATURE |closeComponent| ($ $ (|List| (|NonNegativeInteger|)) (|Boolean|))) (SIGNATURE |defineProperty| ($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|))) (SIGNATURE |traverse| ($ $ (|List| (|NonNegativeInteger|)))) (SIGNATURE |extractPoint| ((|Point| |#2|) $)) (SIGNATURE |extractIndex| ((|NonNegativeInteger|) $)) (SIGNATURE |extractClosed| ((|Boolean|) $)) (SIGNATURE |extractProperty| ((|SubSpaceComponentProperty|) $)) (SIGNATURE |level| ((|NonNegativeInteger|) $)) (SIGNATURE |parent| ($ $)) (SIGNATURE |pointData| ((|List| (|Point| |#2|)) $)))) (|PositiveInteger|) (|Ring|)) (T |SubSpace|)) 
((|leaf?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SubSpace| *3 *4)) (|ofType| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Ring|)))) (|root?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SubSpace| *3 *4)) (|ofType| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Ring|)))) (|internal?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SubSpace| *3 *4)) (|ofType| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Ring|)))) (|new| (*1 *1) (AND (|isDomain| *1 (|SubSpace| *2 *3)) (|ofType| *2 (|PositiveInteger|)) (|ofCategory| *3 (|Ring|)))) (|subspace| (*1 *1) (AND (|isDomain| *1 (|SubSpace| *2 *3)) (|ofType| *2 (|PositiveInteger|)) (|ofCategory| *3 (|Ring|)))) (|birth| (*1 *1 *1) (AND (|isDomain| *1 (|SubSpace| *2 *3)) (|ofType| *2 (|PositiveInteger|)) (|ofCategory| *3 (|Ring|)))) (|child| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|SubSpace| *3 *4)) (|ofType| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Ring|)))) (|children| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|SubSpace| *3 *4))) (|isDomain| *1 (|SubSpace| *3 *4)) (|ofType| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Ring|)))) (|numberOfChildren| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|SubSpace| *3 *4)) (|ofType| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Ring|)))) (|shallowCopy| (*1 *1 *1) (AND (|isDomain| *1 (|SubSpace| *2 *3)) (|ofType| *2 (|PositiveInteger|)) (|ofCategory| *3 (|Ring|)))) (|deepCopy| (*1 *1 *1) (AND (|isDomain| *1 (|SubSpace| *2 *3)) (|ofType| *2 (|PositiveInteger|)) (|ofCategory| *3 (|Ring|)))) (|merge| (*1 *1 *1 *1) (AND (|isDomain| *1 (|SubSpace| *2 *3)) (|ofType| *2 (|PositiveInteger|)) (|ofCategory| *3 (|Ring|)))) (|merge| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|SubSpace| *3 *4))) (|isDomain| *1 (|SubSpace| *3 *4)) (|ofType| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Ring|)))) (|separate| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|SubSpace| *3 *4))) (|isDomain| *1 (|SubSpace| *3 *4)) (|ofType| *3 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(((|SparseUnivariateLaurentSeries| |#1| |#2| |#3|) (|Join| (|UnivariateLaurentSeriesConstructorCategory| |#1| (|SparseUnivariateTaylorSeries| |#1| |#2| |#3|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Variable| |#2|))) (SIGNATURE |differentiate| ($ $ (|Variable| |#2|))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ (|Variable| |#2|))) |noBranch|))) (|Ring|) (|Symbol|) |#1|) (T |SparseUnivariateLaurentSeries|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|)) (|isDomain| *1 (|SparseUnivariateLaurentSeries| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3))) (|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|)) (|isDomain| *1 (|SparseUnivariateLaurentSeries| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3))) (|integrate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|)) (|isDomain| *1 (|SparseUnivariateLaurentSeries| *3 *4 *5)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))) 
(|Join| (|UnivariateLaurentSeriesConstructorCategory| |#1| (|SparseUnivariateTaylorSeries| |#1| |#2| |#3|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Variable| |#2|))) (SIGNATURE |differentiate| ($ $ (|Variable| |#2|))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ (|Variable| |#2|))) |noBranch|))) 
((|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) 26) ((|#2| |#2| (|Symbol|)) 28))) 
(((|FunctionSpaceSum| |#1| |#2|) (CATEGORY |package| (SIGNATURE |sum| (|#2| |#2| (|Symbol|))) (SIGNATURE |sum| (|#2| |#2| (|SegmentBinding| |#2|)))) (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|))) (|Join| (|FunctionSpace| |#1|) (|CombinatorialOpsCategory|) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|))) (T |FunctionSpaceSum|)) 
((|sum| (*1 *2 *2 *3) (AND (|isDomain| *3 (|SegmentBinding| *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *4) (|CombinatorialOpsCategory|) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|))) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|FunctionSpaceSum| *4 *2)))) (|sum| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|FunctionSpaceSum| *4 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *4) (|CombinatorialOpsCategory|) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|)))))) 
(CATEGORY |package| (SIGNATURE |sum| (|#2| |#2| (|Symbol|))) (SIGNATURE |sum| (|#2| |#2| (|SegmentBinding| |#2|)))) 
((|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) 30) (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) 44) (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) 32) (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) 36))) 
(((|RationalFunctionSum| |#1|) (CATEGORY |package| (SIGNATURE |sum| ((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|))) (SIGNATURE |sum| ((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |sum| ((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|)))) (SIGNATURE |sum| ((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))))) (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (T |RationalFunctionSum|)) 
((|sum| (*1 *2 *3 *4) (AND (|isDomain| *4 (|SegmentBinding| (|Fraction| (|Polynomial| *5)))) (|isDomain| *3 (|Fraction| (|Polynomial| *5))) (|ofCategory| *5 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Union| *3 (|Expression| *5))) (|isDomain| *1 (|RationalFunctionSum| *5)))) (|sum| (*1 *2 *3 *4) (AND (|isDomain| *4 (|SegmentBinding| (|Polynomial| *5))) (|isDomain| *3 (|Polynomial| *5)) (|ofCategory| *5 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Fraction| *3)) (|isDomain| *1 (|RationalFunctionSum| *5)))) (|sum| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Union| (|Fraction| (|Polynomial| *5)) (|Expression| *5))) (|isDomain| *1 (|RationalFunctionSum| *5)) (|isDomain| *3 (|Fraction| (|Polynomial| *5))))) (|sum| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Fraction| (|Polynomial| *5))) (|isDomain| *1 (|RationalFunctionSum| *5)) (|isDomain| *3 (|Polynomial| *5))))) 
(CATEGORY |package| (SIGNATURE |sum| ((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|))) (SIGNATURE |sum| ((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |sum| ((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|)))) (SIGNATURE |sum| ((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))))) 
((|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) 13))) 
(((|SparseUnivariatePolynomialFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)))) (|Ring|) (|Ring|)) (T |SparseUnivariatePolynomialFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|SparseUnivariatePolynomial| *5)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|Ring|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *6)) (|isDomain| *1 (|SparseUnivariatePolynomialFunctions2| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |map| ((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) NIL)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) NIL)) (|unvectorise| (($ (|Vector| |#1|)) NIL)) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) NIL)) (|univariate| (((|SparseUnivariatePolynomial| $) $ (|SingletonAsOrderedSet|)) NIL) (((|SparseUnivariatePolynomial| |#1|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|totalDegree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|List| (|SingletonAsOrderedSet|))) NIL)) (|tanh| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|tan| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|subResultantGcd| (($ $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL (|has| |#1| (|GcdDomain|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#1| (|GcdDomain|)))) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|sizeLess?| (((|Boolean|) $ $) NIL (|has| |#1| (|Field|)))) (|sinh| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|sin| (($ $) 22 (|has| |#1| (|TranscendentalFunctionCategory|)))) (|shiftRight| (($ $ (|NonNegativeInteger|)) NIL)) (|shiftLeft| (($ $ (|NonNegativeInteger|)) NIL)) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) NIL (|has| |#1| (|GcdDomain|)))) (|sech| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|sec| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|SingletonAsOrderedSet|) "failed") $) NIL)) (|retract| ((|#1| $) NIL) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|SingletonAsOrderedSet|) $) NIL)) (|resultant| (($ $ $ (|SingletonAsOrderedSet|)) NIL (|has| |#1| (|CommutativeRing|))) ((|#1| $ $) NIL (|has| |#1| (|CommutativeRing|)))) (|rem| (($ $ $) NIL (|has| |#1| (|Field|)))) (|reductum| (($ $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| |#1|) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|quo| (($ $ $) NIL (|has| |#1| (|Field|)))) (|pseudoRemainder| (($ $ $) NIL)) (|pseudoQuotient| (($ $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL (|has| |#1| (|Field|)))) (|primitivePart| (($ $) NIL (|has| |#1| (|GcdDomain|))) (($ $ (|SingletonAsOrderedSet|)) NIL (|has| |#1| (|GcdDomain|)))) (|primitiveMonomials| (((|List| $) $) NIL)) (|prime?| (((|Boolean|) $) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|pomopo!| (($ $ |#1| (|NonNegativeInteger|) $) NIL)) (|pi| (($) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (AND (|has| (|SingletonAsOrderedSet|) (|PatternMatchable| (|Float|))) (|has| |#1| (|PatternMatchable| (|Float|))))) (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (AND (|has| (|SingletonAsOrderedSet|) (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Integer|)))))) (|order| (((|NonNegativeInteger|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|one?| (((|Boolean|) $) NIL)) (|numberOfMonomials| (((|NonNegativeInteger|) $) NIL)) (|nextItem| (((|Union| $ "failed") $) NIL (|has| |#1| (|StepThrough|)))) (|multivariate| (($ (|SparseUnivariatePolynomial| |#1|) (|SingletonAsOrderedSet|)) NIL) (($ (|SparseUnivariatePolynomial| $) (|SingletonAsOrderedSet|)) NIL)) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) (|monomials| (((|List| $) $) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monomial| (($ |#1| (|NonNegativeInteger|)) NIL) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ (|SingletonAsOrderedSet|)) NIL) (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|minimumDegree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|SingletonAsOrderedSet|)) NIL) (((|List| (|NonNegativeInteger|)) $ (|List| (|SingletonAsOrderedSet|))) NIL)) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|mapExponents| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) NIL)) (|mainVariable| (((|Union| (|SingletonAsOrderedSet|) "failed") $) NIL)) (|log| (($ $) 18 (|has| |#1| (|TranscendentalFunctionCategory|)))) (|leadingMonomial| (($ $) NIL)) (|leadingCoefficient| ((|#1| $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| |#1| (|GcdDomain|)))) (|lcm| (($ (|List| $)) NIL (|has| |#1| (|GcdDomain|))) (($ $ $) NIL (|has| |#1| (|GcdDomain|)))) (|latex| (((|String|) $) NIL)) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) NIL)) (|isTimes| (((|Union| (|List| $) "failed") $) NIL)) (|isPlus| (((|Union| (|List| $) "failed") $) NIL)) (|isExpt| (((|Union| (|Record| (|:| |var| (|SingletonAsOrderedSet|)) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) NIL)) (|integrate| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|init| (($) NIL (|has| |#1| (|StepThrough|)) CONST)) (|hash| (((|SingleInteger|) $) NIL)) (|ground?| (((|Boolean|) $) 8)) (|ground| ((|#1| $) 9)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|GcdDomain|)))) (|gcd| (($ (|List| $)) NIL (|has| |#1| (|GcdDomain|))) (($ $ $) NIL (|has| |#1| (|GcdDomain|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL (|has| |#1| (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|exquo| (((|Union| $ "failed") $ |#1|) NIL (|has| |#1| (|IntegralDomain|))) (((|Union| $ "failed") $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) (|exp| (($ $) 20 (|has| |#1| (|TranscendentalFunctionCategory|)))) (|eval| (($ $ (|List| (|Equation| $))) NIL) (($ $ (|Equation| $)) NIL) (($ $ $ $) NIL) (($ $ (|List| $) (|List| $)) NIL) (($ $ (|SingletonAsOrderedSet|) |#1|) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| |#1|)) NIL) (($ $ (|SingletonAsOrderedSet|) $) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| $)) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|Field|)))) (|elt| ((|#1| $ |#1|) NIL) (($ $ $) NIL) (((|Fraction| $) (|Fraction| $) (|Fraction| $)) NIL (|has| |#1| (|IntegralDomain|))) ((|#1| (|Fraction| $) |#1|) NIL (|has| |#1| (|Field|))) (((|Fraction| $) $ (|Fraction| $)) NIL (|has| |#1| (|IntegralDomain|)))) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|Field|)))) (|discriminant| (($ $ (|SingletonAsOrderedSet|)) NIL (|has| |#1| (|CommutativeRing|))) ((|#1| $) NIL (|has| |#1| (|CommutativeRing|)))) (|differentiate| (($ $ (|SingletonAsOrderedSet|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|))) NIL) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL) (($ $ (|Symbol|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#1| |#1|)) NIL) (($ $ (|Mapping| |#1| |#1|) $) NIL)) (|degree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|SingletonAsOrderedSet|)) NIL) (((|List| (|NonNegativeInteger|)) $ (|List| (|SingletonAsOrderedSet|))) NIL)) (|csch| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|csc| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|coth| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|cot| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|cosh| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|cos| (($ $) 26 (|has| |#1| (|TranscendentalFunctionCategory|)))) (|convert| (((|Pattern| (|Float|)) $) NIL (AND (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))))) (((|Pattern| (|Integer|)) $) NIL (AND (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))))) (((|InputForm|) $) NIL (AND (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|InputForm|))) (|has| |#1| (|ConvertibleTo| (|InputForm|)))))) (|content| ((|#1| $) NIL (|has| |#1| (|GcdDomain|))) (($ $ (|SingletonAsOrderedSet|)) NIL (|has| |#1| (|GcdDomain|)))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))))) (|composite| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|IntegralDomain|))) (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) NIL (|has| |#1| (|IntegralDomain|)))) (|coerce| (((|OutputForm|) $) 13) (($ (|Integer|)) NIL) (($ |#1|) 11) (($ (|SingletonAsOrderedSet|)) NIL) (($ (|Fraction| (|Integer|))) NIL (OR (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))))) (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|coefficients| (((|List| |#1|) $) NIL)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) NIL) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|CommutativeRing|)))) (|atanh| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|atan| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|associates?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|asinh| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|asin| (($ $) 24 (|has| |#1| (|TranscendentalFunctionCategory|)))) (|asech| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|asec| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|acsch| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|acsc| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|acoth| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|acot| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|acosh| (($ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (|acos| (($ $) 28 (|has| |#1| (|TranscendentalFunctionCategory|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|One| (($) NIL T CONST)) (D (($ $ (|SingletonAsOrderedSet|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|))) NIL) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL) (($ $ (|Symbol|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#1| |#1|)) NIL)) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (/ (($ $ |#1|) NIL (|has| |#1| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ $) NIL (|has| |#1| (|TranscendentalFunctionCategory|)))) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ |#1| $) NIL) (($ $ |#1|) NIL))) 
(((|SparseUnivariatePolynomialExpressions| |#1|) (|Join| (|UnivariatePolynomialCategory| |#1|) (CATEGORY |package| (IF (|has| |#1| (|TranscendentalFunctionCategory|)) (ATTRIBUTE (|TranscendentalFunctionCategory|)) |noBranch|))) (|Ring|)) (T |SparseUnivariatePolynomialExpressions|)) 
NIL 
(|Join| (|UnivariatePolynomialCategory| |#1|) (CATEGORY |package| (IF (|has| |#1| (|TranscendentalFunctionCategory|)) (ATTRIBUTE (|TranscendentalFunctionCategory|)) |noBranch|))) 
((|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) 50)) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) 51))) 
(((|SupFractionFactorizer| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|)))) (SIGNATURE |squareFree| ((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|GcdDomain|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |SupFractionFactorizer|)) 
((|squareFree| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| (|Fraction| *7)))) (|isDomain| *1 (|SupFractionFactorizer| *4 *5 *6 *7)) (|isDomain| *3 (|SparseUnivariatePolynomial| (|Fraction| *7))))) (|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| (|Fraction| *7)))) (|isDomain| *1 (|SupFractionFactorizer| *4 *5 *6 *7)) (|isDomain| *3 (|SparseUnivariatePolynomial| (|Fraction| *7)))))) 
(CATEGORY |package| (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|)))) (SIGNATURE |squareFree| ((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 30)) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) NIL)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) NIL)) (|unvectorise| (($ (|Vector| |#1|)) NIL)) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) NIL)) (|univariate| (((|SparseUnivariatePolynomial| $) $ (|SingletonAsOrderedSet|)) 59) (((|SparseUnivariatePolynomial| |#1|) $) 48)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) 132 (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|totalDegree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|List| (|SingletonAsOrderedSet|))) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|subResultantGcd| (($ $ $) 126 (|has| |#1| (|IntegralDomain|)))) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 72 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL (|has| |#1| (|GcdDomain|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#1| (|GcdDomain|)))) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 92 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|sizeLess?| (((|Boolean|) $ $) NIL (|has| |#1| (|Field|)))) (|shiftRight| (($ $ (|NonNegativeInteger|)) 42)) (|shiftLeft| (($ $ (|NonNegativeInteger|)) 43)) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) NIL (|has| |#1| (|GcdDomain|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|SingletonAsOrderedSet|) "failed") $) NIL)) (|retract| ((|#1| $) NIL) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|SingletonAsOrderedSet|) $) NIL)) (|resultant| (($ $ $ (|SingletonAsOrderedSet|)) NIL (|has| |#1| (|CommutativeRing|))) ((|#1| $ $) 128 (|has| |#1| (|CommutativeRing|)))) (|rem| (($ $ $) NIL (|has| |#1| (|Field|)))) (|reductum| (($ $) 57)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| |#1|) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|quo| (($ $ $) NIL (|has| |#1| (|Field|)))) (|pseudoRemainder| (($ $ $) 104)) (|pseudoQuotient| (($ $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL (|has| |#1| (|Field|)))) (|primitivePart| (($ $) 133 (|has| |#1| (|GcdDomain|))) (($ $ (|SingletonAsOrderedSet|)) NIL (|has| |#1| (|GcdDomain|)))) (|primitiveMonomials| (((|List| $) $) NIL)) (|prime?| (((|Boolean|) $) NIL (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|pomopo!| (($ $ |#1| (|NonNegativeInteger|) $) 46)) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (AND (|has| (|SingletonAsOrderedSet|) (|PatternMatchable| (|Float|))) (|has| |#1| (|PatternMatchable| (|Float|))))) (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (AND (|has| (|SingletonAsOrderedSet|) (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Integer|)))))) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) 117)) (|order| (((|NonNegativeInteger|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|one?| (((|Boolean|) $) 32)) (|numberOfMonomials| (((|NonNegativeInteger|) $) NIL)) (|nextItem| (((|Union| $ "failed") $) NIL (|has| |#1| (|StepThrough|)))) (|multivariate| (($ (|SparseUnivariatePolynomial| |#1|) (|SingletonAsOrderedSet|)) 50) (($ (|SparseUnivariatePolynomial| $) (|SingletonAsOrderedSet|)) 66)) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) 34)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) (|monomials| (((|List| $) $) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monomial| (($ |#1| (|NonNegativeInteger|)) 64) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ (|SingletonAsOrderedSet|)) NIL) (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 121)) (|minimumDegree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|SingletonAsOrderedSet|)) NIL) (((|List| (|NonNegativeInteger|)) $ (|List| (|SingletonAsOrderedSet|))) NIL)) (|min| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#1| (|OrderedSet|)))) (|mapExponents| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) NIL)) (|mainVariable| (((|Union| (|SingletonAsOrderedSet|) "failed") $) NIL)) (|leadingMonomial| (($ $) NIL)) (|leadingCoefficient| ((|#1| $) 53)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| |#1| (|GcdDomain|)))) (|lcm| (($ (|List| $)) NIL (|has| |#1| (|GcdDomain|))) (($ $ $) NIL (|has| |#1| (|GcdDomain|)))) (|latex| (((|String|) $) NIL)) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) 41)) (|isTimes| (((|Union| (|List| $) "failed") $) NIL)) (|isPlus| (((|Union| (|List| $) "failed") $) NIL)) (|isExpt| (((|Union| (|Record| (|:| |var| (|SingletonAsOrderedSet|)) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) NIL)) (|integrate| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|init| (($) NIL (|has| |#1| (|StepThrough|)) CONST)) (|hash| (((|SingleInteger|) $) NIL)) (|ground?| (((|Boolean|) $) 33)) (|ground| ((|#1| $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 80 (|has| |#1| (|GcdDomain|)))) (|gcd| (($ (|List| $)) NIL (|has| |#1| (|GcdDomain|))) (($ $ $) 135 (|has| |#1| (|GcdDomain|)))) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) 99)) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 78 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 77 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) 85 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL (|has| |#1| (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|exquo| (((|Union| $ "failed") $ |#1|) 131 (|has| |#1| (|IntegralDomain|))) (((|Union| $ "failed") $ $) 100 (|has| |#1| (|IntegralDomain|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) (|eval| (($ $ (|List| (|Equation| $))) NIL) (($ $ (|Equation| $)) NIL) (($ $ $ $) NIL) (($ $ (|List| $) (|List| $)) NIL) (($ $ (|SingletonAsOrderedSet|) |#1|) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| |#1|)) NIL) (($ $ (|SingletonAsOrderedSet|) $) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| $)) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|Field|)))) (|elt| ((|#1| $ |#1|) 119) (($ $ $) 120) (((|Fraction| $) (|Fraction| $) (|Fraction| $)) NIL (|has| |#1| (|IntegralDomain|))) ((|#1| (|Fraction| $) |#1|) NIL (|has| |#1| (|Field|))) (((|Fraction| $) $ (|Fraction| $)) NIL (|has| |#1| (|IntegralDomain|)))) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) 37)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 137 (|has| |#1| (|Field|)))) (|discriminant| (($ $ (|SingletonAsOrderedSet|)) NIL (|has| |#1| (|CommutativeRing|))) ((|#1| $) 124 (|has| |#1| (|CommutativeRing|)))) (|differentiate| (($ $ (|SingletonAsOrderedSet|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|))) NIL) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL) (($ $ (|Symbol|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#1| |#1|)) NIL) (($ $ (|Mapping| |#1| |#1|) $) NIL)) (|degree| (((|NonNegativeInteger|) $) 55) (((|NonNegativeInteger|) $ (|SingletonAsOrderedSet|)) NIL) (((|List| (|NonNegativeInteger|)) $ (|List| (|SingletonAsOrderedSet|))) NIL)) (|convert| (((|Pattern| (|Float|)) $) NIL (AND (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))))) (((|Pattern| (|Integer|)) $) NIL (AND (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))))) (((|InputForm|) $) NIL (AND (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|InputForm|))) (|has| |#1| (|ConvertibleTo| (|InputForm|)))))) (|content| ((|#1| $) 130 (|has| |#1| (|GcdDomain|))) (($ $ (|SingletonAsOrderedSet|)) NIL (|has| |#1| (|GcdDomain|)))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))))) (|composite| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|IntegralDomain|))) (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) NIL (|has| |#1| (|IntegralDomain|)))) (|coerce| (((|OutputForm|) $) 118) (($ (|Integer|)) NIL) (($ |#1|) 54) (($ (|SingletonAsOrderedSet|)) NIL) (($ (|Fraction| (|Integer|))) NIL (OR (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))))) (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|coefficients| (((|List| |#1|) $) NIL)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) NIL) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL)) (|charthRoot| (((|Union| $ "failed") $) NIL (OR (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) 28 (|has| |#1| (|CommutativeRing|)))) (|associates?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) 15) (($ $ (|NonNegativeInteger|)) 16)) (|Zero| (($) 17 T CONST)) (|One| (($) 18 T CONST)) (D (($ $ (|SingletonAsOrderedSet|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|))) NIL) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL) (($ $ (|Symbol|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#1| |#1|)) NIL)) (>= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) 97)) (<= (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#1| (|OrderedSet|)))) (/ (($ $ |#1|) 138 (|has| |#1| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) 67)) (** (($ $ (|PositiveInteger|)) 14) (($ $ (|NonNegativeInteger|)) 12)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 27) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ |#1| $) 102) (($ $ |#1|) NIL))) 
(((|SparseUnivariatePolynomial| |#1|) (|Join| (|UnivariatePolynomialCategory| |#1|) (CATEGORY |domain| (SIGNATURE |outputForm| ((|OutputForm|) $ (|OutputForm|))) (SIGNATURE |fmecg| ($ $ (|NonNegativeInteger|) |#1| $)))) (|Ring|)) (T |SparseUnivariatePolynomial|)) 
((|outputForm| (*1 *2 *1 *2) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|SparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|Ring|)))) (|fmecg| (*1 *1 *1 *2 *3 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|SparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|Ring|))))) 
(|Join| (|UnivariatePolynomialCategory| |#1|) (CATEGORY |domain| (SIGNATURE |outputForm| ((|OutputForm|) $ (|OutputForm|))) (SIGNATURE |fmecg| ($ $ (|NonNegativeInteger|) |#1| $)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) NIL)) (|variable| (((|Symbol|) $) 11)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|truncate| (($ $ (|Fraction| (|Integer|))) NIL) (($ $ (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) NIL)) (|terms| (((|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|))) $) NIL)) (|tanh| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|tan| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL (|has| |#1| (|Field|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#1| (|Field|)))) (|sqrt| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sizeLess?| 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(((|Symbol|) (|Join| (|OrderedSet|) (|ConvertibleTo| (|InputForm|)) (|OpenMath|) (|ConvertibleTo| (|Symbol|)) (|ConvertibleTo| (|Pattern| (|Integer|))) (|ConvertibleTo| (|Pattern| (|Float|))) (|PatternMatchable| (|Integer|)) (|PatternMatchable| (|Float|)) (CATEGORY |domain| (SIGNATURE |new| ($)) (SIGNATURE |new| ($ $)) (SIGNATURE |resetNew| ((|Void|))) (SIGNATURE |coerce| ($ (|String|))) (SIGNATURE |name| ($ $)) (SIGNATURE |scripted?| ((|Boolean|) $)) (SIGNATURE |scripts| ((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $)) (SIGNATURE |script| ($ $ (|List| (|List| (|OutputForm|))))) (SIGNATURE |script| ($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))))) (SIGNATURE |subscript| ($ $ (|List| (|OutputForm|)))) (SIGNATURE |superscript| ($ $ (|List| (|OutputForm|)))) (SIGNATURE |argscript| ($ $ (|List| (|OutputForm|)))) (SIGNATURE |elt| ($ $ (|List| (|OutputForm|)))) (SIGNATURE |string| ((|String|) $)) (SIGNATURE |list| ((|List| $) $)) (SIGNATURE |sample| ($) |constant|)))) (T |Symbol|)) 
((|new| (*1 *1) (|isDomain| *1 (|Symbol|))) (|new| (*1 *1 *1) (|isDomain| *1 (|Symbol|))) (|resetNew| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Symbol|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|Symbol|)))) (|name| (*1 *1 *1) (|isDomain| *1 (|Symbol|))) (|scripted?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Symbol|)))) (|scripts| (*1 *2 *1) (AND (|isDomain| *2 (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) (|isDomain| *1 (|Symbol|)))) (|script| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|List| (|OutputForm|)))) (|isDomain| *1 (|Symbol|)))) (|script| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) (|isDomain| *1 (|Symbol|)))) (|subscript| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|Symbol|)))) (|superscript| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|Symbol|)))) (|argscript| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|Symbol|)))) (|elt| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|Symbol|)))) (|string| (*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|Symbol|)))) (|list| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *1 (|Symbol|)))) (|sample| (*1 *1) (|isDomain| *1 (|Symbol|)))) 
(|Join| (|OrderedSet|) (|ConvertibleTo| (|InputForm|)) (|OpenMath|) (|ConvertibleTo| (|Symbol|)) (|ConvertibleTo| (|Pattern| (|Integer|))) (|ConvertibleTo| (|Pattern| (|Float|))) (|PatternMatchable| (|Integer|)) (|PatternMatchable| (|Float|)) (CATEGORY |domain| (SIGNATURE |new| ($)) (SIGNATURE |new| ($ $)) (SIGNATURE |resetNew| ((|Void|))) (SIGNATURE |coerce| ($ (|String|))) (SIGNATURE |name| ($ $)) (SIGNATURE |scripted?| ((|Boolean|) $)) (SIGNATURE |scripts| ((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $)) (SIGNATURE |script| ($ $ (|List| (|List| (|OutputForm|))))) (SIGNATURE |script| ($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))))) (SIGNATURE |subscript| ($ $ (|List| (|OutputForm|)))) (SIGNATURE |superscript| ($ $ (|List| (|OutputForm|)))) (SIGNATURE |argscript| ($ $ (|List| (|OutputForm|)))) (SIGNATURE |elt| ($ $ (|List| (|OutputForm|)))) (SIGNATURE |string| ((|String|) $)) (SIGNATURE |list| ((|List| $) $)) (SIGNATURE |sample| ($) |constant|))) 
((|symFunc| (((|Vector| |#1|) |#1| (|PositiveInteger|)) 16) (((|Vector| |#1|) (|List| |#1|)) 20))) 
(((|SymmetricFunctions| |#1|) (CATEGORY |package| (SIGNATURE |symFunc| ((|Vector| |#1|) (|List| |#1|))) (SIGNATURE |symFunc| ((|Vector| |#1|) |#1| (|PositiveInteger|)))) (|Ring|)) (T |SymmetricFunctions|)) 
((|symFunc| (*1 *2 *3 *4) (AND (|isDomain| *4 (|PositiveInteger|)) (|isDomain| *2 (|Vector| *3)) (|isDomain| *1 (|SymmetricFunctions| *3)) (|ofCategory| *3 (|Ring|)))) (|symFunc| (*1 *2 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Vector| *4)) (|isDomain| *1 (|SymmetricFunctions| *4))))) 
(CATEGORY |package| (SIGNATURE |symFunc| ((|Vector| |#1|) (|List| |#1|))) (SIGNATURE |symFunc| ((|Vector| |#1|) |#1| (|PositiveInteger|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|Integer|) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| |#1| "failed") $) NIL)) (|retract| (((|Integer|) $) NIL (|has| |#1| (|RetractableTo| (|Integer|)))) (((|Fraction| (|Integer|)) $) NIL (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|#1| $) NIL)) (|reductum| (($ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|primitivePart| (($ $) NIL (|has| |#1| (|GcdDomain|)))) (|pomopo!| (($ $ |#1| (|Partition|) $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|numberOfMonomials| (((|NonNegativeInteger|) $) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monomial| (($ |#1| (|Partition|)) NIL)) (|minimumDegree| (((|Partition|) $) NIL)) (|mapExponents| (($ (|Mapping| (|Partition|) (|Partition|)) $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|leadingMonomial| (($ $) NIL)) (|leadingCoefficient| ((|#1| $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|ground?| (((|Boolean|) $) NIL)) (|ground| ((|#1| $) NIL)) (|fmecg| (($ $ (|Partition|) |#1| $) NIL (AND (|has| (|Partition|) (|CancellationAbelianMonoid|)) (|has| |#1| (|IntegralDomain|))))) (|exquo| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|IntegralDomain|))) (((|Union| $ "failed") $ |#1|) NIL (|has| |#1| (|IntegralDomain|)))) (|degree| (((|Partition|) $) NIL)) (|content| ((|#1| $) NIL (|has| |#1| (|GcdDomain|)))) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ $) NIL (|has| |#1| (|IntegralDomain|))) (($ |#1|) NIL) (($ (|Fraction| (|Integer|))) NIL (OR (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))))) (|coefficients| (((|List| |#1|) $) NIL)) (|coefficient| ((|#1| $ (|Partition|)) NIL)) (|charthRoot| (((|Union| $ "failed") $) NIL (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|CommutativeRing|)))) (|associates?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 9 T CONST)) (|One| (($) 14 T CONST)) (= (((|Boolean|) $ $) 16)) (/ (($ $ |#1|) NIL (|has| |#1| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) 19)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 20) (($ $ |#1|) NIL) (($ |#1| $) 13) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) 
(((|SymmetricPolynomial| |#1|) (|Join| (|FiniteAbelianMonoidRing| |#1| (|Partition|)) (CATEGORY |domain| (IF (|has| |#1| (|IntegralDomain|)) (IF (|has| (|Partition|) (|CancellationAbelianMonoid|)) (SIGNATURE |fmecg| ($ $ (|Partition|) |#1| $)) |noBranch|) |noBranch|) (IF (|has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (ATTRIBUTE |canonicalUnitNormal|) |noBranch|))) (|Ring|)) (T |SymmetricPolynomial|)) 
((|fmecg| (*1 *1 *1 *2 *3 *1) (AND (|isDomain| *2 (|Partition|)) (|ofCategory| *2 (|CancellationAbelianMonoid|)) (|isDomain| *1 (|SymmetricPolynomial| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))))) 
(|Join| (|FiniteAbelianMonoidRing| |#1| (|Partition|)) (CATEGORY |domain| (IF (|has| |#1| (|IntegralDomain|)) (IF (|has| (|Partition|) (|CancellationAbelianMonoid|)) (SIGNATURE |fmecg| ($ $ (|Partition|) |#1| $)) |noBranch|) |noBranch|) (IF (|has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (ATTRIBUTE |canonicalUnitNormal|) |noBranch|))) 
((|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) 24)) (|showTheSymbolTable| (($) 28)) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) 21)) (|returnType!| (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) 40) (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) 41) (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) 42)) (|printTypes| (((|Void|) (|Symbol|)) 57)) (|printHeader| (((|Void|) (|Symbol|) $) 54) (((|Void|) (|Symbol|)) 55) (((|Void|)) 56)) (|newSubProgram| (((|Void|) (|Symbol|)) 36)) (|endSubProgram| (((|Symbol|)) 35)) (|empty| (($) 33)) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) 44) (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) 48) (((|FortranType|) (|Symbol|) (|FortranType|)) 45) (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) 49)) (|currentSubProgram| (((|Symbol|)) 34)) (|coerce| (((|OutputForm|) $) 27)) (|clearTheSymbolTable| (((|Void|)) 29) (((|Void|) (|Symbol|)) 32)) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) 23)) (|argumentList!| (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) 37) (((|Void|) (|Symbol|) (|List| (|Symbol|))) 38) (((|Void|) (|List| (|Symbol|))) 39))) 
(((|TheSymbolTable|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |showTheSymbolTable| ($)) (SIGNATURE |clearTheSymbolTable| ((|Void|))) (SIGNATURE |clearTheSymbolTable| ((|Void|) (|Symbol|))) (SIGNATURE |declare!| ((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $)) (SIGNATURE |declare!| ((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $)) (SIGNATURE |declare!| ((|FortranType|) (|Symbol|) (|FortranType|))) (SIGNATURE |declare!| ((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|))) (SIGNATURE |newSubProgram| ((|Void|) (|Symbol|))) (SIGNATURE |currentSubProgram| ((|Symbol|))) (SIGNATURE |endSubProgram| ((|Symbol|))) (SIGNATURE |argumentList!| ((|Void|) (|Symbol|) (|List| (|Symbol|)) $)) (SIGNATURE |argumentList!| ((|Void|) (|Symbol|) (|List| (|Symbol|)))) (SIGNATURE |argumentList!| ((|Void|) (|List| (|Symbol|)))) (SIGNATURE |returnType!| ((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $)) (SIGNATURE |returnType!| ((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")))) (SIGNATURE |returnType!| ((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")))) (SIGNATURE |printHeader| ((|Void|) (|Symbol|) $)) (SIGNATURE |printHeader| ((|Void|) (|Symbol|))) (SIGNATURE |printHeader| ((|Void|))) (SIGNATURE |printTypes| ((|Void|) (|Symbol|))) (SIGNATURE |empty| ($)) (SIGNATURE |returnTypeOf| ((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $)) (SIGNATURE |argumentListOf| ((|List| (|Symbol|)) (|Symbol|) $)) (SIGNATURE |symbolTableOf| ((|SymbolTable|) (|Symbol|) $))))) (T |TheSymbolTable|)) 
((|showTheSymbolTable| (*1 *1) (|isDomain| *1 (|TheSymbolTable|))) (|clearTheSymbolTable| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|)))) (|clearTheSymbolTable| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|)))) (|declare!| (*1 *2 *3 *2 *3 *1) (AND (|isDomain| *2 (|FortranType|)) (|isDomain| *3 (|Symbol|)) (|isDomain| *1 (|TheSymbolTable|)))) (|declare!| (*1 *2 *3 *2 *4 *1) (AND (|isDomain| *2 (|FortranType|)) (|isDomain| *3 (|List| (|Symbol|))) (|isDomain| *4 (|Symbol|)) (|isDomain| *1 (|TheSymbolTable|)))) (|declare!| (*1 *2 *3 *2) (AND (|isDomain| *2 (|FortranType|)) (|isDomain| *3 (|Symbol|)) (|isDomain| *1 (|TheSymbolTable|)))) (|declare!| (*1 *2 *3 *2 *3) (AND (|isDomain| *2 (|FortranType|)) (|isDomain| *3 (|Symbol|)) (|isDomain| *1 (|TheSymbolTable|)))) (|newSubProgram| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|)))) (|currentSubProgram| (*1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|TheSymbolTable|)))) (|endSubProgram| (*1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|TheSymbolTable|)))) (|argumentList!| (*1 *2 *3 *4 *1) (AND (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|)))) (|argumentList!| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|)))) (|argumentList!| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Symbol|))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|)))) (|returnType!| (*1 *2 *3 *4 *1) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|)))) (|returnType!| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|)))) (|returnType!| (*1 *2 *3) (AND (|isDomain| *3 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|)))) (|printHeader| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|)))) (|printHeader| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|)))) (|printHeader| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|)))) (|printTypes| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|)))) (|empty| (*1 *1) (|isDomain| *1 (|TheSymbolTable|))) (|returnTypeOf| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) (|isDomain| *1 (|TheSymbolTable|)))) (|argumentListOf| (*1 *2 *3 *1) (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *1 (|TheSymbolTable|)) (|isDomain| *3 (|Symbol|)))) (|symbolTableOf| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|SymbolTable|)) (|isDomain| *1 (|TheSymbolTable|))))) 
(|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |showTheSymbolTable| ($)) (SIGNATURE |clearTheSymbolTable| ((|Void|))) (SIGNATURE |clearTheSymbolTable| ((|Void|) (|Symbol|))) (SIGNATURE |declare!| ((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $)) (SIGNATURE |declare!| ((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $)) (SIGNATURE |declare!| ((|FortranType|) (|Symbol|) (|FortranType|))) (SIGNATURE |declare!| ((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|))) (SIGNATURE |newSubProgram| ((|Void|) (|Symbol|))) (SIGNATURE |currentSubProgram| ((|Symbol|))) (SIGNATURE |endSubProgram| ((|Symbol|))) (SIGNATURE |argumentList!| ((|Void|) (|Symbol|) (|List| (|Symbol|)) $)) (SIGNATURE |argumentList!| ((|Void|) (|Symbol|) (|List| (|Symbol|)))) (SIGNATURE |argumentList!| ((|Void|) (|List| (|Symbol|)))) (SIGNATURE |returnType!| ((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $)) (SIGNATURE |returnType!| ((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")))) (SIGNATURE |returnType!| ((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")))) (SIGNATURE |printHeader| ((|Void|) (|Symbol|) $)) (SIGNATURE |printHeader| ((|Void|) (|Symbol|))) (SIGNATURE |printHeader| ((|Void|))) (SIGNATURE |printTypes| ((|Void|) (|Symbol|))) (SIGNATURE |empty| ($)) (SIGNATURE |returnTypeOf| ((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $)) (SIGNATURE |argumentListOf| ((|List| (|Symbol|)) (|Symbol|) $)) (SIGNATURE |symbolTableOf| ((|SymbolTable|) (|Symbol|) $)))) 
((|typeLists| (((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $) 57)) (|typeList| (((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $) 40)) (|symbolTable| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))) 15)) (|printTypes| (((|Void|) $) 65)) (|parametersOf| (((|List| (|Symbol|)) $) 20)) (|newTypeLists| (((|SExpression|) $) 53)) (|fortranTypeOf| (((|FortranType|) (|Symbol|) $) 27)) (|externalList| (((|List| (|Symbol|)) $) 30)) (|empty| (($) 17)) (|declare!| (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $) 25) (((|FortranType|) (|Symbol|) (|FortranType|) $) 24)) (|coerce| (((|OutputForm|) $) 9) (((|Table| (|Symbol|) (|FortranType|)) $) 11))) 
(((|SymbolTable|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |coerce| ((|Table| (|Symbol|) (|FortranType|)) $)) (SIGNATURE |empty| ($)) (SIGNATURE |declare!| ((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $)) (SIGNATURE |declare!| ((|FortranType|) (|Symbol|) (|FortranType|) $)) (SIGNATURE |fortranTypeOf| ((|FortranType|) (|Symbol|) $)) (SIGNATURE |parametersOf| ((|List| (|Symbol|)) $)) (SIGNATURE |typeList| ((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $)) (SIGNATURE |externalList| ((|List| (|Symbol|)) $)) (SIGNATURE |typeLists| ((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $)) (SIGNATURE |newTypeLists| ((|SExpression|) $)) (SIGNATURE |printTypes| ((|Void|) $)) (SIGNATURE |symbolTable| ($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))))))) (T |SymbolTable|)) 
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((|triangularSystems| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| *5)))) (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|List| (|List| (|Polynomial| *5)))) (|isDomain| *1 (|SystemSolvePackage| *5)))) (|solve| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| (|Equation| (|Fraction| (|Polynomial| *4))))) (|isDomain| *1 (|SystemSolvePackage| *4)) (|isDomain| *3 (|Equation| (|Fraction| (|Polynomial| *4)))))) (|solve| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| (|Equation| (|Fraction| (|Polynomial| *4))))) (|isDomain| *1 (|SystemSolvePackage| *4)) (|isDomain| *3 (|Fraction| (|Polynomial| *4))))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|List| (|Equation| (|Fraction| (|Polynomial| *5))))) (|isDomain| *1 (|SystemSolvePackage| *5)) (|isDomain| *3 (|Equation| (|Fraction| (|Polynomial| *5)))))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|List| (|Equation| (|Fraction| (|Polynomial| *5))))) (|isDomain| *1 (|SystemSolvePackage| *5)) (|isDomain| *3 (|Fraction| (|Polynomial| *5))))) (|solve| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| (|List| (|Equation| (|Fraction| (|Polynomial| *4)))))) (|isDomain| *1 (|SystemSolvePackage| *4)) (|isDomain| *3 (|List| (|Equation| (|Fraction| (|Polynomial| *4))))))) (|solve| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| *4)))) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| (|List| (|Equation| (|Fraction| (|Polynomial| *4)))))) (|isDomain| *1 (|SystemSolvePackage| *4)))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|List| (|List| (|Equation| (|Fraction| (|Polynomial| *5)))))) (|isDomain| *1 (|SystemSolvePackage| *5)) (|isDomain| *3 (|List| (|Equation| (|Fraction| (|Polynomial| *5))))))) (|solve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| *5)))) (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|List| (|List| (|Equation| (|Fraction| (|Polynomial| *5)))))) (|isDomain| *1 (|SystemSolvePackage| *5))))) 
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((|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) 38)) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) 24)) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) 34)) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) 30)) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) 37)) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) 36)) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) 28)) (|inverse| (((|List| |#1|) (|List| |#1|)) 31)) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) 18)) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) 15)) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) 13)) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) 39)) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) 41))) 
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((|mr| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |f1| (|List| *4)) (|:| |f2| (|List| (|List| (|List| *4)))) (|:| |f3| (|List| (|List| *4))) (|:| |f4| (|List| (|List| (|List| *4)))))) (|isDomain| *1 (|TableauxBumpers| *4)) (|isDomain| *3 (|List| (|List| (|List| *4)))))) (|maxrow| (*1 *2 *3 *4 *5 *4 *4 *4) (AND (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *3 (|List| *6)) (|isDomain| *5 (|List| *3)) (|isDomain| *2 (|Record| (|:| |f1| *3) (|:| |f2| (|List| *5)) (|:| |f3| *5) (|:| |f4| (|List| *5)))) (|isDomain| *1 (|TableauxBumpers| *6)) (|isDomain| *4 (|List| *5)))) (|inverse| (*1 *2 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|TableauxBumpers| *3)))) (|slex| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|List| (|List| *4))) (|isDomain| *1 (|TableauxBumpers| *4)) (|isDomain| *3 (|List| *4)))) (|lex| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|TableauxBumpers| *3)))) (|tab| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|Tableau| (|List| *4))) (|isDomain| *1 (|TableauxBumpers| *4)) (|isDomain| *3 (|List| *4)))) (|tab1| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|List| (|List| (|List| *4)))) (|isDomain| *1 (|TableauxBumpers| *4)) (|isDomain| *3 (|List| (|List| *4))))) (|bat| (*1 *2 *3) (AND (|isDomain| *3 (|Tableau| (|List| *4))) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|List| (|List| *4))) (|isDomain| *1 (|TableauxBumpers| *4)))) (|bat1| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|List| (|List| *4)))) (|isDomain| *2 (|List| (|List| *4))) (|isDomain| *1 (|TableauxBumpers| *4)) (|ofCategory| *4 (|OrderedSet|)))) (|untab| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| (|List| (|List| *4)))) (|isDomain| *2 (|List| (|List| *4))) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|TableauxBumpers| *4)))) (|bumptab1| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| (|List| (|List| *4)))) (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *1 (|TableauxBumpers| *4)))) (|bumptab| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|List| (|List| (|List| *5)))) (|isDomain| *3 (|Mapping| (|Boolean|) *5 *5)) (|isDomain| *4 (|List| *5)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|TableauxBumpers| *5)))) (|bumprow| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *6 *6)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *4 (|List| *6)) (|isDomain| *2 (|Record| (|:| |fs| (|Boolean|)) (|:| |sd| *4) (|:| |td| (|List| *4)))) (|isDomain| *1 (|TableauxBumpers| *6)) (|isDomain| *5 (|List| *4))))) 
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((|tableau| (($ (|List| (|List| |#1|))) 9)) (|listOfLists| (((|List| (|List| |#1|)) $) 10)) (|coerce| (((|OutputForm|) $) 25))) 
(((|Tableau| |#1|) (CATEGORY |domain| (SIGNATURE |tableau| ($ (|List| (|List| |#1|)))) (SIGNATURE |listOfLists| ((|List| (|List| |#1|)) $)) (SIGNATURE |coerce| ((|OutputForm|) $))) (|SetCategory|)) (T |Tableau|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|Tableau| *3)) (|ofCategory| *3 (|SetCategory|)))) (|listOfLists| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|List| *3))) (|isDomain| *1 (|Tableau| *3)) (|ofCategory| *3 (|SetCategory|)))) (|tableau| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Tableau| *3))))) 
(CATEGORY |domain| (SIGNATURE |tableau| ($ (|List| (|List| |#1|)))) (SIGNATURE |listOfLists| ((|List| (|List| |#1|)) $)) (SIGNATURE |coerce| ((|OutputForm|) $))) 
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(|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) NIL (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))))) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|Table| |#1| |#2|) (|Join| (|TableAggregate| |#1| |#2|) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|))) (|SetCategory|) (|SetCategory|)) (T |Table|)) 
NIL 
(|Join| (|TableAggregate| |#1| |#2|) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|))) 
((|tanSum| ((|#1| (|List| |#1|)) 32)) (|tanNa| ((|#1| |#1| (|Integer|)) 18)) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) 15))) 
(((|TangentExpansions| |#1|) (CATEGORY |package| (SIGNATURE |tanSum| (|#1| (|List| |#1|))) (SIGNATURE |tanAn| ((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|))) (SIGNATURE |tanNa| (|#1| |#1| (|Integer|)))) (|Field|)) (T |TangentExpansions|)) 
((|tanNa| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|TangentExpansions| *2)) (|ofCategory| *2 (|Field|)))) (|tanAn| (*1 *2 *3 *4) (AND (|isDomain| *4 (|PositiveInteger|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) (|isDomain| *1 (|TangentExpansions| *3)) (|ofCategory| *3 (|Field|)))) (|tanSum| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|isDomain| *1 (|TangentExpansions| *2)) (|ofCategory| *2 (|Field|))))) 
(CATEGORY |package| (SIGNATURE |tanSum| (|#1| (|List| |#1|))) (SIGNATURE |tanAn| ((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|))) (SIGNATURE |tanNa| (|#1| |#1| (|Integer|)))) 
((|table| (($) 10) (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) 14)) (|remove!| (($ (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) $) 60) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) $) NIL) (((|Union| |#3| "failed") |#2| $) NIL)) (|parts| (((|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) $) 39) (((|List| |#3|) $) 41)) (|map!| (($ (|Mapping| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) $) 52) (($ (|Mapping| |#3| |#3|) $) 33)) (|map| (($ (|Mapping| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) $) 50) (($ (|Mapping| |#3| |#3|) $) NIL) (($ (|Mapping| |#3| |#3| |#3|) $ $) 38)) (|inspect| (((|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) $) 53)) (|insert!| (($ (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) $) 16)) (|indices| (((|List| |#2|) $) 19)) (|index?| (((|Boolean|) |#2| $) 58)) (|find| (((|Union| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) "failed") (|Mapping| (|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) $) 57)) (|extract!| (((|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) $) 62)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) $) NIL) (((|Boolean|) (|Mapping| (|Boolean|) |#3|) $) 65)) (|entries| (((|List| |#3|) $) 43)) (|elt| ((|#3| $ |#2|) 30) ((|#3| $ |#2| |#3|) 31)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) $) NIL) (((|NonNegativeInteger|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) $) NIL) (((|NonNegativeInteger|) |#3| $) NIL) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#3|) $) 66)) (|coerce| (((|OutputForm|) $) 27)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) $) NIL) (((|Boolean|) (|Mapping| (|Boolean|) |#3|) $) 64)) (= (((|Boolean|) $ $) 48))) 
(((|TableAggregate&| |#1| |#2| |#3|) (CATEGORY |domain| (SIGNATURE = ((|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#3| |#3| |#3|) |#1| |#1|)) (SIGNATURE |table| (|#1| (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))))) (SIGNATURE |table| (|#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#3| |#3|) |#1|)) (SIGNATURE |map!| (|#1| (|Mapping| |#3| |#3|) |#1|)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#3|) |#1|)) (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#3|) |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#3|) |#1|)) (SIGNATURE |parts| ((|List| |#3|) |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) |#3| |#1|)) (SIGNATURE |elt| (|#3| |#1| |#2| |#3|)) (SIGNATURE |elt| (|#3| |#1| |#2|)) (SIGNATURE |entries| ((|List| |#3|) |#1|)) (SIGNATURE |index?| ((|Boolean|) |#2| |#1|)) (SIGNATURE |indices| ((|List| |#2|) |#1|)) (SIGNATURE |remove!| ((|Union| |#3| "failed") |#2| |#1|)) (SIGNATURE |remove!| (|#1| (|Mapping| (|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) |#1|)) (SIGNATURE |remove!| (|#1| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) |#1|)) (SIGNATURE |find| ((|Union| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) "failed") (|Mapping| (|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) |#1|)) (SIGNATURE |inspect| ((|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) |#1|)) (SIGNATURE |insert!| (|#1| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) |#1|)) (SIGNATURE |extract!| ((|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) |#1|)) (SIGNATURE |parts| ((|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) |#1|)) (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) |#1|)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) |#1|)) (SIGNATURE |map!| (|#1| (|Mapping| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) |#1|)) (SIGNATURE |map| (|#1| (|Mapping| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) |#1|))) (|TableAggregate| |#2| |#3|) (|SetCategory|) (|SetCategory|)) (T |TableAggregate&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE = ((|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#3| |#3| |#3|) |#1| |#1|)) (SIGNATURE |table| (|#1| (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))))) (SIGNATURE |table| (|#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#3| |#3|) |#1|)) (SIGNATURE |map!| (|#1| (|Mapping| |#3| |#3|) |#1|)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#3|) |#1|)) (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#3|) |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#3|) |#1|)) (SIGNATURE |parts| ((|List| |#3|) |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) |#3| |#1|)) (SIGNATURE |elt| (|#3| |#1| |#2| |#3|)) (SIGNATURE |elt| (|#3| |#1| |#2|)) (SIGNATURE |entries| ((|List| |#3|) |#1|)) (SIGNATURE |index?| ((|Boolean|) |#2| |#1|)) (SIGNATURE |indices| ((|List| |#2|) |#1|)) (SIGNATURE |remove!| ((|Union| |#3| "failed") |#2| |#1|)) (SIGNATURE |remove!| (|#1| (|Mapping| (|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) |#1|)) (SIGNATURE |remove!| (|#1| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) |#1|)) (SIGNATURE |find| ((|Union| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) "failed") (|Mapping| (|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) |#1|)) (SIGNATURE |inspect| ((|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) |#1|)) (SIGNATURE |insert!| (|#1| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) |#1|)) (SIGNATURE |extract!| ((|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) |#1|)) (SIGNATURE |parts| ((|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) |#1|)) (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) |#1|)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) |#1|)) (SIGNATURE |map!| (|#1| (|Mapping| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) |#1|)) (SIGNATURE |map| (|#1| (|Mapping| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)) (|Record| (|:| |key| |#2|) (|:| |entry| |#3|))) |#1|))) 
((~= (((|Boolean|) $ $) 18 (OR (|has| |#2| (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))))) (|table| (($) 66) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 65)) (|swap!| (((|Void|) $ |#1| |#1|) 93 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setelt| ((|#2| $ |#1| |#2|) 67)) (|select!| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 42 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|select| (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 52 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|search| (((|Union| |#2| "failed") |#1| $) 57)) (|sample| (($) 7 T CONST)) (|removeDuplicates| (($ $) 55 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 44 (|has| $ (ATTRIBUTE |finiteAggregate|))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 43 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| |#2| "failed") |#1| $) 58)) (|remove| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 54 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 51 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 53 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 50 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 49 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| ((|#2| $ |#1| |#2|) 81 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| ((|#2| $ |#1|) 82)) (|parts| (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|List| |#2|) $) 73 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|minIndex| ((|#1| $) 90 (|has| |#1| (|OrderedSet|)))) (|members| (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|List| |#2|) $) 74 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 27 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|Boolean|) |#2| $) 76 (AND (|has| |#2| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|maxIndex| ((|#1| $) 89 (|has| |#1| (|OrderedSet|)))) (|map!| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ (|Mapping| |#2| |#2|) $) 69 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 35) (($ (|Mapping| |#2| |#2|) $) 68) (($ (|Mapping| |#2| |#2| |#2|) $ $) 64)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|latex| (((|String|) $) 22 (OR (|has| |#2| (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))))) (|keys| (((|List| |#1|) $) 59)) (|key?| (((|Boolean|) |#1| $) 60)) (|inspect| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 36)) (|insert!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 37)) (|indices| (((|List| |#1|) $) 87)) (|index?| (((|Boolean|) |#1| $) 86)) (|hash| (((|SingleInteger|) $) 21 (OR (|has| |#2| (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))))) (|first| ((|#2| $) 91 (|has| |#1| (|OrderedSet|)))) (|find| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 48)) (|fill!| (($ $ |#2|) 92 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|extract!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 38)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 71 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) 26 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ $ (|Equation| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 25 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 24 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ $ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 23 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)))) (($ $ (|List| |#2|) (|List| |#2|)) 80 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ |#2| |#2|) 79 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|Equation| |#2|)) 78 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|)))) (($ $ (|List| (|Equation| |#2|))) 77 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|entry?| (((|Boolean|) |#2| $) 88 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#2| (|SetCategory|))))) (|entries| (((|List| |#2|) $) 85)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| ((|#2| $ |#1|) 84) ((|#2| $ |#1| |#2|) 83)) (|dictionary| (($) 46) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 45)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 28 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|NonNegativeInteger|) |#2| $) 75 (AND (|has| |#2| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) 72 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) 13)) (|convert| (((|InputForm|) $) 56 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 47)) (|coerce| (((|OutputForm|) $) 20 (OR (|has| |#2| (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))))) (|bag| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 39)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) 70 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (OR (|has| |#2| (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|TableAggregate| |#1| |#2|) (|Category|) (|SetCategory|) (|SetCategory|)) (T |TableAggregate|)) 
((|setelt| (*1 *2 *1 *3 *2) (AND (|ofCategory| *1 (|TableAggregate| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)))) (|table| (*1 *1) (AND (|ofCategory| *1 (|TableAggregate| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|table| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |key| *3) (|:| |entry| *4)))) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *1 (|TableAggregate| *3 *4)))) (|map| (*1 *1 *2 *1 *1) (AND (|isDomain| *2 (|Mapping| *4 *4 *4)) (|ofCategory| *1 (|TableAggregate| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))))) 
(|Join| (|KeyedDictionary| |t#1| |t#2|) (|IndexedAggregate| |t#1| |t#2|) (CATEGORY |domain| (SIGNATURE |setelt| (|t#2| $ |t#1| |t#2|)) (SIGNATURE |table| ($)) (SIGNATURE |table| ($ (|List| (|Record| (|:| |key| |t#1|) (|:| |entry| |t#2|))))) (SIGNATURE |map| ($ (|Mapping| |t#2| |t#2| |t#2|) $ $)))) 
(((|Aggregate|) . T) ((|BagAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|BasicType|) OR (|has| |#2| (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#2| (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))) ((|Collection| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|ConvertibleTo| (|InputForm|)) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|ConvertibleTo| (|InputForm|))) ((|Dictionary| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|DictionaryOperations| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|Eltable| |#1| |#2|) . T) ((|EltableAggregate| |#1| |#2|) . T) ((|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|HomogeneousAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|HomogeneousAggregate| |#2|) . T) ((|IndexedAggregate| |#1| |#2|) . T) ((|InnerEvalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))) ((|InnerEvalable| |#2| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|KeyedDictionary| |#1| |#2|) . T) ((|SetCategory|) OR (|has| |#2| (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))) ((|Type|) . T)) 
((|usingTable?| (((|Boolean|)) 24)) (|startStats!| (((|Void|) (|String|)) 26)) (|printingInfo?| (((|Boolean|)) 36)) (|printStats!| (((|Void|)) 34)) (|printInfo!| (((|Void|) (|String|) (|String|)) 25)) (|makingStats?| (((|Boolean|)) 37)) (|insert!| (((|Void|) |#1| |#2|) 44)) (|initTable!| (((|Void|)) 20)) (|extractIfCan| (((|Union| |#2| "failed") |#1|) 42)) (|clearTable!| (((|Void|)) 35))) 
(((|TabulatedComputationPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |initTable!| ((|Void|))) (SIGNATURE |printInfo!| ((|Void|) (|String|) (|String|))) (SIGNATURE |startStats!| ((|Void|) (|String|))) (SIGNATURE |printStats!| ((|Void|))) (SIGNATURE |clearTable!| ((|Void|))) (SIGNATURE |usingTable?| ((|Boolean|))) (SIGNATURE |printingInfo?| ((|Boolean|))) (SIGNATURE |makingStats?| ((|Boolean|))) (SIGNATURE |extractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |insert!| ((|Void|) |#1| |#2|))) (|SetCategory|) (|SetCategory|)) (T |TabulatedComputationPackage|)) 
((|insert!| (*1 *2 *3 *4) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TabulatedComputationPackage| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)))) (|extractIfCan| (*1 *2 *3) (|partial| AND (|ofCategory| *2 (|SetCategory|)) (|isDomain| *1 (|TabulatedComputationPackage| *3 *2)) (|ofCategory| *3 (|SetCategory|)))) (|makingStats?| (*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|TabulatedComputationPackage| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)))) (|printingInfo?| (*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|TabulatedComputationPackage| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)))) (|usingTable?| (*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|TabulatedComputationPackage| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)))) (|clearTable!| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TabulatedComputationPackage| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)))) (|printStats!| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TabulatedComputationPackage| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)))) (|startStats!| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TabulatedComputationPackage| *4 *5)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)))) (|printInfo!| (*1 *2 *3 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TabulatedComputationPackage| *4 *5)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)))) (|initTable!| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TabulatedComputationPackage| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))))) 
(CATEGORY |package| (SIGNATURE |initTable!| ((|Void|))) (SIGNATURE |printInfo!| ((|Void|) (|String|) (|String|))) (SIGNATURE |startStats!| ((|Void|) (|String|))) (SIGNATURE |printStats!| ((|Void|))) (SIGNATURE |clearTable!| ((|Void|))) (SIGNATURE |usingTable?| ((|Boolean|))) (SIGNATURE |printingInfo?| ((|Boolean|))) (SIGNATURE |makingStats?| ((|Boolean|))) (SIGNATURE |extractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |insert!| ((|Void|) |#1| |#2|))) 
((|stripCommentsAndBlanks| (((|String|) (|String|)) 18)) (|interpretString| (((|Any|) (|String|)) 21))) 
(((|TemplateUtilities|) (CATEGORY |package| (SIGNATURE |interpretString| ((|Any|) (|String|))) (SIGNATURE |stripCommentsAndBlanks| ((|String|) (|String|))))) (T |TemplateUtilities|)) 
((|stripCommentsAndBlanks| (*1 *2 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|TemplateUtilities|)))) (|interpretString| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|TemplateUtilities|))))) 
(CATEGORY |package| (SIGNATURE |interpretString| ((|Any|) (|String|))) (SIGNATURE |stripCommentsAndBlanks| ((|String|) (|String|)))) 
((|coerce| (((|TexFormat|) |#1|) 11))) 
(((|TexFormat1| |#1|) (CATEGORY |package| (SIGNATURE |coerce| ((|TexFormat|) |#1|))) (|SetCategory|)) (T |TexFormat1|)) 
((|coerce| (*1 *2 *3) (AND (|isDomain| *2 (|TexFormat|)) (|isDomain| *1 (|TexFormat1| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(CATEGORY |package| (SIGNATURE |coerce| ((|TexFormat|) |#1|))) 
((~= (((|Boolean|) $ $) NIL)) (|tex| (((|List| (|String|)) $) 33)) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) 36)) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) 35)) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) 37)) (|prologue| (((|List| (|String|)) $) 32)) (|new| (($) 22)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|epilogue| (((|List| (|String|)) $) 34)) (|display| (((|Void|) $ (|Integer|)) 29) (((|Void|) $) 30)) (|convert| (($ (|OutputForm|) (|Integer|)) 26) (($ (|OutputForm|) (|Integer|) (|OutputForm|)) NIL)) (|coerce| (((|OutputForm|) $) 39) (($ (|OutputForm|)) 24)) (= (((|Boolean|) $ $) NIL))) 
(((|TexFormat|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|OutputForm|))) (SIGNATURE |convert| ($ (|OutputForm|) (|Integer|))) (SIGNATURE |convert| ($ (|OutputForm|) (|Integer|) (|OutputForm|))) (SIGNATURE |display| ((|Void|) $ (|Integer|))) (SIGNATURE |display| ((|Void|) $)) (SIGNATURE |epilogue| ((|List| (|String|)) $)) (SIGNATURE |tex| ((|List| (|String|)) $)) (SIGNATURE |new| ($)) (SIGNATURE |prologue| ((|List| (|String|)) $)) (SIGNATURE |setEpilogue!| ((|List| (|String|)) $ (|List| (|String|)))) (SIGNATURE |setTex!| ((|List| (|String|)) $ (|List| (|String|)))) (SIGNATURE |setPrologue!| ((|List| (|String|)) $ (|List| (|String|))))))) (T |TexFormat|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|TexFormat|)))) (|convert| (*1 *1 *2 *3) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|TexFormat|)))) (|convert| (*1 *1 *2 *3 *2) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|TexFormat|)))) (|display| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TexFormat|)))) (|display| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TexFormat|)))) (|epilogue| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|TexFormat|)))) (|tex| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|TexFormat|)))) (|new| (*1 *1) (|isDomain| *1 (|TexFormat|))) (|prologue| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|TexFormat|)))) (|setEpilogue!| (*1 *2 *1 *2) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|TexFormat|)))) (|setTex!| (*1 *2 *1 *2) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|TexFormat|)))) (|setPrologue!| (*1 *2 *1 *2) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|TexFormat|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|OutputForm|))) (SIGNATURE |convert| ($ (|OutputForm|) (|Integer|))) (SIGNATURE |convert| ($ (|OutputForm|) (|Integer|) (|OutputForm|))) (SIGNATURE |display| ((|Void|) $ (|Integer|))) (SIGNATURE |display| ((|Void|) $)) (SIGNATURE |epilogue| ((|List| (|String|)) $)) (SIGNATURE |tex| ((|List| (|String|)) $)) (SIGNATURE |new| ($)) (SIGNATURE |prologue| ((|List| (|String|)) $)) (SIGNATURE |setEpilogue!| ((|List| (|String|)) $ (|List| (|String|)))) (SIGNATURE |setTex!| ((|List| (|String|)) $ (|List| (|String|)))) (SIGNATURE |setPrologue!| ((|List| (|String|)) $ (|List| (|String|)))))) 
((~= (((|Boolean|) $ $) NIL)) (|writeLine!| (((|String|) $ (|String|)) 15) (((|String|) $) 14)) (|write!| (((|String|) $ (|String|)) 13)) (|reopen!| (($ $ (|String|)) NIL)) (|readLineIfCan!| (((|Union| (|String|) "failed") $) 11)) (|readLine!| (((|String|) $) 8)) (|readIfCan!| (((|Union| (|String|) "failed") $) 12)) (|read!| (((|String|) $) 9)) (|open| (($ (|FileName|)) NIL) (($ (|FileName|) (|String|)) NIL)) (|name| (((|FileName|) $) NIL)) (|latex| (((|String|) $) NIL)) (|iomode| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|flush| (((|Void|) $) NIL)) (|endOfFile?| (((|Boolean|) $) 17)) (|coerce| (((|OutputForm|) $) NIL)) (|close!| (($ $) NIL)) (= (((|Boolean|) $ $) NIL))) 
(((|TextFile|) (|Join| (|FileCategory| (|FileName|) (|String|)) (CATEGORY |domain| (SIGNATURE |writeLine!| ((|String|) $ (|String|))) (SIGNATURE |writeLine!| ((|String|) $)) (SIGNATURE |readLine!| ((|String|) $)) (SIGNATURE |readLineIfCan!| ((|Union| (|String|) "failed") $)) (SIGNATURE |readIfCan!| ((|Union| (|String|) "failed") $)) (SIGNATURE |endOfFile?| ((|Boolean|) $))))) (T |TextFile|)) 
((|writeLine!| (*1 *2 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|TextFile|)))) (|writeLine!| (*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|TextFile|)))) (|readLine!| (*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|TextFile|)))) (|readLineIfCan!| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|TextFile|)))) (|readIfCan!| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|TextFile|)))) (|endOfFile?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|TextFile|))))) 
(|Join| (|FileCategory| (|FileName|) (|String|)) (CATEGORY |domain| (SIGNATURE |writeLine!| ((|String|) $ (|String|))) (SIGNATURE |writeLine!| ((|String|) $)) (SIGNATURE |readLine!| ((|String|) $)) (SIGNATURE |readLineIfCan!| ((|Union| (|String|) "failed") $)) (SIGNATURE |readIfCan!| ((|Union| (|String|) "failed") $)) (SIGNATURE |endOfFile?| ((|Boolean|) $)))) 
((|sign| (((|Union| (|Integer|) "failed") |#1|) 19)) (|nonQsign| (((|Union| (|Integer|) "failed") |#1|) 13)) (|direction| (((|Integer|) (|String|)) 28))) 
(((|ToolsForSign| |#1|) (CATEGORY |package| (SIGNATURE |sign| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |nonQsign| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |direction| ((|Integer|) (|String|)))) (|Ring|)) (T |ToolsForSign|)) 
((|direction| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|ToolsForSign| *4)) (|ofCategory| *4 (|Ring|)))) (|nonQsign| (*1 *2 *3) (|partial| AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|ToolsForSign| *3)) (|ofCategory| *3 (|Ring|)))) (|sign| (*1 *2 *3) (|partial| AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|ToolsForSign| *3)) (|ofCategory| *3 (|Ring|))))) 
(CATEGORY |package| (SIGNATURE |sign| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |nonQsign| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |direction| ((|Integer|) (|String|)))) 
((|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) 8))) 
(((|TopLevelThreeSpace|) (CATEGORY |package| (SIGNATURE |createThreeSpace| ((|ThreeSpace| (|DoubleFloat|)))))) (T |TopLevelThreeSpace|)) 
((|createThreeSpace| (*1 *2) (AND (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|))) (|isDomain| *1 (|TopLevelThreeSpace|))))) 
(CATEGORY |package| (SIGNATURE |createThreeSpace| ((|ThreeSpace| (|DoubleFloat|))))) 
((|pi| (($) 11)) (|atanh| (($ $) 35)) (|asinh| (($ $) 33)) (|asin| (($ $) 25)) (|asech| (($ $) 17)) (|acsch| (($ $) 15)) (|acoth| (($ $) 19)) (|acot| (($ $) 30)) (|acosh| (($ $) 34)) (|acos| (($ $) 29))) 
(((|TranscendentalFunctionCategory&| |#1|) (CATEGORY |domain| (SIGNATURE |pi| (|#1|)) (SIGNATURE |atanh| (|#1| |#1|)) (SIGNATURE |asinh| (|#1| |#1|)) (SIGNATURE |asech| (|#1| |#1|)) (SIGNATURE |acsch| (|#1| |#1|)) (SIGNATURE |acoth| (|#1| |#1|)) (SIGNATURE |acosh| (|#1| |#1|)) (SIGNATURE |asin| (|#1| |#1|)) (SIGNATURE |acot| (|#1| |#1|)) (SIGNATURE |acos| (|#1| |#1|))) (|TranscendentalFunctionCategory|)) (T |TranscendentalFunctionCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |pi| (|#1|)) (SIGNATURE |atanh| (|#1| |#1|)) (SIGNATURE |asinh| (|#1| |#1|)) (SIGNATURE |asech| (|#1| |#1|)) (SIGNATURE |acsch| (|#1| |#1|)) (SIGNATURE |acoth| (|#1| |#1|)) (SIGNATURE |acosh| (|#1| |#1|)) (SIGNATURE |asin| (|#1| |#1|)) (SIGNATURE |acot| (|#1| |#1|)) (SIGNATURE |acos| (|#1| |#1|))) 
((|tanh| (($ $) 26)) (|tan| (($ $) 11)) (|sinh| (($ $) 27)) (|sin| (($ $) 10)) (|sech| (($ $) 28)) (|sec| (($ $) 9)) (|pi| (($) 16)) (|log| (($ $) 19)) (|exp| (($ $) 18)) (|csch| (($ $) 29)) (|csc| (($ $) 8)) (|coth| (($ $) 30)) (|cot| (($ $) 7)) (|cosh| (($ $) 31)) (|cos| (($ $) 6)) (|atanh| (($ $) 20)) (|atan| (($ $) 32)) (|asinh| (($ $) 21)) (|asin| (($ $) 33)) (|asech| (($ $) 22)) (|asec| (($ $) 34)) (|acsch| (($ $) 23)) (|acsc| (($ $) 35)) (|acoth| (($ $) 24)) (|acot| (($ $) 36)) (|acosh| (($ $) 25)) (|acos| (($ $) 37)) (** (($ $ $) 17))) 
(((|TranscendentalFunctionCategory|) (|Category|)) (T |TranscendentalFunctionCategory|)) 
((|pi| (*1 *1) (|ofCategory| *1 (|TranscendentalFunctionCategory|)))) 
(|Join| (|TrigonometricFunctionCategory|) (|ArcTrigonometricFunctionCategory|) (|HyperbolicFunctionCategory|) (|ArcHyperbolicFunctionCategory|) (|ElementaryFunctionCategory|) (CATEGORY |domain| (SIGNATURE |pi| ($)))) 
(((|ArcHyperbolicFunctionCategory|) . T) ((|ArcTrigonometricFunctionCategory|) . T) ((|ElementaryFunctionCategory|) . T) ((|HyperbolicFunctionCategory|) . T) ((|TrigonometricFunctionCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) 17)) (|tree| (($ |#1| (|List| $)) 23) (($ (|List| |#1|)) 27) (($ |#1|) 25)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 46)) (|setvalue!| ((|#1| $ |#1|) 14 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) 13 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sample| (($) NIL T CONST)) (|parts| (((|List| |#1|) $) 50 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) 41)) (|node?| (((|Boolean|) $ $) 32 (|has| |#1| (|SetCategory|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 39)) (|members| (((|List| |#1|) $) 51 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 49 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 24 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 22)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 38)) (|leaves| (((|List| |#1|) $) 36)) (|leaf?| (((|Boolean|) $) 35)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 48 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) NIL (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 73)) (|empty?| (((|Boolean|) $) 9)) (|empty| (($) 10)) (|elt| ((|#1| $ "value") NIL)) (|distance| (((|Integer|) $ $) 31)) (|cyclicParents| (((|List| $) $) 57)) (|cyclicEqual?| (((|Boolean|) $ $) 75)) (|cyclicEntries| (((|List| $) $) 70)) (|cyclicCopy| (($ $) 71)) (|cyclic?| (((|Boolean|) $) 54)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 20 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 16 (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#1| (|SetCategory|))))) (|copy| (($ $) 56)) (|coerce| (((|OutputForm|) $) 59 (|has| |#1| (|SetCategory|)))) (|children| (((|List| $) $) 12)) (|child?| (((|Boolean|) $ $) 29 (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 47 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 28 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 37 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|Tree| |#1|) (|Join| (|RecursiveAggregate| |#1|) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (ATTRIBUTE |shallowlyMutable|) (SIGNATURE |tree| ($ |#1| (|List| $))) (SIGNATURE |tree| ($ (|List| |#1|))) (SIGNATURE |tree| ($ |#1|)) (SIGNATURE |cyclic?| ((|Boolean|) $)) (SIGNATURE |cyclicCopy| ($ $)) (SIGNATURE |cyclicEntries| ((|List| $) $)) (SIGNATURE |cyclicEqual?| ((|Boolean|) $ $)) (SIGNATURE |cyclicParents| ((|List| $) $)))) (|SetCategory|)) (T |Tree|)) 
((|cyclic?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Tree| *3)) (|ofCategory| *3 (|SetCategory|)))) (|tree| (*1 *1 *2 *3) (AND (|isDomain| *3 (|List| (|Tree| *2))) (|isDomain| *1 (|Tree| *2)) (|ofCategory| *2 (|SetCategory|)))) (|tree| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Tree| *3)))) (|tree| (*1 *1 *2) (AND (|isDomain| *1 (|Tree| *2)) (|ofCategory| *2 (|SetCategory|)))) (|cyclicCopy| (*1 *1 *1) (AND (|isDomain| *1 (|Tree| *2)) (|ofCategory| *2 (|SetCategory|)))) (|cyclicEntries| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Tree| *3))) (|isDomain| *1 (|Tree| *3)) (|ofCategory| *3 (|SetCategory|)))) (|cyclicEqual?| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Tree| *3)) (|ofCategory| *3 (|SetCategory|)))) (|cyclicParents| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Tree| *3))) (|isDomain| *1 (|Tree| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(|Join| (|RecursiveAggregate| |#1|) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (ATTRIBUTE |shallowlyMutable|) (SIGNATURE |tree| ($ |#1| (|List| $))) (SIGNATURE |tree| ($ (|List| |#1|))) (SIGNATURE |tree| ($ |#1|)) (SIGNATURE |cyclic?| ((|Boolean|) $)) (SIGNATURE |cyclicCopy| ($ $)) (SIGNATURE |cyclicEntries| ((|List| $) $)) (SIGNATURE |cyclicEqual?| ((|Boolean|) $ $)) (SIGNATURE |cyclicParents| ((|List| $) $)))) 
((|tan| (($ $) 15)) (|sec| (($ $) 12)) (|csc| (($ $) 10)) (|cot| (($ $) 17))) 
(((|TrigonometricFunctionCategory&| |#1|) (CATEGORY |domain| (SIGNATURE |cot| (|#1| |#1|)) (SIGNATURE |csc| (|#1| |#1|)) (SIGNATURE |sec| (|#1| |#1|)) (SIGNATURE |tan| (|#1| |#1|))) (|TrigonometricFunctionCategory|)) (T |TrigonometricFunctionCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |cot| (|#1| |#1|)) (SIGNATURE |csc| (|#1| |#1|)) (SIGNATURE |sec| (|#1| |#1|)) (SIGNATURE |tan| (|#1| |#1|))) 
((|tan| (($ $) 11)) (|sin| (($ $) 10)) (|sec| (($ $) 9)) (|csc| (($ $) 8)) (|cot| (($ $) 7)) (|cos| (($ $) 6))) 
(((|TrigonometricFunctionCategory|) (|Category|)) (T |TrigonometricFunctionCategory|)) 
((|tan| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|))) (|sin| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|))) (|sec| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|))) (|csc| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|))) (|cot| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|))) (|cos| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|)))) 
(|Join| (CATEGORY |domain| (SIGNATURE |cos| ($ $)) (SIGNATURE |cot| ($ $)) (SIGNATURE |csc| ($ $)) (SIGNATURE |sec| ($ $)) (SIGNATURE |sin| ($ $)) (SIGNATURE |tan| ($ $)))) 
((|trigs| ((|#2| |#2|) 85)) (|real?| (((|Boolean|) |#2|) 25)) (|real| ((|#2| |#2|) 29)) (|imag| ((|#2| |#2|) 31)) (|complexNormalize| ((|#2| |#2| (|Symbol|)) 79) ((|#2| |#2|) 80)) (|complexForm| (((|Complex| |#2|) |#2|) 27)) (|complexElementary| ((|#2| |#2| (|Symbol|)) 81) ((|#2| |#2|) 82))) 
(((|TrigonometricManipulations| |#1| |#2|) (CATEGORY |package| (SIGNATURE |complexNormalize| (|#2| |#2|)) (SIGNATURE |complexNormalize| (|#2| |#2| (|Symbol|))) (SIGNATURE |complexElementary| (|#2| |#2|)) (SIGNATURE |complexElementary| (|#2| |#2| (|Symbol|))) (SIGNATURE |trigs| (|#2| |#2|)) (SIGNATURE |real| (|#2| |#2|)) (SIGNATURE |imag| (|#2| |#2|)) (SIGNATURE |real?| ((|Boolean|) |#2|)) (SIGNATURE |complexForm| ((|Complex| |#2|) |#2|))) (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|))) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |TrigonometricManipulations|)) 
((|complexForm| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Complex| *3)) (|isDomain| *1 (|TrigonometricManipulations| *4 *3)) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *4))))) (|real?| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|TrigonometricManipulations| *4 *3)) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *4))))) (|imag| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|TrigonometricManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *3))))) (|real| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|TrigonometricManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *3))))) (|trigs| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|TrigonometricManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *3))))) (|complexElementary| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|TrigonometricManipulations| *4 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *4))))) (|complexElementary| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|TrigonometricManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *3))))) (|complexNormalize| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|TrigonometricManipulations| *4 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *4))))) (|complexNormalize| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|GcdDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)))) (|isDomain| *1 (|TrigonometricManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *3)))))) 
(CATEGORY |package| (SIGNATURE |complexNormalize| (|#2| |#2|)) (SIGNATURE |complexNormalize| (|#2| |#2| (|Symbol|))) (SIGNATURE |complexElementary| (|#2| |#2|)) (SIGNATURE |complexElementary| (|#2| |#2| (|Symbol|))) (SIGNATURE |trigs| (|#2| |#2|)) (SIGNATURE |real| (|#2| |#2|)) (SIGNATURE |imag| (|#2| |#2|)) (SIGNATURE |real?| ((|Boolean|) |#2|)) (SIGNATURE |complexForm| ((|Complex| |#2|) |#2|))) 
((|UpTriBddDenomInv| ((|#4| |#4| |#1|) 27)) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) 28))) 
(((|TriangularMatrixOperations| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |UpTriBddDenomInv| (|#4| |#4| |#1|)) (SIGNATURE |LowTriBddDenomInv| (|#4| |#4| |#1|))) (|IntegralDomain|) (|FiniteLinearAggregate| |#1|) (|FiniteLinearAggregate| |#1|) (|MatrixCategory| |#1| |#2| |#3|)) (T |TriangularMatrixOperations|)) 
((|LowTriBddDenomInv| (*1 *2 *2 *3) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *1 (|TriangularMatrixOperations| *3 *4 *5 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *4 *5)))) (|UpTriBddDenomInv| (*1 *2 *2 *3) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *1 (|TriangularMatrixOperations| *3 *4 *5 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *4 *5))))) 
(CATEGORY |package| (SIGNATURE |UpTriBddDenomInv| (|#4| |#4| |#1|)) (SIGNATURE |LowTriBddDenomInv| (|#4| |#4| |#1|))) 
((|tanh2trigh| ((|#2| |#2|) 144)) (|tanh2coth| ((|#2| |#2|) 142)) (|tan2trig| ((|#2| |#2|) 134)) (|tan2cot| ((|#2| |#2|) 131)) (|sinh2csch| ((|#2| |#2|) 139)) (|sin2csc| ((|#2| |#2|) 127)) (|simplifyLog| ((|#2| |#2|) 59)) (|simplifyExp| ((|#2| |#2|) 109)) (|simplify| ((|#2| |#2|) 89)) (|sech2cosh| ((|#2| |#2|) 141)) (|sec2cos| ((|#2| |#2|) 129)) (|removeSinhSq| ((|#2| |#2|) 149)) (|removeSinSq| ((|#2| |#2|) 147)) (|removeCoshSq| ((|#2| |#2|) 148)) (|removeCosSq| ((|#2| |#2|) 146)) (|htrigs| ((|#2| |#2|) 158)) (|expandTrigProducts| ((|#2| |#2|) 48 (AND (|has| |#2| (|ConvertibleTo| (|Pattern| |#1|))) (|has| |#2| (|PatternMatchable| |#1|)) (|has| |#1| (|ConvertibleTo| (|Pattern| |#1|))) (|has| |#1| (|PatternMatchable| |#1|))))) (|expandPower| ((|#2| |#2|) 90)) (|expandLog| ((|#2| |#2|) 150)) (|expand| ((|#2| |#2|) 151)) (|csch2sinh| ((|#2| |#2|) 140)) (|csc2sin| ((|#2| |#2|) 128)) (|coth2trigh| ((|#2| |#2|) 145)) (|coth2tanh| ((|#2| |#2|) 143)) (|cot2trig| ((|#2| |#2|) 135)) (|cot2tan| ((|#2| |#2|) 133)) (|cosh2sech| ((|#2| |#2|) 137)) (|cos2sec| ((|#2| |#2|) 125))) 
(((|TranscendentalManipulations| |#1| |#2|) (CATEGORY |package| (SIGNATURE |expand| (|#2| |#2|)) (SIGNATURE |simplify| (|#2| |#2|)) (SIGNATURE |htrigs| (|#2| |#2|)) (SIGNATURE |simplifyExp| (|#2| |#2|)) (SIGNATURE |simplifyLog| (|#2| |#2|)) (SIGNATURE |expandPower| (|#2| |#2|)) (SIGNATURE |expandLog| (|#2| |#2|)) (SIGNATURE |cos2sec| (|#2| |#2|)) (SIGNATURE |cosh2sech| (|#2| |#2|)) (SIGNATURE |cot2trig| (|#2| |#2|)) (SIGNATURE |coth2trigh| (|#2| |#2|)) (SIGNATURE |csc2sin| (|#2| |#2|)) (SIGNATURE |csch2sinh| (|#2| |#2|)) (SIGNATURE |sec2cos| (|#2| |#2|)) (SIGNATURE |sech2cosh| (|#2| |#2|)) (SIGNATURE |sin2csc| (|#2| |#2|)) (SIGNATURE |sinh2csch| (|#2| |#2|)) (SIGNATURE |tan2trig| (|#2| |#2|)) (SIGNATURE |tanh2trigh| (|#2| |#2|)) (SIGNATURE |tan2cot| (|#2| |#2|)) (SIGNATURE |tanh2coth| (|#2| |#2|)) (SIGNATURE |cot2tan| (|#2| |#2|)) (SIGNATURE |coth2tanh| (|#2| |#2|)) (SIGNATURE |removeCosSq| (|#2| |#2|)) (SIGNATURE |removeSinSq| (|#2| |#2|)) (SIGNATURE |removeCoshSq| (|#2| |#2|)) (SIGNATURE |removeSinhSq| (|#2| |#2|)) (IF (|has| |#1| (|PatternMatchable| |#1|)) (IF (|has| |#1| (|ConvertibleTo| (|Pattern| |#1|))) (IF (|has| |#2| (|ConvertibleTo| (|Pattern| |#1|))) (IF (|has| |#2| (|PatternMatchable| |#1|)) (SIGNATURE |expandTrigProducts| (|#2| |#2|)) |noBranch|) |noBranch|) |noBranch|) |noBranch|)) (|Join| (|OrderedSet|) (|GcdDomain|)) (|Join| (|FunctionSpace| |#1|) (|TranscendentalFunctionCategory|))) (T |TranscendentalManipulations|)) 
((|expandTrigProducts| (*1 *2 *2) (AND (|ofCategory| *3 (|ConvertibleTo| (|Pattern| *3))) (|ofCategory| *3 (|PatternMatchable| *3)) (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|ConvertibleTo| (|Pattern| *3))) (|ofCategory| *2 (|PatternMatchable| *3)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|removeSinhSq| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|removeCoshSq| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|removeSinSq| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|removeCosSq| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|coth2tanh| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|cot2tan| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|tanh2coth| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|tan2cot| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|tanh2trigh| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|tan2trig| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|sinh2csch| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|sin2csc| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|sech2cosh| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|sec2cos| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|csch2sinh| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|csc2sin| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|coth2trigh| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|cot2trig| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|cosh2sech| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|cos2sec| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|expandLog| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|expandPower| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|simplifyLog| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|simplifyExp| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|htrigs| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|simplify| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|expand| (*1 *2 *2) (AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|GcdDomain|))) (|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|)))))) 
(CATEGORY |package| (SIGNATURE |expand| (|#2| |#2|)) (SIGNATURE |simplify| (|#2| |#2|)) (SIGNATURE |htrigs| (|#2| |#2|)) (SIGNATURE |simplifyExp| (|#2| |#2|)) (SIGNATURE |simplifyLog| (|#2| |#2|)) (SIGNATURE |expandPower| (|#2| |#2|)) (SIGNATURE |expandLog| (|#2| |#2|)) (SIGNATURE |cos2sec| (|#2| |#2|)) (SIGNATURE |cosh2sech| (|#2| |#2|)) (SIGNATURE |cot2trig| (|#2| |#2|)) (SIGNATURE |coth2trigh| (|#2| |#2|)) (SIGNATURE |csc2sin| (|#2| |#2|)) (SIGNATURE |csch2sinh| (|#2| |#2|)) (SIGNATURE |sec2cos| (|#2| |#2|)) (SIGNATURE |sech2cosh| (|#2| |#2|)) (SIGNATURE |sin2csc| (|#2| |#2|)) (SIGNATURE |sinh2csch| (|#2| |#2|)) (SIGNATURE |tan2trig| (|#2| |#2|)) (SIGNATURE |tanh2trigh| (|#2| |#2|)) (SIGNATURE |tan2cot| (|#2| |#2|)) (SIGNATURE |tanh2coth| (|#2| |#2|)) (SIGNATURE |cot2tan| (|#2| |#2|)) (SIGNATURE |coth2tanh| (|#2| |#2|)) (SIGNATURE |removeCosSq| (|#2| |#2|)) (SIGNATURE |removeSinSq| (|#2| |#2|)) (SIGNATURE |removeCoshSq| (|#2| |#2|)) (SIGNATURE |removeSinhSq| (|#2| |#2|)) (IF (|has| |#1| (|PatternMatchable| |#1|)) (IF (|has| |#1| (|ConvertibleTo| (|Pattern| |#1|))) (IF (|has| |#2| (|ConvertibleTo| (|Pattern| |#1|))) (IF (|has| |#2| (|PatternMatchable| |#1|)) (SIGNATURE |expandTrigProducts| (|#2| |#2|)) |noBranch|) |noBranch|) |noBranch|) |noBranch|)) 
((|stronglyReduced?| (((|Boolean|) |#5| $) 59) (((|Boolean|) $) 101)) (|stronglyReduce| ((|#5| |#5| $) 74)) (|select| (($ (|Mapping| (|Boolean|) |#5|) $) NIL) (((|Union| |#5| "failed") $ |#4|) 118)) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) 72)) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) 125)) (|rest| (((|Union| $ "failed") $) 111)) (|removeZero| ((|#5| |#5| $) 93)) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) 30)) (|reduceByQuasiMonic| ((|#5| |#5| $) 97)) (|reduce| ((|#5| (|Mapping| |#5| |#5| |#5|) $ |#5| |#5|) NIL) ((|#5| (|Mapping| |#5| |#5| |#5|) $ |#5|) NIL) ((|#5| (|Mapping| |#5| |#5| |#5|) $) NIL) ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) 68)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) 54)) (|normalized?| (((|Boolean|) |#5| $) 57) (((|Boolean|) $) 102)) (|mvar| ((|#4| $) 107)) (|last| (((|Union| |#5| "failed") $) 109)) (|initials| (((|List| |#5|) $) 48)) (|initiallyReduced?| (((|Boolean|) |#5| $) 66) (((|Boolean|) $) 106)) (|initiallyReduce| ((|#5| |#5| $) 80)) (|infRittWu?| (((|Boolean|) $ $) 26)) (|headReduced?| (((|Boolean|) |#5| $) 62) (((|Boolean|) $) 104)) (|headReduce| ((|#5| |#5| $) 77)) (|first| (((|Union| |#5| "failed") $) 108)) (|extend| (($ $ |#5|) 126)) (|degree| (((|NonNegativeInteger|) $) 51)) (|construct| (($ (|List| |#5|)) 123)) (|collectUpper| (($ $ |#4|) 121)) (|collectUnder| (($ $ |#4|) 120)) (|collectQuasiMonic| (($ $) 119)) (|coerce| (((|OutputForm|) $) NIL) (((|List| |#5|) $) 112)) (|coHeight| (((|NonNegativeInteger|) $) 129)) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) 42) (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) 44)) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) 99)) (|algebraicVariables| (((|List| |#4|) $) 114)) (|algebraic?| (((|Boolean|) |#4| $) 117)) (= (((|Boolean|) $ $) 19))) 
(((|TriangularSetCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |domain| (SIGNATURE |coHeight| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |extend| (|#1| |#1| |#5|)) (SIGNATURE |select| ((|Union| |#5| "failed") |#1| |#4|)) (SIGNATURE |algebraic?| ((|Boolean|) |#4| |#1|)) (SIGNATURE |algebraicVariables| ((|List| |#4|) |#1|)) (SIGNATURE |rest| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |last| ((|Union| |#5| "failed") |#1|)) (SIGNATURE |first| ((|Union| |#5| "failed") |#1|)) (SIGNATURE |reduceByQuasiMonic| (|#5| |#5| |#1|)) (SIGNATURE |collectQuasiMonic| (|#1| |#1|)) (SIGNATURE |removeZero| (|#5| |#5| |#1|)) (SIGNATURE |initiallyReduce| (|#5| |#5| |#1|)) (SIGNATURE |headReduce| (|#5| |#5| |#1|)) (SIGNATURE |stronglyReduce| (|#5| |#5| |#1|)) (SIGNATURE |rewriteSetWithReduction| ((|List| |#5|) (|List| |#5|) |#1| (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|))) (SIGNATURE |reduce| (|#5| |#5| |#1| (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|))) (SIGNATURE |initiallyReduced?| ((|Boolean|) |#1|)) (SIGNATURE |headReduced?| ((|Boolean|) |#1|)) (SIGNATURE |stronglyReduced?| ((|Boolean|) |#1|)) (SIGNATURE |autoReduced?| ((|Boolean|) |#1| (|Mapping| (|Boolean|) |#5| (|List| |#5|)))) (SIGNATURE |initiallyReduced?| ((|Boolean|) |#5| |#1|)) (SIGNATURE |headReduced?| ((|Boolean|) |#5| |#1|)) (SIGNATURE |stronglyReduced?| ((|Boolean|) |#5| |#1|)) (SIGNATURE |reduced?| ((|Boolean|) |#5| |#1| (|Mapping| (|Boolean|) |#5| |#5|))) (SIGNATURE |normalized?| ((|Boolean|) |#1|)) (SIGNATURE |normalized?| ((|Boolean|) |#5| |#1|)) (SIGNATURE |quasiComponent| ((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) |#1|)) (SIGNATURE |degree| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |initials| ((|List| |#5|) |#1|)) (SIGNATURE |basicSet| ((|Union| (|Record| (|:| |bas| |#1|) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|))) (SIGNATURE |basicSet| ((|Union| (|Record| (|:| |bas| |#1|) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|))) (SIGNATURE |infRittWu?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |collectUpper| (|#1| |#1| |#4|)) (SIGNATURE |collectUnder| (|#1| |#1| |#4|)) (SIGNATURE |mvar| (|#4| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#1| "failed") (|List| |#5|))) (SIGNATURE |coerce| ((|List| |#5|) |#1|)) (SIGNATURE |construct| (|#1| (|List| |#5|))) (SIGNATURE |reduce| (|#5| (|Mapping| |#5| |#5| |#5|) |#1|)) (SIGNATURE |reduce| (|#5| (|Mapping| |#5| |#5| |#5|) |#1| |#5|)) (SIGNATURE |select| (|#1| (|Mapping| (|Boolean|) |#5|) |#1|)) (SIGNATURE |reduce| (|#5| (|Mapping| |#5| |#5| |#5|) |#1| |#5| |#5|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|))) (|TriangularSetCategory| |#2| |#3| |#4| |#5|) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#2| |#3| |#4|)) (T |TriangularSetCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |coHeight| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |extend| (|#1| |#1| |#5|)) (SIGNATURE |select| ((|Union| |#5| "failed") |#1| |#4|)) (SIGNATURE |algebraic?| ((|Boolean|) |#4| |#1|)) (SIGNATURE |algebraicVariables| ((|List| |#4|) |#1|)) (SIGNATURE |rest| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |last| ((|Union| |#5| "failed") |#1|)) (SIGNATURE |first| ((|Union| |#5| "failed") |#1|)) (SIGNATURE |reduceByQuasiMonic| (|#5| |#5| |#1|)) (SIGNATURE |collectQuasiMonic| (|#1| |#1|)) (SIGNATURE |removeZero| (|#5| |#5| |#1|)) (SIGNATURE |initiallyReduce| (|#5| |#5| |#1|)) (SIGNATURE |headReduce| (|#5| |#5| |#1|)) (SIGNATURE |stronglyReduce| (|#5| |#5| |#1|)) (SIGNATURE |rewriteSetWithReduction| ((|List| |#5|) (|List| |#5|) |#1| (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|))) (SIGNATURE |reduce| (|#5| |#5| |#1| (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|))) (SIGNATURE |initiallyReduced?| ((|Boolean|) |#1|)) (SIGNATURE |headReduced?| ((|Boolean|) |#1|)) (SIGNATURE |stronglyReduced?| ((|Boolean|) |#1|)) (SIGNATURE |autoReduced?| ((|Boolean|) |#1| (|Mapping| (|Boolean|) |#5| (|List| |#5|)))) (SIGNATURE |initiallyReduced?| ((|Boolean|) |#5| |#1|)) (SIGNATURE |headReduced?| ((|Boolean|) |#5| |#1|)) (SIGNATURE |stronglyReduced?| ((|Boolean|) |#5| |#1|)) (SIGNATURE |reduced?| ((|Boolean|) |#5| |#1| (|Mapping| (|Boolean|) |#5| |#5|))) (SIGNATURE |normalized?| ((|Boolean|) |#1|)) (SIGNATURE |normalized?| ((|Boolean|) |#5| |#1|)) (SIGNATURE |quasiComponent| ((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) |#1|)) (SIGNATURE |degree| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |initials| ((|List| |#5|) |#1|)) (SIGNATURE |basicSet| ((|Union| (|Record| (|:| |bas| |#1|) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|))) (SIGNATURE |basicSet| ((|Union| (|Record| (|:| |bas| |#1|) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|))) (SIGNATURE |infRittWu?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |collectUpper| (|#1| |#1| |#4|)) (SIGNATURE |collectUnder| (|#1| |#1| |#4|)) (SIGNATURE |mvar| (|#4| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#1| "failed") (|List| |#5|))) (SIGNATURE |coerce| ((|List| |#5|) |#1|)) (SIGNATURE |construct| (|#1| (|List| |#5|))) (SIGNATURE |reduce| (|#5| (|Mapping| |#5| |#5| |#5|) |#1|)) (SIGNATURE |reduce| (|#5| (|Mapping| |#5| |#5| |#5|) |#1| |#5|)) (SIGNATURE |select| (|#1| (|Mapping| (|Boolean|) |#5|) |#1|)) (SIGNATURE |reduce| (|#5| (|Mapping| |#5| |#5| |#5|) |#1| |#5| |#5|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 78)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 79)) (|variables| (((|List| |#3|) $) 32)) (|trivialIdeal?| (((|Boolean|) $) 25)) (|triangular?| (((|Boolean|) $) 16 (|has| |#1| (|IntegralDomain|)))) (|stronglyReduced?| (((|Boolean|) |#4| $) 94) (((|Boolean|) $) 90)) (|stronglyReduce| ((|#4| |#4| $) 85)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 26)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 43)) (|select| (($ (|Mapping| (|Boolean|) |#4|) $) 64 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| |#4| "failed") $ |#3|) 72)) (|sample| (($) 44 T CONST)) (|roughUnitIdeal?| (((|Boolean|) $) 21 (|has| |#1| (|IntegralDomain|)))) (|roughSubIdeal?| (((|Boolean|) $ $) 23 (|has| |#1| (|IntegralDomain|)))) (|roughEqualIdeals?| (((|Boolean|) $ $) 22 (|has| |#1| (|IntegralDomain|)))) (|roughBase?| (((|Boolean|) $) 24 (|has| |#1| (|IntegralDomain|)))) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 86)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) 17 (|has| |#1| (|IntegralDomain|)))) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) 18 (|has| |#1| (|IntegralDomain|)))) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 35)) (|retract| (($ (|List| |#4|)) 34)) (|rest| (((|Union| $ "failed") $) 75)) (|removeZero| ((|#4| |#4| $) 82)) (|removeDuplicates| (($ $) 67 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|remove| (($ |#4| $) 66 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (($ (|Mapping| (|Boolean|) |#4|) $) 63 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 19 (|has| |#1| (|IntegralDomain|)))) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) 95)) (|reduceByQuasiMonic| ((|#4| |#4| $) 80)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 65 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 62 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 61 (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 87)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 98)) (|parts| (((|List| |#4|) $) 51 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|normalized?| (((|Boolean|) |#4| $) 97) (((|Boolean|) $) 96)) (|mvar| ((|#3| $) 33)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 42)) (|members| (((|List| |#4|) $) 52 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#4| $) 54 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#4| |#4|) $) 47 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#4| |#4|) $) 46)) (|mainVariables| (((|List| |#3|) $) 31)) (|mainVariable?| (((|Boolean|) |#3| $) 30)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 41)) (|latex| (((|String|) $) 9)) (|last| (((|Union| |#4| "failed") $) 76)) (|initials| (((|List| |#4|) $) 100)) (|initiallyReduced?| (((|Boolean|) |#4| $) 92) (((|Boolean|) $) 88)) (|initiallyReduce| ((|#4| |#4| $) 83)) (|infRittWu?| (((|Boolean|) $ $) 103)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 20 (|has| |#1| (|IntegralDomain|)))) (|headReduced?| (((|Boolean|) |#4| $) 93) (((|Boolean|) $) 89)) (|headReduce| ((|#4| |#4| $) 84)) (|hash| (((|SingleInteger|) $) 10)) (|first| (((|Union| |#4| "failed") $) 77)) (|find| (((|Union| |#4| "failed") (|Mapping| (|Boolean|) |#4|) $) 60)) (|extendIfCan| (((|Union| $ "failed") $ |#4|) 71)) (|extend| (($ $ |#4|) 70)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) 49 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 58 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ |#4| |#4|) 57 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|Equation| |#4|)) 56 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|List| (|Equation| |#4|))) 55 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 37)) (|empty?| (((|Boolean|) $) 40)) (|empty| (($) 39)) (|degree| (((|NonNegativeInteger|) $) 99)) (|count| (((|NonNegativeInteger|) |#4| $) 53 (AND (|has| |#4| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#4|) $) 50 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) 38)) (|convert| (((|InputForm|) $) 68 (|has| |#4| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#4|)) 59)) (|collectUpper| (($ $ |#3|) 27)) (|collectUnder| (($ $ |#3|) 29)) (|collectQuasiMonic| (($ $) 81)) (|collect| (($ $ |#3|) 28)) (|coerce| (((|OutputForm|) $) 11) (((|List| |#4|) $) 36)) (|coHeight| (((|NonNegativeInteger|) $) 69 (|has| |#3| (|Finite|)))) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 102) (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 101)) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) 91)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) 48 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|algebraicVariables| (((|List| |#3|) $) 74)) (|algebraic?| (((|Boolean|) |#3| $) 73)) (= (((|Boolean|) $ $) 6)) (|#| (((|NonNegativeInteger|) $) 45 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|TriangularSetCategory| |#1| |#2| |#3| |#4|) (|Category|) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |t#1| |t#2| |t#3|)) (T |TriangularSetCategory|)) 
((|infRittWu?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Boolean|)))) (|basicSet| (*1 *2 *3 *4) (|partial| AND (|isDomain| *4 (|Mapping| (|Boolean|) *8 *8)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |bas| *1) (|:| |top| (|List| *8)))) (|isDomain| *3 (|List| *8)) (|ofCategory| *1 (|TriangularSetCategory| *5 *6 *7 *8)))) (|basicSet| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *4 (|Mapping| (|Boolean|) *9)) (|isDomain| *5 (|Mapping| (|Boolean|) *9 *9)) (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8)) (|ofCategory| *6 (|IntegralDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |bas| *1) (|:| |top| (|List| *9)))) (|isDomain| *3 (|List| *9)) (|ofCategory| *1 (|TriangularSetCategory| *6 *7 *8 *9)))) (|initials| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|List| *6)))) (|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|NonNegativeInteger|)))) (|quasiComponent| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Record| (|:| |close| (|List| *6)) (|:| |open| (|List| *6)))))) (|normalized?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|normalized?| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Boolean|)))) (|reduced?| (*1 *2 *3 *1 *4) (AND (|isDomain| *4 (|Mapping| (|Boolean|) *3 *3)) (|ofCategory| *1 (|TriangularSetCategory| *5 *6 *7 *3)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Boolean|)))) (|stronglyReduced?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|headReduced?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|initiallyReduced?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|autoReduced?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *7 (|List| *7))) (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *7)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|stronglyReduced?| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Boolean|)))) (|headReduced?| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Boolean|)))) (|initiallyReduced?| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Boolean|)))) (|reduce| (*1 *2 *2 *1 *3 *4) (AND (|isDomain| *3 (|Mapping| *2 *2 *2)) (|isDomain| *4 (|Mapping| (|Boolean|) *2 *2)) (|ofCategory| *1 (|TriangularSetCategory| *5 *6 *7 *2)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *5 *6 *7)))) (|rewriteSetWithReduction| (*1 *2 *2 *1 *3 *4) (AND (|isDomain| *2 (|List| *8)) (|isDomain| *3 (|Mapping| *8 *8 *8)) (|isDomain| *4 (|Mapping| (|Boolean|) *8 *8)) (|ofCategory| *1 (|TriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)))) (|stronglyReduce| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|headReduce| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|initiallyReduce| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|removeZero| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|collectQuasiMonic| (*1 *1 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *2 *3 *4 *5)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|RecursivePolynomialCategory| *2 *3 *4)))) (|reduceByQuasiMonic| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|zeroSetSplit| (*1 *2 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *7)))) (|zeroSetSplitIntoTriangularSystems| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| (|Record| (|:| |close| *1) (|:| |open| (|List| *7))))) (|isDomain| *3 (|List| *7)) (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *7)))) (|first| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|last| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|rest| (*1 *1 *1) (|partial| AND (|ofCategory| *1 (|TriangularSetCategory| *2 *3 *4 *5)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|RecursivePolynomialCategory| *2 *3 *4)))) (|algebraicVariables| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|List| *5)))) (|algebraic?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *3 *6)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *4 *5 *3)) (|isDomain| *2 (|Boolean|)))) (|select| (*1 *2 *1 *3) (|partial| AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *3 *2)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *4 *5 *3)))) (|extendIfCan| (*1 *1 *1 *2) (|partial| AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|extend| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|coHeight| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *5 (|Finite|)) (|isDomain| *2 (|NonNegativeInteger|))))) 
(|Join| (|PolynomialSetCategory| |t#1| |t#2| |t#3| |t#4|) (CATEGORY |domain| (ATTRIBUTE |finiteAggregate|) (ATTRIBUTE |shallowlyMutable|) (SIGNATURE |infRittWu?| ((|Boolean|) $ $)) (SIGNATURE |basicSet| ((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |t#4|))) "failed") (|List| |t#4|) (|Mapping| (|Boolean|) |t#4| |t#4|))) (SIGNATURE |basicSet| ((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |t#4|))) "failed") (|List| |t#4|) (|Mapping| (|Boolean|) |t#4|) (|Mapping| (|Boolean|) |t#4| |t#4|))) (SIGNATURE |initials| ((|List| |t#4|) $)) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |quasiComponent| ((|Record| (|:| |close| (|List| |t#4|)) (|:| |open| (|List| |t#4|))) $)) (SIGNATURE |normalized?| ((|Boolean|) |t#4| $)) (SIGNATURE |normalized?| ((|Boolean|) $)) (SIGNATURE |reduced?| ((|Boolean|) |t#4| $ (|Mapping| (|Boolean|) |t#4| |t#4|))) (SIGNATURE |stronglyReduced?| ((|Boolean|) |t#4| $)) (SIGNATURE |headReduced?| ((|Boolean|) |t#4| $)) (SIGNATURE |initiallyReduced?| ((|Boolean|) |t#4| $)) (SIGNATURE |autoReduced?| ((|Boolean|) $ (|Mapping| (|Boolean|) |t#4| (|List| |t#4|)))) (SIGNATURE |stronglyReduced?| ((|Boolean|) $)) (SIGNATURE |headReduced?| ((|Boolean|) $)) (SIGNATURE |initiallyReduced?| ((|Boolean|) $)) (SIGNATURE |reduce| (|t#4| |t#4| $ (|Mapping| |t#4| |t#4| |t#4|) (|Mapping| (|Boolean|) |t#4| |t#4|))) (SIGNATURE |rewriteSetWithReduction| ((|List| |t#4|) (|List| |t#4|) $ (|Mapping| |t#4| |t#4| |t#4|) (|Mapping| (|Boolean|) |t#4| |t#4|))) (SIGNATURE |stronglyReduce| (|t#4| |t#4| $)) (SIGNATURE |headReduce| (|t#4| |t#4| $)) (SIGNATURE |initiallyReduce| (|t#4| |t#4| $)) (SIGNATURE |removeZero| (|t#4| |t#4| $)) (SIGNATURE |collectQuasiMonic| ($ $)) (SIGNATURE |reduceByQuasiMonic| (|t#4| |t#4| $)) (SIGNATURE |zeroSetSplit| ((|List| $) (|List| |t#4|))) (SIGNATURE |zeroSetSplitIntoTriangularSystems| ((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |t#4|)))) (|List| |t#4|))) (SIGNATURE |first| ((|Union| |t#4| "failed") $)) (SIGNATURE |last| ((|Union| |t#4| "failed") $)) (SIGNATURE |rest| ((|Union| $ "failed") $)) (SIGNATURE |algebraicVariables| ((|List| |t#3|) $)) (SIGNATURE |algebraic?| ((|Boolean|) |t#3| $)) (SIGNATURE |select| ((|Union| |t#4| "failed") $ |t#3|)) (SIGNATURE |extendIfCan| ((|Union| $ "failed") $ |t#4|)) (SIGNATURE |extend| ($ $ |t#4|)) (IF (|has| |t#3| (|Finite|)) (SIGNATURE |coHeight| ((|NonNegativeInteger|) $)) |noBranch|))) 
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(((|TaylorSeries| |#1|) (|Join| (|MultivariateTaylorSeriesCategory| |#1| (|Symbol|)) (CATEGORY |domain| (SIGNATURE |coefficient| ((|Polynomial| |#1|) $ (|NonNegativeInteger|))) (SIGNATURE |coerce| ($ (|Symbol|))) (SIGNATURE |coerce| ($ (|Polynomial| |#1|))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |integrate| ($ $ (|Symbol|) |#1|)) (SIGNATURE |fintegrate| ($ (|Mapping| $) (|Symbol|) |#1|))) |noBranch|))) (|Ring|)) (T |TaylorSeries|)) 
((|coefficient| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Polynomial| *4)) (|isDomain| *1 (|TaylorSeries| *4)) (|ofCategory| *4 (|Ring|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|TaylorSeries| *3)) (|ofCategory| *3 (|Ring|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|TaylorSeries| *3)))) (|integrate| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|TaylorSeries| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *3 (|Ring|)))) (|fintegrate| (*1 *1 *2 *3 *4) (AND (|isDomain| *2 (|Mapping| (|TaylorSeries| *4))) (|isDomain| *3 (|Symbol|)) (|isDomain| *1 (|TaylorSeries| *4)) (|ofCategory| *4 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *4 (|Ring|))))) 
(|Join| (|MultivariateTaylorSeriesCategory| |#1| (|Symbol|)) (CATEGORY |domain| (SIGNATURE |coefficient| ((|Polynomial| |#1|) $ (|NonNegativeInteger|))) (SIGNATURE |coerce| ($ (|Symbol|))) (SIGNATURE |coerce| ($ (|Polynomial| |#1|))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |integrate| ($ $ (|Symbol|) |#1|)) (SIGNATURE |fintegrate| ($ (|Mapping| $) (|Symbol|) |#1|))) |noBranch|))) 
((|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) 15)) (|setClosed| (((|Boolean|) $ (|Boolean|)) 14)) (|open?| (((|Boolean|) $) 13)) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) 10)) (|getCurve| ((|#1| $) 8)) (|closed?| (((|Boolean|) $) 12))) 
(((|TubePlot| |#1|) (CATEGORY |domain| (SIGNATURE |getCurve| (|#1| $)) (SIGNATURE |listLoops| ((|List| (|List| (|Point| (|DoubleFloat|)))) $)) (SIGNATURE |closed?| ((|Boolean|) $)) (SIGNATURE |open?| ((|Boolean|) $)) (SIGNATURE |setClosed| ((|Boolean|) $ (|Boolean|))) (SIGNATURE |tube| ($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)))) (|PlottableSpaceCurveCategory|)) (T |TubePlot|)) 
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(((|TubePlotTools|) (CATEGORY |package| (SIGNATURE |point| ((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (SIGNATURE * ((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|)))) (SIGNATURE + ((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) (SIGNATURE - ((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) (SIGNATURE |dot| ((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) (SIGNATURE |cross| ((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) (SIGNATURE |unitVector| ((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) (SIGNATURE |cosSinInfo| ((|List| (|List| (|DoubleFloat|))) (|Integer|))) (SIGNATURE |loopPoints| ((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|))))))) (T |TubePlotTools|)) 
((|loopPoints| (*1 *2 *3 *3 *3 *4 *5) (AND (|isDomain| *5 (|List| (|List| (|DoubleFloat|)))) (|isDomain| *4 (|DoubleFloat|)) (|isDomain| *2 (|List| (|Point| *4))) (|isDomain| *1 (|TubePlotTools|)) (|isDomain| *3 (|Point| *4)))) (|cosSinInfo| (*1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|List| (|List| (|DoubleFloat|)))) (|isDomain| *1 (|TubePlotTools|)))) (|unitVector| (*1 *2 *2) (AND (|isDomain| *2 (|Point| (|DoubleFloat|))) (|isDomain| *1 (|TubePlotTools|)))) (|cross| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Point| (|DoubleFloat|))) (|isDomain| *1 (|TubePlotTools|)))) (|dot| (*1 *2 *3 *3) (AND (|isDomain| *3 (|Point| (|DoubleFloat|))) (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|TubePlotTools|)))) (- (*1 *2 *2 *2) (AND (|isDomain| *2 (|Point| (|DoubleFloat|))) (|isDomain| *1 (|TubePlotTools|)))) (+ (*1 *2 *2 *2) (AND (|isDomain| *2 (|Point| (|DoubleFloat|))) (|isDomain| *1 (|TubePlotTools|)))) (* (*1 *2 *3 *2) (AND (|isDomain| *2 (|Point| (|DoubleFloat|))) (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *1 (|TubePlotTools|)))) (|point| (*1 *2 *3 *3 *3 *3) (AND (|isDomain| *2 (|Point| (|DoubleFloat|))) (|isDomain| *1 (|TubePlotTools|)) (|isDomain| *3 (|DoubleFloat|))))) 
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(((|Tuple| |#1|) (|Join| (|CoercibleTo| (|PrimitiveArray| |#1|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|PrimitiveArray| |#1|))) (SIGNATURE |select| (|#1| $ (|NonNegativeInteger|))) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (IF (|has| |#1| (|SetCategory|)) (ATTRIBUTE (|SetCategory|)) |noBranch|))) (|Type|)) (T |Tuple|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|PrimitiveArray| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|Tuple| *3)))) (|select| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|Tuple| *2)) (|ofCategory| *2 (|Type|)))) (|length| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Tuple| *3)) (|ofCategory| *3 (|Type|))))) 
(|Join| (|CoercibleTo| (|PrimitiveArray| |#1|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|PrimitiveArray| |#1|))) (SIGNATURE |select| (|#1| $ (|NonNegativeInteger|))) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (IF (|has| |#1| (|SetCategory|)) (ATTRIBUTE (|SetCategory|)) |noBranch|))) 
((|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) 79)) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) 73)) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) 58))) 
(((|TwoFactorize| |#1|) (CATEGORY |package| (SIGNATURE |generalTwoFactor| ((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)))) (SIGNATURE |generalSqFr| ((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)))) (SIGNATURE |twoFactor| ((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)))) (|FiniteFieldCategory|)) (T |TwoFactorize|)) 
((|twoFactor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Integer|)) (|ofCategory| *5 (|FiniteFieldCategory|)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *5)))) (|isDomain| *1 (|TwoFactorize| *5)) (|isDomain| *3 (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *5))))) (|generalSqFr| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4)))) (|isDomain| *1 (|TwoFactorize| *4)) (|isDomain| *3 (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4))))) (|generalTwoFactor| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4)))) (|isDomain| *1 (|TwoFactorize| *4)) (|isDomain| *3 (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4)))))) 
(CATEGORY |package| (SIGNATURE |generalTwoFactor| ((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)))) (SIGNATURE |generalSqFr| ((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)))) (SIGNATURE |twoFactor| ((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)))) 
NIL 
(((|Type|) (|Category|)) (T |Type|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
((~= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|SetCategory|)))) (|zero?| (((|Boolean|) $) NIL)) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) NIL)) (|vertConcat| (($ $ $) NIL)) (|transpose| (($ (|U16Vector|)) NIL) (($ $) NIL)) (|symmetric?| (((|Boolean|) $) NIL)) (|swapRows!| (($ $ (|Integer|) (|Integer|)) NIL)) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) NIL)) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) NIL)) (|squareTop| (($ $) NIL)) (|square?| (((|Boolean|) $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) NIL)) (|setelt| (((|Integer|) $ (|Integer|) (|Integer|) (|Integer|)) 17) (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) NIL)) (|setRow!| (($ $ (|Integer|) (|U16Vector|)) NIL)) (|setColumn!| (($ $ (|Integer|) (|U16Vector|)) NIL)) (|scalarMatrix| (($ (|NonNegativeInteger|) (|Integer|)) NIL)) (|sample| (($) NIL T CONST)) (|rowEchelon| (($ $) NIL (|has| (|Integer|) (|EuclideanDomain|)))) (|row| (((|U16Vector|) $ (|Integer|)) NIL)) (|rank| (((|NonNegativeInteger|) $) NIL (|has| (|Integer|) (|IntegralDomain|)))) (|qsetelt!| (((|Integer|) $ (|Integer|) (|Integer|) (|Integer|)) 16)) (|qnew| (($ (|Integer|) (|Integer|)) 19)) (|qelt| (((|Integer|) $ (|Integer|) (|Integer|)) 14)) (|pfaffian| (((|Integer|) $) NIL (|has| (|Integer|) (|CommutativeRing|)))) (|parts| (((|List| (|Integer|)) $) NIL)) (|nullity| (((|NonNegativeInteger|) $) NIL (|has| (|Integer|) (|IntegralDomain|)))) (|nullSpace| (((|List| (|U16Vector|)) $) NIL (|has| (|Integer|) (|IntegralDomain|)))) (|nrows| (((|NonNegativeInteger|) $) 10)) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) 20)) (|ncols| (((|NonNegativeInteger|) $) 11)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minordet| (((|Integer|) $) NIL (|has| (|Integer|) (ATTRIBUTE (|commutative| "*"))))) (|minRowIndex| (((|Integer|) $) 7)) (|minColIndex| (((|Integer|) $) 8)) (|members| (((|List| (|Integer|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|Integer|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Integer|) (|SetCategory|))))) (|maxRowIndex| (((|Integer|) $) 12)) (|maxColIndex| (((|Integer|) $) 13)) (|matrix| (($ (|List| (|List| (|Integer|)))) NIL) (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| (|Integer|) (|Integer|) (|Integer|))) NIL)) (|map!| (($ (|Mapping| (|Integer|) (|Integer|)) $) NIL)) (|map| (($ (|Mapping| (|Integer|) (|Integer|)) $) NIL) (($ (|Mapping| (|Integer|) (|Integer|) (|Integer|)) $ $) NIL) (($ (|Mapping| (|Integer|) (|Integer|) (|Integer|)) $ $ (|Integer|)) NIL)) (|listOfLists| (((|List| (|List| (|Integer|))) $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| (|Integer|) (|SetCategory|)))) (|inverse| (((|Union| $ "failed") $) NIL (|has| (|Integer|) (|Field|)))) (|horizConcat| (($ $ $) NIL)) (|hash| (((|SingleInteger|) $) NIL (|has| (|Integer|) (|SetCategory|)))) (|fill!| (($ $ (|Integer|)) NIL)) (|exquo| (((|Union| $ "failed") $ (|Integer|)) NIL (|has| (|Integer|) (|IntegralDomain|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) (|Integer|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| (|Integer|)))) NIL (AND (|has| (|Integer|) (|Evalable| (|Integer|))) (|has| (|Integer|) (|SetCategory|)))) (($ $ (|Equation| (|Integer|))) NIL (AND (|has| (|Integer|) (|Evalable| (|Integer|))) (|has| (|Integer|) (|SetCategory|)))) (($ $ (|Integer|) (|Integer|)) NIL (AND (|has| (|Integer|) (|Evalable| (|Integer|))) (|has| (|Integer|) (|SetCategory|)))) (($ $ (|List| (|Integer|)) (|List| (|Integer|))) NIL (AND (|has| (|Integer|) (|Evalable| (|Integer|))) (|has| (|Integer|) (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) 18)) (|elt| (((|Integer|) $ (|Integer|) (|Integer|)) 15) (((|Integer|) $ (|Integer|) (|Integer|) (|Integer|)) NIL) (($ $ (|List| (|Integer|)) (|List| (|Integer|))) NIL)) (|diagonalMatrix| (($ (|List| (|Integer|))) NIL) (($ (|List| $)) NIL)) (|diagonal?| (((|Boolean|) $) NIL)) (|determinant| (((|Integer|) $) NIL (|has| (|Integer|) (ATTRIBUTE (|commutative| "*"))))) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|Integer|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) (|Integer|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Integer|) (|SetCategory|))))) (|copy| (($ $) NIL)) (|columnSpace| (((|List| (|U16Vector|)) $) NIL (|has| (|Integer|) (|EuclideanDomain|)))) (|column| (((|U16Vector|) $ (|Integer|)) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| (|Integer|) (|SetCategory|))) (($ (|U16Vector|)) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|Integer|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|antisymmetric?| (((|Boolean|) $) NIL)) (= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|SetCategory|)))) (/ (($ $ (|Integer|)) NIL (|has| (|Integer|) (|Field|)))) (- (($ $ $) NIL) (($ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| (|Integer|) (|Field|)))) (* (($ $ $) NIL) (($ (|Integer|) $) NIL) (($ $ (|Integer|)) NIL) (($ (|Integer|) $) NIL) (((|U16Vector|) $ (|U16Vector|)) NIL) (((|U16Vector|) (|U16Vector|) $) NIL)) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|U16Matrix|) (|Join| (|MatrixCategory| (|Integer|) (|U16Vector|) (|U16Vector|)) (CATEGORY |domain| (SIGNATURE |qnew| ($ (|Integer|) (|Integer|)))))) (T |U16Matrix|)) 
((|qnew| (*1 *1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|U16Matrix|))))) 
(|Join| (|MatrixCategory| (|Integer|) (|U16Vector|) (|U16Vector|)) (CATEGORY |domain| (SIGNATURE |qnew| ($ (|Integer|) (|Integer|))))) 
((~= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|SetCategory|)))) (|swap!| (((|Void|) $ (|Integer|) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) (|Integer|) (|Integer|)) $) NIL) (((|Boolean|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|sort!| (($ (|Mapping| (|Boolean|) (|Integer|) (|Integer|)) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $) NIL (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|has| (|Integer|) (|OrderedSet|))))) (|sort| (($ (|Mapping| (|Boolean|) (|Integer|) (|Integer|)) $) NIL) (($ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setelt| (((|Integer|) $ (|Integer|) (|Integer|)) 15 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (((|Integer|) $ (|UniversalSegment| (|Integer|)) (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|select| (($ (|Mapping| (|Boolean|) (|Integer|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|sample| (($) NIL T CONST)) (|reverse!| (($ $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|reverse| (($ $) NIL)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Integer|) (|SetCategory|))))) (|remove| (($ (|Integer|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Integer|) (|SetCategory|)))) (($ (|Mapping| (|Boolean|) (|Integer|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|reduce| (((|Integer|) (|Mapping| (|Integer|) (|Integer|) (|Integer|)) $ (|Integer|) (|Integer|)) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Integer|) (|SetCategory|)))) (((|Integer|) (|Mapping| (|Integer|) (|Integer|) (|Integer|)) $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Integer|) (|Mapping| (|Integer|) (|Integer|) (|Integer|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|qsetelt!| (((|Integer|) $ (|Integer|) (|Integer|)) 14 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|qelt| (((|Integer|) $ (|Integer|)) 12)) (|position| (((|Integer|) (|Mapping| (|Boolean|) (|Integer|)) $) NIL) (((|Integer|) (|Integer|) $) NIL (|has| (|Integer|) (|SetCategory|))) (((|Integer|) (|Integer|) $ (|Integer|)) NIL (|has| (|Integer|) (|SetCategory|)))) (|parts| (((|List| (|Integer|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|new| (($ (|NonNegativeInteger|) (|Integer|)) 11)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minIndex| (((|Integer|) $) 9 (|has| (|Integer|) (|OrderedSet|)))) (|min| (($ $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|merge| (($ (|Mapping| (|Boolean|) (|Integer|) (|Integer|)) $ $) NIL) (($ $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|members| (((|List| (|Integer|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) (|Integer|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Integer|) (|SetCategory|))))) (|maxIndex| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|map!| (($ (|Mapping| (|Integer|) (|Integer|)) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| (|Integer|) (|Integer|)) $) NIL) (($ (|Mapping| (|Integer|) (|Integer|) (|Integer|)) $ $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL (|has| (|Integer|) (|SetCategory|)))) (|insert| (($ (|Integer|) $ (|Integer|)) NIL) (($ $ $ (|Integer|)) NIL)) (|indices| (((|List| (|Integer|)) $) NIL)) (|index?| (((|Boolean|) (|Integer|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL (|has| (|Integer|) (|SetCategory|)))) (|first| (((|Integer|) $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|find| (((|Union| (|Integer|) "failed") (|Mapping| (|Boolean|) (|Integer|)) $) NIL)) (|fill!| (($ $ (|Integer|)) 16 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) (|Integer|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| (|Integer|)))) NIL (AND (|has| (|Integer|) (|Evalable| (|Integer|))) (|has| (|Integer|) (|SetCategory|)))) (($ $ (|Equation| (|Integer|))) NIL (AND (|has| (|Integer|) (|Evalable| (|Integer|))) (|has| (|Integer|) (|SetCategory|)))) (($ $ (|Integer|) (|Integer|)) NIL (AND (|has| (|Integer|) (|Evalable| (|Integer|))) (|has| (|Integer|) (|SetCategory|)))) (($ $ (|List| (|Integer|)) (|List| (|Integer|))) NIL (AND (|has| (|Integer|) (|Evalable| (|Integer|))) (|has| (|Integer|) (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|entry?| (((|Boolean|) (|Integer|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Integer|) (|SetCategory|))))) (|entries| (((|List| (|Integer|)) $) NIL)) (|empty?| (((|Boolean|) $) NIL)) (|empty| (($) 10)) (|elt| (((|Integer|) $ (|Integer|) (|Integer|)) NIL) (((|Integer|) $ (|Integer|)) 13) (($ $ (|UniversalSegment| (|Integer|))) NIL)) (|delete| (($ $ (|Integer|)) NIL) (($ $ (|UniversalSegment| (|Integer|))) NIL)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) (|Integer|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) (|Integer|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Integer|) (|SetCategory|))))) (|copyInto!| (($ $ $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) NIL (|has| (|Integer|) (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| (|Integer|))) NIL)) (|concat| (($ $ (|Integer|)) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ (|List| $)) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| (|Integer|) (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|Integer|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (>= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|SetCategory|)))) (<= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|#| (((|NonNegativeInteger|) $) 7 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|U16Vector|) (|OneDimensionalArrayAggregate| (|Integer|))) (T |U16Vector|)) 
NIL 
(|OneDimensionalArrayAggregate| (|Integer|)) 
((~= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|SetCategory|)))) (|zero?| (((|Boolean|) $) NIL)) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) NIL)) (|vertConcat| (($ $ $) NIL)) (|transpose| (($ (|U32Vector|)) NIL) (($ $) NIL)) (|symmetric?| (((|Boolean|) $) NIL)) (|swapRows!| (($ $ (|Integer|) (|Integer|)) NIL)) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) NIL)) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) NIL)) (|squareTop| (($ $) NIL)) (|square?| (((|Boolean|) $) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) NIL)) (|setelt| (((|Integer|) $ (|Integer|) (|Integer|) (|Integer|)) 17) (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) NIL)) (|setRow!| (($ $ (|Integer|) (|U32Vector|)) NIL)) (|setColumn!| (($ $ (|Integer|) (|U32Vector|)) NIL)) (|scalarMatrix| (($ (|NonNegativeInteger|) (|Integer|)) NIL)) (|sample| (($) NIL T CONST)) (|rowEchelon| (($ $) NIL (|has| (|Integer|) (|EuclideanDomain|)))) (|row| (((|U32Vector|) $ (|Integer|)) NIL)) (|rank| (((|NonNegativeInteger|) $) NIL (|has| (|Integer|) (|IntegralDomain|)))) (|qsetelt!| (((|Integer|) $ (|Integer|) (|Integer|) (|Integer|)) 16)) (|qnew| (($ (|Integer|) (|Integer|)) 19)) (|qelt| (((|Integer|) $ (|Integer|) (|Integer|)) 14)) (|pfaffian| (((|Integer|) $) NIL (|has| (|Integer|) (|CommutativeRing|)))) (|parts| (((|List| (|Integer|)) $) NIL)) (|nullity| (((|NonNegativeInteger|) $) NIL (|has| (|Integer|) (|IntegralDomain|)))) (|nullSpace| (((|List| (|U32Vector|)) $) NIL (|has| (|Integer|) (|IntegralDomain|)))) (|nrows| (((|NonNegativeInteger|) $) 10)) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) 20)) (|ncols| (((|NonNegativeInteger|) $) 11)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|minordet| (((|Integer|) $) NIL (|has| (|Integer|) (ATTRIBUTE (|commutative| "*"))))) (|minRowIndex| (((|Integer|) $) 7)) (|minColIndex| (((|Integer|) $) 8)) (|members| (((|List| 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|finiteAggregate|))) (((|NonNegativeInteger|) (|Integer|) $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| (|Integer|) (|SetCategory|))))) (|copyInto!| (($ $ $ (|Integer|)) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) NIL (|has| (|Integer|) (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| (|Integer|))) NIL)) (|concat| (($ $ (|Integer|)) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ (|List| $)) NIL)) (|coerce| (((|OutputForm|) $) NIL (|has| (|Integer|) (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) (|Integer|)) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (>= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|SetCategory|)))) (<= (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| (|Integer|) (|OrderedSet|)))) (|#| (((|NonNegativeInteger|) $) 7 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|U8Vector|) (|OneDimensionalArrayAggregate| (|Integer|))) (T |U8Vector|)) 
NIL 
(|OneDimensionalArrayAggregate| (|Integer|)) 
((|userOrdered?| (((|Boolean|)) 14)) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) 18) (((|Void|) (|List| |#1|)) 19)) (|more?| (((|Boolean|) |#1| |#1|) 30 (|has| |#1| (|OrderedSet|)))) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) 26) (((|Union| (|Boolean|) "failed") |#1| |#1|) 24)) (|largest| ((|#1| (|List| |#1|)) 31 (|has| |#1| (|OrderedSet|))) ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) 27)) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) 16))) 
(((|UserDefinedPartialOrdering| |#1|) (CATEGORY |package| (SIGNATURE |setOrder| ((|Void|) (|List| |#1|))) (SIGNATURE |setOrder| ((|Void|) (|List| |#1|) (|List| |#1|))) (SIGNATURE |getOrder| ((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|))))) (SIGNATURE |less?| ((|Union| (|Boolean|) "failed") |#1| |#1|)) (SIGNATURE |less?| ((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|))) (SIGNATURE |largest| (|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|))) (SIGNATURE |userOrdered?| ((|Boolean|))) (IF (|has| |#1| (|OrderedSet|)) (PROGN (SIGNATURE |largest| (|#1| (|List| |#1|))) (SIGNATURE |more?| ((|Boolean|) |#1| |#1|))) |noBranch|)) (|SetCategory|)) (T |UserDefinedPartialOrdering|)) 
((|more?| (*1 *2 *3 *3) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|UserDefinedPartialOrdering| *3)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *3 (|SetCategory|)))) (|largest| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|OrderedSet|)) (|isDomain| *1 (|UserDefinedPartialOrdering| *2)))) (|userOrdered?| (*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|UserDefinedPartialOrdering| *3)) (|ofCategory| *3 (|SetCategory|)))) (|largest| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *2)) (|isDomain| *4 (|Mapping| (|Boolean|) *2 *2)) (|isDomain| *1 (|UserDefinedPartialOrdering| *2)) (|ofCategory| *2 (|SetCategory|)))) (|less?| (*1 *2 *3 *3 *4) (AND (|isDomain| *4 (|Mapping| (|Boolean|) *3 *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|UserDefinedPartialOrdering| *3)))) (|less?| (*1 *2 *3 *3) (|partial| AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|UserDefinedPartialOrdering| *3)) (|ofCategory| *3 (|SetCategory|)))) (|getOrder| (*1 *2) (AND (|isDomain| *2 (|Record| (|:| |low| (|List| *3)) (|:| |high| (|List| *3)))) (|isDomain| *1 (|UserDefinedPartialOrdering| *3)) (|ofCategory| *3 (|SetCategory|)))) (|setOrder| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|UserDefinedPartialOrdering| *4)))) (|setOrder| (*1 *2 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|UserDefinedPartialOrdering| *4))))) 
(CATEGORY |package| (SIGNATURE |setOrder| ((|Void|) (|List| |#1|))) (SIGNATURE |setOrder| ((|Void|) (|List| |#1|) (|List| |#1|))) (SIGNATURE |getOrder| ((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|))))) (SIGNATURE |less?| ((|Union| (|Boolean|) "failed") |#1| |#1|)) (SIGNATURE |less?| ((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|))) (SIGNATURE |largest| (|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|))) (SIGNATURE |userOrdered?| ((|Boolean|))) (IF (|has| |#1| (|OrderedSet|)) (PROGN (SIGNATURE |largest| (|#1| (|List| |#1|))) (SIGNATURE |more?| ((|Boolean|) |#1| |#1|))) |noBranch|)) 
((|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) 12) (((|Void|) (|List| (|Symbol|))) 10)) (|resetVariableOrder| (((|Void|)) 13)) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) 17))) 
(((|UserDefinedVariableOrdering|) (CATEGORY |package| (SIGNATURE |setVariableOrder| ((|Void|) (|List| (|Symbol|)))) (SIGNATURE |setVariableOrder| ((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|)))) (SIGNATURE |getVariableOrder| ((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|)))))) (SIGNATURE |resetVariableOrder| ((|Void|))))) (T |UserDefinedVariableOrdering|)) 
((|resetVariableOrder| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|UserDefinedVariableOrdering|)))) (|getVariableOrder| (*1 *2) (AND (|isDomain| *2 (|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) (|isDomain| *1 (|UserDefinedVariableOrdering|)))) (|setVariableOrder| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| (|Symbol|))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|UserDefinedVariableOrdering|)))) (|setVariableOrder| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Symbol|))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|UserDefinedVariableOrdering|))))) 
(CATEGORY |package| (SIGNATURE |setVariableOrder| ((|Void|) (|List| (|Symbol|)))) (SIGNATURE |setVariableOrder| ((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|)))) (SIGNATURE |getVariableOrder| ((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|)))))) (SIGNATURE |resetVariableOrder| ((|Void|)))) 
((|squareFreePart| (($ $) 16)) (|prime?| (((|Boolean|) $) 23))) 
(((|UniqueFactorizationDomain&| |#1|) (CATEGORY |domain| (SIGNATURE |squareFreePart| (|#1| |#1|)) (SIGNATURE |prime?| ((|Boolean|) |#1|))) (|UniqueFactorizationDomain|)) (T |UniqueFactorizationDomain&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |squareFreePart| (|#1| |#1|)) (SIGNATURE |prime?| ((|Boolean|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 50)) (|squareFree| (((|Factored| $) $) 51)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|prime?| (((|Boolean|) $) 52)) (|one?| (((|Boolean|) $) 30)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|factor| (((|Factored| $) $) 49)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42)) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23))) 
(((|UniqueFactorizationDomain|) (|Category|)) (T |UniqueFactorizationDomain|)) 
((|prime?| (*1 *2 *1) (AND (|ofCategory| *1 (|UniqueFactorizationDomain|)) (|isDomain| *2 (|Boolean|)))) (|squareFree| (*1 *2 *1) (AND (|isDomain| *2 (|Factored| *1)) (|ofCategory| *1 (|UniqueFactorizationDomain|)))) (|squareFreePart| (*1 *1 *1) (|ofCategory| *1 (|UniqueFactorizationDomain|))) (|factor| (*1 *2 *1) (AND (|isDomain| *2 (|Factored| *1)) (|ofCategory| *1 (|UniqueFactorizationDomain|))))) 
(|Join| (|GcdDomain|) (CATEGORY |domain| (SIGNATURE |prime?| ((|Boolean|) $)) (SIGNATURE |squareFree| ((|Factored| $) $)) (SIGNATURE |squareFreePart| ($ $)) (SIGNATURE |factor| ((|Factored| $) $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|hadamard| (((|UnivariateFormalPowerSeries| |#1|) (|UnivariateFormalPowerSeries| |#1|) (|UnivariateFormalPowerSeries| |#1|)) 15))) 
(((|UnivariateFormalPowerSeriesFunctions| |#1|) (CATEGORY |package| (SIGNATURE |hadamard| ((|UnivariateFormalPowerSeries| |#1|) (|UnivariateFormalPowerSeries| |#1|) (|UnivariateFormalPowerSeries| |#1|)))) (|Ring|)) (T |UnivariateFormalPowerSeriesFunctions|)) 
((|hadamard| (*1 *2 *2 *2) (AND (|isDomain| *2 (|UnivariateFormalPowerSeries| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|UnivariateFormalPowerSeriesFunctions| *3))))) 
(CATEGORY |package| (SIGNATURE |hadamard| ((|UnivariateFormalPowerSeries| |#1|) (|UnivariateFormalPowerSeries| |#1|) (|UnivariateFormalPowerSeries| |#1|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) NIL)) (|variable| (((|Symbol|) $) NIL)) (|univariatePolynomial| (((|UnivariatePolynomial| (QUOTE |x|) |#1|) $ (|NonNegativeInteger|)) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|truncate| (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|NonNegativeInteger|) (|NonNegativeInteger|)) NIL)) (|terms| (((|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|))) $) NIL)) (|tanh| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|tan| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sqrt| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sinh| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sin| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|series| (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) NIL) (($ (|Stream| |#1|)) NIL)) (|sech| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sec| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sample| (($) NIL T CONST)) (|revert| (($ $) NIL)) (|reductum| (($ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|quoByVar| (($ $) NIL)) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) NIL) (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) NIL)) (|pole?| (((|Boolean|) $) NIL)) (|pi| (($) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|order| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) NIL)) (|one?| (((|Boolean|) $) NIL)) (|oddlambert| (($ $) NIL)) (|nthRoot| (($ $ (|Integer|)) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|multisect| (($ (|Integer|) (|Integer|) $) NIL)) (|multiplyExponents| (($ $ (|PositiveInteger|)) NIL)) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monomial| (($ |#1| (|NonNegativeInteger|)) NIL) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|log| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|leadingMonomial| (($ $) NIL)) (|leadingCoefficient| ((|#1| $) NIL)) (|latex| (((|String|) $) NIL)) (|lambert| (($ $) NIL)) (|lagrange| (($ $) NIL)) (|invmultisect| (($ (|Integer|) (|Integer|) $) NIL)) (|integrate| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Symbol|)) NIL (OR (AND (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| (|Symbol|)))) (|has| |#1| (SIGNATURE |variables| ((|List| (|Symbol|)) |#1|))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (AND 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(|Symbol|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)))) (($ $) NIL (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)))) (($ $ (|Variable| (QUOTE |x|))) NIL)) (|degree| (((|NonNegativeInteger|) $) NIL)) (|csch| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|csc| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|coth| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cot| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| 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NIL) (($ $ |#1|) NIL (|has| |#1| (|Field|))) (($ $ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ |#1|) NIL) (($ |#1| $) NIL) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) 
(((|UnivariateFormalPowerSeries| |#1|) (|Join| (|UnivariateTaylorSeriesCategory| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|UnivariatePolynomial| (QUOTE |x|) |#1|))) (SIGNATURE |univariatePolynomial| ((|UnivariatePolynomial| (QUOTE |x|) |#1|) $ (|NonNegativeInteger|))) (SIGNATURE |coerce| ($ (|Variable| (QUOTE |x|)))) (SIGNATURE |differentiate| ($ $ (|Variable| (QUOTE |x|)))) (SIGNATURE |lagrange| ($ $)) (SIGNATURE |lambert| ($ $)) (SIGNATURE |oddlambert| ($ $)) (SIGNATURE |evenlambert| ($ $)) (SIGNATURE |generalLambert| ($ $ (|Integer|) (|Integer|))) (SIGNATURE |revert| ($ $)) (SIGNATURE |multisect| ($ (|Integer|) (|Integer|) $)) (SIGNATURE |invmultisect| ($ (|Integer|) (|Integer|) $)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ (|Variable| (QUOTE |x|)))) |noBranch|))) (|Ring|)) (T |UnivariateFormalPowerSeries|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|UnivariatePolynomial| (QUOTE |x|) *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|UnivariateFormalPowerSeries| *3)))) (|univariatePolynomial| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|UnivariatePolynomial| (QUOTE |x|) *4)) (|isDomain| *1 (|UnivariateFormalPowerSeries| *4)) (|ofCategory| *4 (|Ring|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Variable| (QUOTE |x|))) (|isDomain| *1 (|UnivariateFormalPowerSeries| *3)) (|ofCategory| *3 (|Ring|)))) (|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Variable| (QUOTE |x|))) (|isDomain| *1 (|UnivariateFormalPowerSeries| *3)) (|ofCategory| *3 (|Ring|)))) (|lagrange| (*1 *1 *1) (AND (|isDomain| *1 (|UnivariateFormalPowerSeries| *2)) (|ofCategory| *2 (|Ring|)))) (|lambert| (*1 *1 *1) (AND (|isDomain| *1 (|UnivariateFormalPowerSeries| *2)) (|ofCategory| *2 (|Ring|)))) (|oddlambert| (*1 *1 *1) (AND (|isDomain| *1 (|UnivariateFormalPowerSeries| *2)) (|ofCategory| *2 (|Ring|)))) (|evenlambert| (*1 *1 *1) (AND (|isDomain| *1 (|UnivariateFormalPowerSeries| *2)) (|ofCategory| *2 (|Ring|)))) (|generalLambert| (*1 *1 *1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|UnivariateFormalPowerSeries| *3)) (|ofCategory| *3 (|Ring|)))) (|revert| (*1 *1 *1) (AND (|isDomain| *1 (|UnivariateFormalPowerSeries| *2)) (|ofCategory| *2 (|Ring|)))) (|multisect| (*1 *1 *2 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|UnivariateFormalPowerSeries| *3)) (|ofCategory| *3 (|Ring|)))) (|invmultisect| (*1 *1 *2 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|UnivariateFormalPowerSeries| *3)) (|ofCategory| *3 (|Ring|)))) (|integrate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Variable| (QUOTE |x|))) (|isDomain| *1 (|UnivariateFormalPowerSeries| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *3 (|Ring|))))) 
(|Join| (|UnivariateTaylorSeriesCategory| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|UnivariatePolynomial| (QUOTE |x|) |#1|))) (SIGNATURE |univariatePolynomial| ((|UnivariatePolynomial| (QUOTE |x|) |#1|) $ (|NonNegativeInteger|))) (SIGNATURE |coerce| ($ (|Variable| (QUOTE |x|)))) (SIGNATURE |differentiate| ($ $ (|Variable| (QUOTE |x|)))) (SIGNATURE |lagrange| ($ $)) (SIGNATURE |lambert| ($ $)) (SIGNATURE |oddlambert| ($ $)) (SIGNATURE |evenlambert| ($ $)) (SIGNATURE |generalLambert| ($ $ (|Integer|) (|Integer|))) (SIGNATURE |revert| ($ $)) (SIGNATURE |multisect| ($ (|Integer|) (|Integer|) $)) (SIGNATURE |invmultisect| ($ (|Integer|) (|Integer|) $)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ (|Variable| (QUOTE |x|)))) |noBranch|))) 
((|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) 23))) 
(((|UnivariateLaurentSeriesFunctions2| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |map| ((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)))) (|Ring|) (|Ring|) (|Symbol|) (|Symbol|) |#1| |#2|) (T |UnivariateLaurentSeriesFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|UnivariateLaurentSeries| *5 *7 *9)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|Ring|)) (|ofType| *7 (|Symbol|)) (|ofType| *9 *5) (|ofType| *10 *6) (|isDomain| *2 (|UnivariateLaurentSeries| *6 *8 *10)) (|isDomain| *1 (|UnivariateLaurentSeriesFunctions2| *5 *6 *7 *8 *9 *10)) (|ofType| *8 (|Symbol|))))) 
(CATEGORY |package| (SIGNATURE |map| ((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)))) 
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(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 151 (|has| |#1| (|Field|)))) (|extend| (($ $ (|Integer|)) 90)) (|exquo| (((|Union| $ "failed") $ $) 49 (|has| |#1| (|IntegralDomain|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 145 (|has| |#1| (|Field|)))) (|exp| (($ $) 135 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|eval| (((|Stream| |#1|) $ |#1|) 89 (|has| |#1| (SIGNATURE ** (|#1| |#1| (|Integer|)))))) (|euclideanSize| (((|NonNegativeInteger|) $) 147 (|has| |#1| (|Field|)))) (|elt| ((|#1| $ (|Integer|)) 99) (($ $ $) 76 (|has| (|Integer|) (|SemiGroup|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 148 (|has| |#1| (|Field|)))) (|differentiate| (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 84 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 83 (AND (|has| |#1| (|PartialDifferentialRing| 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(($ (|Integer|)) 27) (($ |#1|) 46 (|has| |#1| (|CommutativeRing|))) (($ (|Fraction| (|Integer|))) 56 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $) 48 (|has| |#1| (|IntegralDomain|)))) (|coefficient| ((|#1| $ (|Integer|)) 58)) (|charthRoot| (((|Union| $ "failed") $) 47 (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|center| ((|#1| $) 97)) (|atanh| (($ $) 133 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|atan| (($ $) 121 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|associates?| (((|Boolean|) $ $) 52 (|has| |#1| (|IntegralDomain|)))) (|asinh| (($ $) 132 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asin| (($ $) 120 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asech| (($ $) 131 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asec| (($ $) 119 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|approximate| ((|#1| $ (|Integer|)) 91 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| (|Integer|)))) (|has| |#1| (SIGNATURE |coerce| (|#1| (|Symbol|))))))) (|acsch| (($ $) 130 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acsc| (($ $) 118 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acoth| (($ $) 129 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acot| (($ $) 117 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acosh| (($ $) 128 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acos| (($ $) 116 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 159 (|has| |#1| (|Field|)))) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 88 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 87 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) (($ $ (|List| (|Symbol|))) 86 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) (($ $ (|Symbol|)) 85 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) (($ $ (|NonNegativeInteger|)) 80 (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) (($ $) 78 (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) (= (((|Boolean|) $ $) 6)) (/ (($ $ |#1|) 57 (|has| |#1| (|Field|))) (($ $ $) 161 (|has| |#1| (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 160 (|has| |#1| (|Field|))) (($ $ $) 136 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) 107 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 67) (($ |#1| $) 66) (($ (|Fraction| (|Integer|)) $) 55 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) 54 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) 
(((|UnivariateLaurentSeriesCategory| |#1|) (|Category|) (|Ring|)) (T |UnivariateLaurentSeriesCategory|)) 
((|series| (*1 *1 *2) (AND (|isDomain| *2 (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| *3)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *3)))) (|multiplyCoefficients| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 (|Integer|))) (|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|rationalFunction| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *4)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Fraction| (|Polynomial| *4))))) (|rationalFunction| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *4)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Fraction| (|Polynomial| *4))))) (|integrate| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))))) (|integrate| (*1 *1 *1 *2) (OR (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)) (AND (|ofCategory| *3 (|AlgebraicallyClosedFunctionSpace| (|Integer|))) (|ofCategory| *3 (|PrimitiveFunctionCategory|)) (|ofCategory| *3 (|TranscendentalFunctionCategory|)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))))) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)) (AND (|has| *3 (SIGNATURE |variables| ((|List| *2) *3))) (|has| *3 (SIGNATURE |integrate| (*3 *3 *2))) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))))))) 
(|Join| (|UnivariatePowerSeriesCategory| |t#1| (|Integer|)) (CATEGORY |domain| (SIGNATURE |series| ($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |t#1|))))) (SIGNATURE |multiplyCoefficients| ($ (|Mapping| |t#1| (|Integer|)) $)) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |rationalFunction| ((|Fraction| (|Polynomial| |t#1|)) $ (|Integer|))) (SIGNATURE |rationalFunction| ((|Fraction| (|Polynomial| |t#1|)) $ (|Integer|) (|Integer|)))) |noBranch|) (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |integrate| ($ $)) (IF (|has| |t#1| (SIGNATURE |integrate| (|t#1| |t#1| (|Symbol|)))) (IF (|has| |t#1| (SIGNATURE |variables| ((|List| (|Symbol|)) |t#1|))) (SIGNATURE |integrate| ($ $ (|Symbol|))) |noBranch|) |noBranch|) (IF (|has| |t#1| (|TranscendentalFunctionCategory|)) (IF (|has| |t#1| (|PrimitiveFunctionCategory|)) (IF (|has| |t#1| (|AlgebraicallyClosedFunctionSpace| (|Integer|))) (SIGNATURE |integrate| ($ $ (|Symbol|))) |noBranch|) |noBranch|) |noBranch|) (ATTRIBUTE (|RadicalCategory|)) (ATTRIBUTE (|TranscendentalFunctionCategory|))) |noBranch|) (IF (|has| |t#1| (|Field|)) (ATTRIBUTE (|Field|)) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| (|Integer|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| $ $) |has| (|Integer|) (|SemiGroup|)) ((|EntireRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Field|) |has| |#1| (|Field|)) ((|GcdDomain|) |has| |#1| (|Field|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|IntegralDomain|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|LeftModule| (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) |has| |#1| (|Field|)) ((|Module| (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|PartialDifferentialRing| (|Symbol|)) AND (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PowerSeriesCategory| |#1| (|Integer|) (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariatePowerSeriesCategory| |#1| (|Integer|)) . T)) 
((|zero?| (((|Boolean|) $) 12)) (|retractIfCan| (((|Union| |#3| "failed") $) 17) (((|Union| (|Symbol|) "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL) (((|Union| (|Integer|) "failed") $) NIL)) (|retract| ((|#3| $) 14) (((|Symbol|) $) NIL) (((|Fraction| (|Integer|)) $) NIL) (((|Integer|) $) NIL))) 
(((|UnivariateLaurentSeriesConstructorCategory&| |#1| |#2| |#3|) (CATEGORY |domain| (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |retract| ((|Symbol|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Symbol|) "failed") |#1|)) (SIGNATURE |retract| (|#3| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#3| "failed") |#1|)) (SIGNATURE |zero?| ((|Boolean|) |#1|))) (|UnivariateLaurentSeriesConstructorCategory| |#2| |#3|) (|Ring|) (|UnivariateTaylorSeriesCategory| |#2|)) (T |UnivariateLaurentSeriesConstructorCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |retract| ((|Symbol|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Symbol|) "failed") |#1|)) (SIGNATURE |retract| (|#3| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#3| "failed") |#1|)) (SIGNATURE |zero?| ((|Boolean|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|wholePart| ((|#2| $) 220 (|and| (|has| |#2| (|EuclideanDomain|)) (|has| |#1| (|Field|))))) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) 70)) (|variable| (((|Symbol|) $) 98)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 50 (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) 51 (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) 53 (|has| |#1| (|IntegralDomain|)))) (|truncate| (($ $ (|Integer|)) 93) (($ $ (|Integer|) (|Integer|)) 92)) (|terms| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) 100)) (|taylorRep| ((|#2| $) 256)) (|taylorIfCan| (((|Union| |#2| "failed") $) 252)) (|taylor| ((|#2| $) 253)) (|tanh| (($ $) 127 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|tan| (($ $) 110 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 229 (|and| (|has| |#2| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|Field|))))) (|squareFreePart| (($ $) 155 (|has| |#1| (|Field|)))) (|squareFree| (((|Factored| $) $) 156 (|has| |#1| (|Field|)))) (|sqrt| (($ $) 109 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 226 (|and| (|has| |#2| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|Field|))))) (|sizeLess?| (((|Boolean|) $ $) 146 (|has| |#1| (|Field|)))) (|sinh| (($ $) 126 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sin| (($ $) 111 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sign| (((|Integer|) $) 238 (|and| (|has| |#2| (|OrderedIntegralDomain|)) (|has| |#1| (|Field|))))) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) 167)) (|sech| (($ $) 125 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sec| (($ $) 112 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) 259) (((|Union| (|Integer|) "failed") $) 248 (|and| (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#1| (|Field|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) 246 (|and| (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#1| (|Field|)))) (((|Union| (|Symbol|) "failed") $) 231 (|and| (|has| |#2| (|RetractableTo| (|Symbol|))) (|has| |#1| (|Field|))))) (|retract| ((|#2| $) 258) (((|Integer|) $) 249 (|and| (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#1| (|Field|)))) (((|Fraction| (|Integer|)) $) 247 (|and| (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#1| (|Field|)))) (((|Symbol|) $) 232 (|and| (|has| |#2| (|RetractableTo| (|Symbol|))) (|has| |#1| (|Field|))))) (|removeZeroes| (($ $) 255) (($ (|Integer|) $) 254)) (|rem| (($ $ $) 150 (|has| |#1| (|Field|)))) (|reductum| (($ $) 59)) (|reducedSystem| (((|Matrix| |#2|) (|Matrix| $)) 210 (|has| |#1| (|Field|))) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| $) (|Vector| $)) 209 (|has| |#1| (|Field|))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) 208 (|and| (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Field|)))) (((|Matrix| (|Integer|)) (|Matrix| $)) 207 (|and| (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Field|))))) (|recip| (((|Union| $ "failed") $) 33)) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) 165 (|has| |#1| (|IntegralDomain|))) (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) 164 (|has| |#1| (|IntegralDomain|)))) (|random| (($) 222 (|and| (|has| |#2| (|IntegerNumberSystem|)) (|has| |#1| (|Field|))))) (|quo| (($ $ $) 149 (|has| |#1| (|Field|)))) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 144 (|has| |#1| (|Field|)))) (|prime?| (((|Boolean|) $) 157 (|has| |#1| (|Field|)))) (|positive?| (((|Boolean|) $) 236 (|and| (|has| |#2| (|OrderedIntegralDomain|)) (|has| |#1| (|Field|))))) (|pole?| (((|Boolean|) $) 69)) (|pi| (($) 137 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) 214 (|and| (|has| |#2| (|PatternMatchable| (|Float|))) (|has| |#1| (|Field|)))) (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) 213 (|and| (|has| |#2| (|PatternMatchable| (|Integer|))) (|has| |#1| (|Field|))))) (|order| (((|Integer|) $) 95) (((|Integer|) $ (|Integer|)) 94)) (|one?| (((|Boolean|) $) 30)) (|numerator| (($ $) 218 (|has| |#1| (|Field|)))) (|numer| ((|#2| $) 216 (|has| |#1| (|Field|)))) (|nthRoot| (($ $ (|Integer|)) 108 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|nextItem| (((|Union| $ "failed") $) 250 (|and| (|has| |#2| (|StepThrough|)) (|has| |#1| (|Field|))))) (|negative?| (((|Boolean|) $) 237 (|and| (|has| |#2| (|OrderedIntegralDomain|)) (|has| |#1| (|Field|))))) (|multiplyExponents| (($ $ (|PositiveInteger|)) 96)) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) 166)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 153 (|has| |#1| (|Field|)))) (|monomial?| (((|Boolean|) $) 61)) (|monomial| (($ |#1| (|Integer|)) 60) (($ $ (|SingletonAsOrderedSet|) (|Integer|)) 72) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|Integer|))) 71)) (|min| (($ $ $) 240 (|and| (|has| |#2| (|OrderedSet|)) (|has| |#1| (|Field|))))) (|max| (($ $ $) 241 (|and| (|has| |#2| (|OrderedSet|)) (|has| |#1| (|Field|))))) (|map| (($ (|Mapping| |#1| |#1|) $) 62) (($ (|Mapping| |#2| |#2|) $) 202 (|has| |#1| (|Field|)))) (|log| (($ $) 134 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|leadingMonomial| (($ $) 64)) (|leadingCoefficient| ((|#1| $) 65)) (|lcmCoef| (((|Record| (|:| 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(|Field|))))) (|complete| (($ $) 68)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ |#1|) 46 (|has| |#1| (|CommutativeRing|))) (($ |#2|) 260) (($ (|Symbol|)) 230 (|and| (|has| |#2| (|RetractableTo| (|Symbol|))) (|has| |#1| (|Field|)))) (($ (|Fraction| (|Integer|))) 56 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $) 48 (|has| |#1| (|IntegralDomain|)))) (|coefficient| ((|#1| $ (|Integer|)) 58)) (|charthRoot| (((|Union| $ "failed") $) 47 (OR (|and| (OR (|has| |#2| (|CharacteristicNonZero|)) (|and| (|has| $ (|CharacteristicNonZero|)) (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|has| |#1| (|Field|))) (|has| |#1| (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|center| ((|#1| $) 97)) (|ceiling| ((|#2| $) 223 (|and| (|has| |#2| (|IntegerNumberSystem|)) (|has| |#1| (|Field|))))) (|atanh| (($ $) 133 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|atan| (($ $) 121 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|associates?| (((|Boolean|) $ $) 52 (|has| |#1| (|IntegralDomain|)))) (|asinh| (($ $) 132 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asin| (($ $) 120 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asech| (($ $) 131 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asec| (($ $) 119 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|approximate| ((|#1| $ (|Integer|)) 91 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| (|Integer|)))) (|has| |#1| (SIGNATURE |coerce| (|#1| (|Symbol|))))))) (|acsch| (($ $) 130 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acsc| (($ $) 118 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acoth| (($ $) 129 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acot| (($ $) 117 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acosh| (($ $) 128 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acos| (($ $) 116 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|abs| (($ $) 239 (|and| (|has| |#2| 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|#1| (|Field|))) (($ $ $) 161 (|has| |#1| (|Field|))) (($ |#2| |#2|) 215 (|has| |#1| (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 160 (|has| |#1| (|Field|))) (($ $ $) 136 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) 107 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 67) (($ |#1| $) 66) (($ $ |#2|) 194 (|has| |#1| (|Field|))) (($ |#2| $) 193 (|has| |#1| (|Field|))) (($ (|Fraction| (|Integer|)) $) 55 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) 54 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) 
(((|UnivariateLaurentSeriesConstructorCategory| |#1| |#2|) (|Category|) (|Ring|) (|UnivariateTaylorSeriesCategory| |t#1|)) (T |UnivariateLaurentSeriesConstructorCategory|)) 
((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *2 (|Integer|)))) (|coerce| (*1 *1 *2) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|laurent| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *4 *3)) (|ofCategory| *3 (|UnivariateTaylorSeriesCategory| *4)))) (|taylorRep| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|removeZeroes| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|UnivariateTaylorSeriesCategory| *2)))) (|removeZeroes| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)))) (|taylor| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|taylorIfCan| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))) 
(|Join| (|UnivariateLaurentSeriesCategory| |t#1|) (|RetractableTo| |t#2|) (CATEGORY |domain| (SIGNATURE |laurent| ($ (|Integer|) |t#2|)) (SIGNATURE |degree| ((|Integer|) $)) (SIGNATURE |taylorRep| (|t#2| $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |removeZeroes| ($ (|Integer|) $)) (SIGNATURE |coerce| ($ |t#2|)) (SIGNATURE |taylor| (|t#2| $)) (SIGNATURE |taylorIfCan| ((|Union| |t#2| "failed") $)) (IF (|has| |t#1| (|Field|)) (ATTRIBUTE (|QuotientFieldCategory| |t#2|)) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| (|Integer|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| |#2|) |has| |#1| (|Field|)) ((|Algebra| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| |#2| |#2|) |has| |#1| (|Field|)) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|CharacteristicNonZero|))) (|has| |#1| (|CharacteristicNonZero|))) ((|CharacteristicZero|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|CharacteristicZero|))) (|has| |#1| (|CharacteristicZero|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|ConvertibleTo| (|DoubleFloat|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|RealConstant|))) ((|ConvertibleTo| (|Float|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|RealConstant|))) ((|ConvertibleTo| (|InputForm|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|ConvertibleTo| (|InputForm|)))) ((|ConvertibleTo| (|Pattern| (|Float|))) AND (|has| |#1| (|Field|)) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Float|))))) ((|ConvertibleTo| (|Pattern| (|Integer|))) AND (|has| |#1| (|Field|)) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Integer|))))) ((|DifferentialExtension| |#2|) |has| |#1| (|Field|)) ((|DifferentialRing|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialRing|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| |#2| $) AND (|has| |#1| (|Field|)) (|has| |#2| (|Eltable| |#2| |#2|))) ((|Eltable| $ $) |has| (|Integer|) (|SemiGroup|)) ((|EntireRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Evalable| |#2|) AND (|has| |#1| (|Field|)) (|has| |#2| (|Evalable| |#2|))) ((|Field|) |has| |#1| (|Field|)) ((|FullyEvalableOver| |#2|) |has| |#1| (|Field|)) ((|FullyLinearlyExplicitRingOver| |#2|) |has| |#1| (|Field|)) ((|FullyPatternMatchable| |#2|) |has| |#1| (|Field|)) ((|GcdDomain|) |has| |#1| (|Field|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|InnerEvalable| (|Symbol|) |#2|) AND (|has| |#1| (|Field|)) (|has| |#2| (|InnerEvalable| (|Symbol|) |#2|))) ((|InnerEvalable| |#2| |#2|) AND (|has| |#1| (|Field|)) (|has| |#2| (|Evalable| |#2|))) ((|IntegralDomain|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|LeftModule| (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftModule| |#1|) . T) ((|LeftModule| |#2|) |has| |#1| (|Field|)) ((|LeftModule| $) . T) ((|LeftOreRing|) |has| |#1| (|Field|)) ((|LinearlyExplicitRingOver| (|Integer|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) ((|LinearlyExplicitRingOver| |#2|) |has| |#1| (|Field|)) ((|Module| (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#2|) |has| |#1| (|Field|)) ((|Module| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|OrderedAbelianGroup|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedAbelianMonoid|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedAbelianSemiGroup|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedCancellationAbelianMonoid|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedIntegralDomain|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedRing|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedSet|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedSet|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|)))) ((|PartialDifferentialRing| (|Symbol|)) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (AND (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) ((|PatternMatchable| (|Float|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|PatternMatchable| (|Float|)))) ((|PatternMatchable| (|Integer|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|PatternMatchable| (|Integer|)))) ((|Patternable| |#2|) |has| |#1| (|Field|)) ((|PolynomialFactorizationExplicit|) AND (|has| |#1| (|Field|)) (|has| |#2| (|PolynomialFactorizationExplicit|))) ((|PowerSeriesCategory| |#1| (|Integer|) (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|QuotientFieldCategory| |#2|) |has| |#1| (|Field|)) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RealConstant|) AND (|has| |#1| (|Field|)) (|has| |#2| (|RealConstant|))) ((|RetractableTo| (|Fraction| (|Integer|))) AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Integer|)))) ((|RetractableTo| (|Integer|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Integer|)))) ((|RetractableTo| (|Symbol|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Symbol|)))) ((|RetractableTo| |#2|) . T) ((|RightModule| (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightModule| |#1|) . T) ((|RightModule| |#2|) |has| |#1| (|Field|)) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|StepThrough|) AND (|has| |#1| (|Field|)) (|has| |#2| (|StepThrough|))) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) |has| |#1| (|Field|)) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariateLaurentSeriesCategory| |#1|) . T) ((|UnivariatePowerSeriesCategory| |#1| (|Integer|)) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 70)) (|wholePart| ((|#2| $) NIL (AND (|has| |#2| (|EuclideanDomain|)) (|has| |#1| (|Field|))))) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) NIL)) (|variable| (((|Symbol|) $) 88)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|truncate| (($ $ (|Integer|)) 97) (($ $ (|Integer|) (|Integer|)) 99)) (|terms| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) 47)) (|taylorRep| ((|#2| $) 11)) (|taylorIfCan| (((|Union| |#2| "failed") $) 30)) (|taylor| ((|#2| $) 31)) (|tanh| (($ $) 192 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|tan| (($ $) 168 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (AND (|has| |#2| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|Field|))))) (|squareFreePart| (($ $) NIL (|has| |#1| (|Field|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#1| (|Field|)))) (|sqrt| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (AND (|has| |#2| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|Field|))))) (|sizeLess?| (((|Boolean|) $ $) NIL (|has| |#1| (|Field|)))) (|sinh| (($ $) 188 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sin| (($ $) 164 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sign| (((|Integer|) $) NIL (AND (|has| |#2| (|OrderedIntegralDomain|)) (|has| |#1| (|Field|))))) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) 57)) (|sech| (($ $) 196 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sec| (($ $) 172 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) 144) (((|Union| (|Integer|) "failed") $) NIL (AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#1| (|Field|)))) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#1| (|Field|)))) (((|Union| (|Symbol|) "failed") $) NIL (AND (|has| |#2| (|RetractableTo| (|Symbol|))) (|has| |#1| (|Field|))))) (|retract| ((|#2| $) 143) (((|Integer|) $) NIL (AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#1| (|Field|)))) (((|Fraction| (|Integer|)) $) NIL (AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#1| (|Field|)))) (((|Symbol|) $) NIL (AND (|has| |#2| (|RetractableTo| (|Symbol|))) (|has| |#1| (|Field|))))) (|removeZeroes| (($ $) 61) (($ (|Integer|) $) 24)) (|rem| (($ $ $) NIL (|has| |#1| (|Field|)))) (|reductum| (($ $) NIL)) (|reducedSystem| (((|Matrix| |#2|) (|Matrix| $)) NIL (|has| |#1| (|Field|))) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| $) (|Vector| $)) NIL (|has| |#1| (|Field|))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Field|)))) (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Field|))))) (|recip| (((|Union| $ "failed") $) 77)) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) 112 (|has| |#1| (|IntegralDomain|))) (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) 114 (|has| |#1| (|IntegralDomain|)))) (|random| (($) NIL (AND (|has| |#2| (|IntegerNumberSystem|)) (|has| |#1| (|Field|))))) (|quo| (($ $ $) NIL (|has| |#1| (|Field|)))) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL (|has| |#1| (|Field|)))) (|prime?| (((|Boolean|) $) NIL (|has| |#1| (|Field|)))) (|positive?| (((|Boolean|) $) NIL (AND (|has| |#2| (|OrderedIntegralDomain|)) (|has| |#1| (|Field|))))) (|pole?| (((|Boolean|) $) 64)) (|pi| (($) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (AND (|has| |#2| (|PatternMatchable| (|Float|))) (|has| |#1| (|Field|)))) (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (AND (|has| |#2| (|PatternMatchable| (|Integer|))) (|has| |#1| (|Field|))))) (|order| (((|Integer|) $) 93) (((|Integer|) $ (|Integer|)) 95)) (|one?| (((|Boolean|) $) NIL)) (|numerator| (($ $) NIL (|has| |#1| (|Field|)))) (|numer| ((|#2| $) 151 (|has| |#1| (|Field|)))) (|nthRoot| (($ $ (|Integer|)) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|nextItem| (((|Union| $ "failed") $) NIL (AND (|has| |#2| (|StepThrough|)) (|has| |#1| (|Field|))))) (|negative?| (((|Boolean|) $) NIL (AND (|has| |#2| (|OrderedIntegralDomain|)) (|has| |#1| (|Field|))))) (|multiplyExponents| (($ $ (|PositiveInteger|)) 136)) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) 132)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) (|monomial?| (((|Boolean|) $) NIL)) (|monomial| (($ |#1| (|Integer|)) 19) (($ $ (|SingletonAsOrderedSet|) (|Integer|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|Integer|))) NIL)) (|min| (($ $ $) NIL (AND (|has| |#2| (|OrderedSet|)) (|has| |#1| (|Field|))))) (|max| (($ $ $) NIL (AND (|has| |#2| (|OrderedSet|)) (|has| |#1| (|Field|))))) (|map| (($ (|Mapping| |#1| |#1|) $) 129) (($ (|Mapping| |#2| |#2|) $) NIL (|has| |#1| (|Field|)))) (|log| (($ $) 162 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|leadingMonomial| (($ $) NIL)) (|leadingCoefficient| ((|#1| $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| |#1| (|Field|)))) (|lcm| (($ (|List| $)) NIL (|has| |#1| (|Field|))) (($ $ $) NIL (|has| |#1| (|Field|)))) (|laurent| (($ (|Integer|) |#2|) 10)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 145 (|has| |#1| (|Field|)))) (|integrate| (($ $) 214 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Symbol|)) 219 (OR (AND (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| (|Symbol|)))) (|has| |#1| (SIGNATURE |variables| ((|List| (|Symbol|)) |#1|))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (AND (|has| |#1| (|AlgebraicallyClosedFunctionSpace| (|Integer|))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|)))))) (|init| (($) NIL (AND (|has| |#2| (|StepThrough|)) (|has| |#1| (|Field|))) CONST)) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|Field|)))) (|gcd| (($ (|List| $)) NIL (|has| |#1| (|Field|))) (($ $ $) NIL (|has| |#1| (|Field|)))) (|fractionPart| (($ $) NIL (AND (|has| |#2| (|EuclideanDomain|)) (|has| |#1| (|Field|))))) (|floor| ((|#2| $) NIL (AND (|has| |#2| (|IntegerNumberSystem|)) (|has| |#1| (|Field|))))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (AND (|has| |#2| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|Field|))))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (AND (|has| |#2| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|Field|))))) (|factor| (((|Factored| $) $) NIL (|has| |#1| (|Field|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL (|has| |#1| (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|extend| (($ $ (|Integer|)) 126)) (|exquo| (((|Union| $ "failed") $ $) 116 (|has| |#1| (|IntegralDomain|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) (|exp| (($ $) 160 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|eval| (((|Stream| |#1|) $ |#1|) 85 (|has| |#1| (SIGNATURE ** (|#1| |#1| (|Integer|))))) (($ $ (|Symbol|) |#2|) NIL (AND (|has| |#2| (|InnerEvalable| (|Symbol|) |#2|)) (|has| |#1| (|Field|)))) (($ $ (|List| (|Symbol|)) (|List| |#2|)) NIL (AND (|has| |#2| (|InnerEvalable| (|Symbol|) |#2|)) (|has| |#1| (|Field|)))) (($ $ (|List| (|Equation| |#2|))) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#1| (|Field|)))) (($ $ (|Equation| |#2|)) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#1| (|Field|)))) (($ $ |#2| |#2|) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#1| (|Field|)))) (($ $ (|List| |#2|) (|List| |#2|)) NIL (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#1| (|Field|))))) (|euclideanSize| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|Field|)))) (|elt| ((|#1| $ (|Integer|)) 91) (($ $ $) 79 (|has| (|Integer|) (|SemiGroup|))) (($ $ |#2|) NIL (AND (|has| |#2| (|Eltable| |#2| |#2|)) (|has| |#1| (|Field|))))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|Field|)))) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) NIL (|has| |#1| (|Field|))) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) NIL (|has| |#1| (|Field|))) (($ $ (|NonNegativeInteger|)) NIL (OR (AND (|has| |#2| (|DifferentialRing|)) (|has| |#1| (|Field|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) (($ $) 137 (OR (AND (|has| |#2| (|DifferentialRing|)) (|has| |#1| (|Field|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (OR (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|Field|))) (AND (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (OR (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|Field|))) (AND (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))))) (($ $ (|List| (|Symbol|))) NIL (OR (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|Field|))) (AND (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))))) (($ $ (|Symbol|)) 140 (OR (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|Field|))) (AND (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))))) (|denominator| (($ $) NIL (|has| |#1| (|Field|)))) (|denom| ((|#2| $) 152 (|has| |#1| (|Field|)))) (|degree| (((|Integer|) $) 12)) (|csch| (($ $) 198 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|csc| (($ $) 174 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|coth| (($ $) 194 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cot| (($ $) 170 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cosh| (($ $) 190 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cos| (($ $) 166 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|convert| (((|DoubleFloat|) $) NIL (AND (|has| |#2| (|RealConstant|)) (|has| |#1| (|Field|)))) (((|Float|) $) NIL (AND (|has| |#2| (|RealConstant|)) (|has| |#1| (|Field|)))) (((|InputForm|) $) NIL (AND (|has| |#2| (|ConvertibleTo| (|InputForm|))) (|has| |#1| (|Field|)))) (((|Pattern| (|Float|)) $) NIL (AND (|has| |#2| (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#1| (|Field|)))) (((|Pattern| (|Integer|)) $) NIL (AND (|has| |#2| (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#1| (|Field|))))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) NIL (AND (|has| $ (|CharacteristicNonZero|)) (|has| |#2| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|Field|))))) (|complete| (($ $) 124)) (|coerce| (((|OutputForm|) $) 242) (($ (|Integer|)) 23) (($ |#1|) 21 (|has| |#1| 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(((|UnivariateLaurentSeriesConstructor| |#1| |#2|) (|UnivariateLaurentSeriesConstructorCategory| |#1| |#2|) (|Ring|) (|UnivariateTaylorSeriesCategory| |#1|)) (T |UnivariateLaurentSeriesConstructor|)) 
NIL 
(|UnivariateLaurentSeriesConstructorCategory| |#1| |#2|) 
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(((|UnivariateLaurentSeries| |#1| |#2| |#3|) (|Join| (|UnivariateLaurentSeriesConstructorCategory| |#1| (|UnivariateTaylorSeries| |#1| |#2| |#3|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Variable| |#2|))) (SIGNATURE |differentiate| ($ $ (|Variable| |#2|))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ (|Variable| |#2|))) |noBranch|))) (|Ring|) (|Symbol|) |#1|) (T |UnivariateLaurentSeries|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|)) (|isDomain| *1 (|UnivariateLaurentSeries| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3))) (|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|)) (|isDomain| *1 (|UnivariateLaurentSeries| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3))) (|integrate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|)) (|isDomain| *1 (|UnivariateLaurentSeries| *3 *4 *5)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))) 
(|Join| (|UnivariateLaurentSeriesConstructorCategory| |#1| (|UnivariateTaylorSeries| |#1| |#2| |#3|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Variable| |#2|))) (SIGNATURE |differentiate| ($ $ (|Variable| |#2|))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ (|Variable| |#2|))) |noBranch|))) 
((|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) 10)) (|factorSquareFree| (((|Factored| |#1|) |#1|) 21)) (|factor| (((|Factored| |#1|) |#1|) 20))) 
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((|henselFact| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Boolean|)) (|isDomain| *2 (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| *3) (|:| |pow| (|Integer|))))))) (|isDomain| *1 (|UnivariateFactorize| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|factorSquareFree| (*1 *2 *3) (AND (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|UnivariateFactorize| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|factor| (*1 *2 *3) (AND (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|UnivariateFactorize| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
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(((|UniversalSegmentFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|))) (IF (|has| |#1| (|OrderedRing|)) (SIGNATURE |map| ((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|))) |noBranch|)) (|Type|) (|Type|)) (T |UniversalSegmentFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|UniversalSegment| *5)) (|ofCategory| *5 (|OrderedRing|)) (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|Stream| *6)) (|isDomain| *1 (|UniversalSegmentFunctions2| *5 *6)))) (|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|UniversalSegment| *5)) (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|UniversalSegment| *6)) (|isDomain| *1 (|UniversalSegmentFunctions2| *5 *6))))) 
(CATEGORY |package| (SIGNATURE |map| ((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|))) (IF (|has| |#1| (|OrderedRing|)) (SIGNATURE |map| ((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|))) |noBranch|)) 
((~= (((|Boolean|) $ $) NIL (|has| |#1| (|SetCategory|)))) (|segment| (($ |#1| |#1|) 9) (($ |#1|) 8)) (|map| (((|Stream| |#1|) (|Mapping| |#1| |#1|) $) 41 (|has| |#1| (|OrderedRing|)))) (|low| ((|#1| $) 14)) (|lo| ((|#1| $) 10)) (|latex| (((|String|) $) NIL (|has| |#1| (|SetCategory|)))) (|incr| (((|Integer|) $) 18)) (|high| ((|#1| $) 17)) (|hi| ((|#1| $) 11)) (|hash| (((|SingleInteger|) $) NIL (|has| |#1| (|SetCategory|)))) (|hasHi| (((|Boolean|) $) 16)) (|expand| (((|Stream| |#1|) $) 38 (|has| |#1| (|OrderedRing|))) (((|Stream| |#1|) (|List| $)) 37 (|has| |#1| (|OrderedRing|)))) (|convert| (($ |#1|) 25)) (|coerce| (($ (|Segment| |#1|)) 24) (((|OutputForm|) $) 34 (|has| |#1| (|SetCategory|)))) (SEGMENT (($ |#1| |#1|) 20) (($ |#1|) 19)) (BY (($ $ (|Integer|)) 13)) (= (((|Boolean|) $ $) 27 (|has| |#1| (|SetCategory|))))) 
(((|UniversalSegment| |#1|) (|Join| (|SegmentCategory| |#1|) (CATEGORY |domain| (SIGNATURE SEGMENT ($ |#1|)) (SIGNATURE |segment| ($ |#1|)) (SIGNATURE |coerce| ($ (|Segment| |#1|))) (SIGNATURE |hasHi| ((|Boolean|) $)) (IF (|has| |#1| (|SetCategory|)) (ATTRIBUTE (|SetCategory|)) |noBranch|) (IF (|has| |#1| (|OrderedRing|)) (ATTRIBUTE (|SegmentExpansionCategory| |#1| (|Stream| |#1|))) |noBranch|))) (|Type|)) (T |UniversalSegment|)) 
((SEGMENT (*1 *1 *2) (AND (|isDomain| *1 (|UniversalSegment| *2)) (|ofCategory| *2 (|Type|)))) (|segment| (*1 *1 *2) (AND (|isDomain| *1 (|UniversalSegment| *2)) (|ofCategory| *2 (|Type|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Segment| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|UniversalSegment| *3)))) (|hasHi| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|UniversalSegment| *3)) (|ofCategory| *3 (|Type|))))) 
(|Join| (|SegmentCategory| |#1|) (CATEGORY |domain| (SIGNATURE SEGMENT ($ |#1|)) (SIGNATURE |segment| ($ |#1|)) (SIGNATURE |coerce| ($ (|Segment| |#1|))) (SIGNATURE |hasHi| ((|Boolean|) $)) (IF (|has| |#1| (|SetCategory|)) (ATTRIBUTE (|SetCategory|)) |noBranch|) (IF (|has| |#1| (|OrderedRing|)) (ATTRIBUTE (|SegmentExpansionCategory| |#1| (|Stream| |#1|))) |noBranch|))) 
((|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) 15))) 
(((|UnivariatePolynomialFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| ((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)))) (|Symbol|) (|Ring|) (|Symbol|) (|Ring|)) (T |UnivariatePolynomialFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *8 *6)) (|isDomain| *4 (|UnivariatePolynomial| *5 *6)) (|ofType| *5 (|Symbol|)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *8 (|Ring|)) (|isDomain| *2 (|UnivariatePolynomial| *7 *8)) (|isDomain| *1 (|UnivariatePolynomialFunctions2| *5 *6 *7 *8)) (|ofType| *7 (|Symbol|))))) 
(CATEGORY |package| (SIGNATURE |map| ((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)))) 
((|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) 21)) (|commonDenominator| ((|#1| |#3|) 13)) (|clearDenominator| ((|#3| |#3|) 19))) 
(((|UnivariatePolynomialCommonDenominator| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |commonDenominator| (|#1| |#3|)) (SIGNATURE |clearDenominator| (|#3| |#3|)) (SIGNATURE |splitDenominator| ((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|))) (|IntegralDomain|) (|QuotientFieldCategory| |#1|) (|UnivariatePolynomialCategory| |#2|)) (T |UnivariatePolynomialCommonDenominator|)) 
((|splitDenominator| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|QuotientFieldCategory| *4)) (|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| *4))) (|isDomain| *1 (|UnivariatePolynomialCommonDenominator| *4 *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|clearDenominator| (*1 *2 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|QuotientFieldCategory| *3)) (|isDomain| *1 (|UnivariatePolynomialCommonDenominator| *3 *4 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)))) (|commonDenominator| (*1 *2 *3) (AND (|ofCategory| *4 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|isDomain| *1 (|UnivariatePolynomialCommonDenominator| *2 *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |commonDenominator| (|#1| |#3|)) (SIGNATURE |clearDenominator| (|#3| |#3|)) (SIGNATURE |splitDenominator| ((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|))) 
((|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) 29)) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) 30)) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) 42)) (|monicCompleteDecompose| (((|List| |#2|) |#2|) 44)) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) 39))) 
(((|UnivariatePolynomialDecompositionPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |monicRightFactorIfCan| ((|Union| |#2| "failed") |#2| (|NonNegativeInteger|))) (SIGNATURE |rightFactorIfCan| ((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|)) (SIGNATURE |leftFactorIfCan| ((|Union| |#2| "failed") |#2| |#2|)) (SIGNATURE |monicDecomposeIfCan| ((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|)) (SIGNATURE |monicCompleteDecompose| ((|List| |#2|) |#2|))) (|Join| (|IntegralDomain|) (|CharacteristicZero|)) (|UnivariatePolynomialCategory| |#1|)) (T |UnivariatePolynomialDecompositionPackage|)) 
((|monicCompleteDecompose| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|UnivariatePolynomialDecompositionPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|monicDecomposeIfCan| (*1 *2 *3) (|partial| AND (|ofCategory| *4 (|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *2 (|Record| (|:| |left| *3) (|:| |right| *3))) (|isDomain| *1 (|UnivariatePolynomialDecompositionPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|leftFactorIfCan| (*1 *2 *2 *2) (|partial| AND (|ofCategory| *3 (|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *1 (|UnivariatePolynomialDecompositionPackage| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|rightFactorIfCan| (*1 *2 *2 *3 *4) (|partial| AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *1 (|UnivariatePolynomialDecompositionPackage| *4 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)))) (|monicRightFactorIfCan| (*1 *2 *2 *3) (|partial| AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *1 (|UnivariatePolynomialDecompositionPackage| *4 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |monicRightFactorIfCan| ((|Union| |#2| "failed") |#2| (|NonNegativeInteger|))) (SIGNATURE |rightFactorIfCan| ((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|)) (SIGNATURE |leftFactorIfCan| ((|Union| |#2| "failed") |#2| |#2|)) (SIGNATURE |monicDecomposeIfCan| ((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|)) (SIGNATURE |monicCompleteDecompose| ((|List| |#2|) |#2|))) 
((|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) 31))) 
(((|UnivariatePolynomialDivisionPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |divideIfCan| ((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|))) (|IntegralDomain|) (|UnivariatePolynomialCategory| |#1|)) (T |UnivariatePolynomialDivisionPackage|)) 
((|divideIfCan| (*1 *2 *3 *3) (|partial| AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) (|isDomain| *1 (|UnivariatePolynomialDivisionPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(CATEGORY |package| (SIGNATURE |divideIfCan| ((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|))) 
((|noKaratsuba| ((|#2| |#2| |#2|) 19)) (|karatsubaOnce| ((|#2| |#2| |#2|) 30)) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) 36))) 
(((|UnivariatePolynomialMultiplicationPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |noKaratsuba| (|#2| |#2| |#2|)) (SIGNATURE |karatsubaOnce| (|#2| |#2| |#2|)) (SIGNATURE |karatsuba| (|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)))) (|Ring|) (|UnivariatePolynomialCategory| |#1|)) (T |UnivariatePolynomialMultiplicationPackage|)) 
((|karatsuba| (*1 *2 *2 *2 *3 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|UnivariatePolynomialMultiplicationPackage| *4 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)))) (|karatsubaOnce| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|UnivariatePolynomialMultiplicationPackage| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|noKaratsuba| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|UnivariatePolynomialMultiplicationPackage| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(CATEGORY |package| (SIGNATURE |noKaratsuba| (|#2| |#2| |#2|)) (SIGNATURE |karatsubaOnce| (|#2| |#2| |#2|)) (SIGNATURE |karatsuba| (|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) NIL)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) NIL)) (|unvectorise| (($ (|Vector| |#2|)) NIL)) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) NIL)) (|univariate| (((|SparseUnivariatePolynomial| $) $ (|SingletonAsOrderedSet|)) NIL) (((|SparseUnivariatePolynomial| |#2|) $) NIL)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#2| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#2| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#2| (|IntegralDomain|)))) (|totalDegree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|List| (|SingletonAsOrderedSet|))) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|subResultantGcd| (($ $ $) NIL (|has| |#2| (|IntegralDomain|)))) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|squareFreePart| (($ $) NIL (|has| |#2| (|GcdDomain|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#2| (|GcdDomain|)))) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|sizeLess?| (((|Boolean|) $ $) NIL (|has| |#2| (|Field|)))) (|shiftRight| (($ $ (|NonNegativeInteger|)) NIL)) (|shiftLeft| (($ $ (|NonNegativeInteger|)) NIL)) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) NIL (|has| |#2| (|GcdDomain|)))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) NIL) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Union| (|Integer|) "failed") $) NIL (|has| |#2| (|RetractableTo| (|Integer|)))) (((|Union| (|SingletonAsOrderedSet|) "failed") $) NIL)) (|retract| ((|#2| $) NIL) (((|Fraction| (|Integer|)) $) NIL (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Integer|) $) NIL (|has| |#2| (|RetractableTo| (|Integer|)))) (((|SingletonAsOrderedSet|) $) NIL)) (|resultant| (($ $ $ (|SingletonAsOrderedSet|)) NIL (|has| |#2| (|CommutativeRing|))) ((|#2| $ $) NIL (|has| |#2| (|CommutativeRing|)))) (|rem| (($ $ $) NIL (|has| |#2| (|Field|)))) (|reductum| (($ $) NIL)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) NIL (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) NIL (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) (|Matrix| $) (|Vector| $)) NIL) (((|Matrix| |#2|) (|Matrix| $)) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|quo| (($ $ $) NIL (|has| |#2| (|Field|)))) (|pseudoRemainder| (($ $ $) NIL)) (|pseudoQuotient| (($ $ $) NIL (|has| |#2| (|IntegralDomain|)))) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#2| (|IntegralDomain|)))) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL (|has| |#2| (|Field|)))) (|primitivePart| (($ $) NIL (|has| |#2| (|GcdDomain|))) (($ $ (|SingletonAsOrderedSet|)) NIL (|has| |#2| (|GcdDomain|)))) (|primitiveMonomials| (((|List| $) $) NIL)) (|prime?| (((|Boolean|) $) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|pomopo!| (($ $ |#2| (|NonNegativeInteger|) $) NIL)) (|patternMatch| (((|PatternMatchResult| (|Float|) $) $ (|Pattern| (|Float|)) (|PatternMatchResult| (|Float|) $)) NIL (AND (|has| (|SingletonAsOrderedSet|) (|PatternMatchable| (|Float|))) (|has| |#2| (|PatternMatchable| (|Float|))))) (((|PatternMatchResult| (|Integer|) $) $ (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) $)) NIL (AND (|has| (|SingletonAsOrderedSet|) (|PatternMatchable| (|Integer|))) (|has| |#2| (|PatternMatchable| (|Integer|)))))) (|order| (((|NonNegativeInteger|) $ $) NIL (|has| |#2| (|IntegralDomain|)))) (|one?| (((|Boolean|) $) NIL)) (|numberOfMonomials| (((|NonNegativeInteger|) $) NIL)) (|nextItem| (((|Union| $ "failed") $) NIL (|has| |#2| (|StepThrough|)))) (|multivariate| (($ (|SparseUnivariatePolynomial| |#2|) (|SingletonAsOrderedSet|)) NIL) (($ (|SparseUnivariatePolynomial| $) (|SingletonAsOrderedSet|)) NIL)) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#2| (|Field|)))) (|monomials| (((|List| $) $) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monomial| (($ |#2| (|NonNegativeInteger|)) 17) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ (|SingletonAsOrderedSet|)) NIL) (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL)) (|minimumDegree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|SingletonAsOrderedSet|)) NIL) (((|List| (|NonNegativeInteger|)) $ (|List| (|SingletonAsOrderedSet|))) NIL)) (|min| (($ $ $) NIL (|has| |#2| (|OrderedSet|)))) (|max| (($ $ $) NIL (|has| |#2| (|OrderedSet|)))) (|mapExponents| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) NIL)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL)) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) NIL)) (|mainVariable| (((|Union| (|SingletonAsOrderedSet|) "failed") $) NIL)) (|leadingMonomial| (($ $) NIL)) (|leadingCoefficient| ((|#2| $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| |#2| (|GcdDomain|)))) (|lcm| (($ (|List| $)) NIL (|has| |#2| (|GcdDomain|))) (($ $ $) NIL (|has| |#2| (|GcdDomain|)))) (|latex| (((|String|) $) NIL)) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) NIL)) (|isTimes| (((|Union| (|List| $) "failed") $) NIL)) (|isPlus| (((|Union| (|List| $) "failed") $) NIL)) (|isExpt| (((|Union| (|Record| (|:| |var| (|SingletonAsOrderedSet|)) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) NIL)) (|integrate| (($ $) NIL (|has| |#2| (|Algebra| (|Fraction| (|Integer|)))))) (|init| (($) NIL (|has| |#2| (|StepThrough|)) CONST)) (|hash| (((|SingleInteger|) $) NIL)) (|ground?| (((|Boolean|) $) NIL)) (|ground| ((|#2| $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|GcdDomain|)))) (|gcd| (($ (|List| $)) NIL (|has| |#2| (|GcdDomain|))) (($ $ $) NIL (|has| |#2| (|GcdDomain|)))) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) NIL)) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) NIL (|has| |#2| (|PolynomialFactorizationExplicit|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL (|has| |#2| (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#2| (|Field|)))) (|exquo| (((|Union| $ "failed") $ |#2|) NIL (|has| |#2| (|IntegralDomain|))) (((|Union| $ "failed") $ $) NIL (|has| |#2| (|IntegralDomain|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#2| (|Field|)))) (|eval| (($ $ (|List| (|Equation| $))) NIL) (($ $ (|Equation| $)) NIL) (($ $ $ $) NIL) (($ $ (|List| $) (|List| $)) NIL) (($ $ (|SingletonAsOrderedSet|) |#2|) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| |#2|)) NIL) (($ $ (|SingletonAsOrderedSet|) $) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| $)) NIL)) (|euclideanSize| (((|NonNegativeInteger|) $) NIL (|has| |#2| (|Field|)))) (|elt| ((|#2| $ |#2|) NIL) (($ $ $) NIL) (((|Fraction| $) (|Fraction| $) (|Fraction| $)) NIL (|has| |#2| (|IntegralDomain|))) ((|#2| (|Fraction| $) |#2|) NIL (|has| |#2| (|Field|))) (((|Fraction| $) $ (|Fraction| $)) NIL (|has| |#2| (|IntegralDomain|)))) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) NIL)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#2| (|Field|)))) (|discriminant| (($ $ (|SingletonAsOrderedSet|)) NIL (|has| |#2| (|CommutativeRing|))) ((|#2| $) NIL (|has| |#2| (|CommutativeRing|)))) (|differentiate| (($ $ (|SingletonAsOrderedSet|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|))) NIL) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $) NIL) (($ $ (|Symbol|)) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) NIL (|has| |#2| 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(|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#2| |#2|)) NIL)) (>= (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (> (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (= (((|Boolean|) $ $) NIL)) (<= (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (< (((|Boolean|) $ $) NIL (|has| |#2| (|OrderedSet|)))) (/ (($ $ |#2|) NIL (|has| |#2| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#2| (|Algebra| (|Fraction| (|Integer|))))) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#2| (|Algebra| (|Fraction| (|Integer|))))) (($ |#2| $) NIL) (($ $ |#2|) NIL))) 
(((|UnivariatePolynomial| |#1| |#2|) (|Join| (|UnivariatePolynomialCategory| |#2|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Variable| |#1|))) (SIGNATURE |fmecg| ($ $ (|NonNegativeInteger|) |#2| $)))) (|Symbol|) (|Ring|)) (T |UnivariatePolynomial|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Variable| *3)) (|ofType| *3 (|Symbol|)) (|isDomain| *1 (|UnivariatePolynomial| *3 *4)) (|ofCategory| *4 (|Ring|)))) (|fmecg| (*1 *1 *1 *2 *3 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|UnivariatePolynomial| *4 *3)) (|ofType| *4 (|Symbol|)) (|ofCategory| *3 (|Ring|))))) 
(|Join| (|UnivariatePolynomialCategory| |#2|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Variable| |#1|))) (SIGNATURE |fmecg| ($ $ (|NonNegativeInteger|) |#2| $)))) 
((|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) 22))) 
(((|UnivariatePolynomialCategoryFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#3| |#1|) |#2|))) (|Ring|) (|UnivariatePolynomialCategory| |#1|) (|Ring|) (|UnivariatePolynomialCategory| |#3|)) (T |UnivariatePolynomialCategoryFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *6)) (|isDomain| *1 (|UnivariatePolynomialCategoryFunctions2| *5 *4 *6 *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#3| |#1|) |#2|))) 
((|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) 113)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) 15)) (|unvectorise| (($ (|Vector| |#2|)) 115)) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) 66)) (|totalDegree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|List| (|SingletonAsOrderedSet|))) 18)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 185)) (|squareFreePart| (($ $) 175)) (|squareFree| (((|Factored| $) $) 173)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 81)) (|shiftRight| (($ $ (|NonNegativeInteger|)) 70)) (|shiftLeft| (($ $ (|NonNegativeInteger|)) 72)) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) 131)) (|retractIfCan| (((|Union| |#2| "failed") $) 118) (((|Union| (|Fraction| (|Integer|)) "failed") $) NIL) (((|Union| (|Integer|) "failed") $) NIL) (((|Union| (|SingletonAsOrderedSet|) "failed") $) NIL)) (|retract| ((|#2| $) 116) (((|Fraction| (|Integer|)) $) NIL) (((|Integer|) $) NIL) (((|SingletonAsOrderedSet|) $) NIL)) (|pseudoQuotient| (($ $ $) 152)) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) 154)) (|order| (((|NonNegativeInteger|) $ $) 170)) (|nextItem| (((|Union| $ "failed") $) 124)) (|monomial| (($ |#2| (|NonNegativeInteger|)) NIL) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) 46) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL)) (|minimumDegree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|SingletonAsOrderedSet|)) 41) (((|List| (|NonNegativeInteger|)) $ (|List| (|SingletonAsOrderedSet|))) 42)) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) 58)) (|mainVariable| (((|Union| (|SingletonAsOrderedSet|) "failed") $) 39)) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) 69)) (|integrate| (($ $) 196)) (|init| (($) 120)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 182)) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 87)) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 85)) (|factor| (((|Factored| $) $) 105)) (|eval| (($ $ (|List| (|Equation| $))) 38) (($ $ (|Equation| $)) NIL) (($ $ $ $) NIL) (($ $ (|List| $) (|List| $)) NIL) (($ $ (|SingletonAsOrderedSet|) |#2|) 31) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| |#2|)) 28) (($ $ (|SingletonAsOrderedSet|) $) 25) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| $)) 23)) (|euclideanSize| (((|NonNegativeInteger|) $) 188)) (|elt| ((|#2| $ |#2|) NIL) (($ $ $) NIL) (((|Fraction| $) (|Fraction| $) (|Fraction| $)) 148) ((|#2| (|Fraction| $) |#2|) 187) (((|Fraction| $) $ (|Fraction| $)) 169)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 191)) (|differentiate| (($ $ (|SingletonAsOrderedSet|)) 141) (($ $ (|List| (|SingletonAsOrderedSet|))) NIL) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $) 139) (($ $ (|Symbol|)) NIL) (($ $ (|List| (|Symbol|))) NIL) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL) (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) NIL) (($ $ (|Mapping| |#2| |#2|)) 138) (($ $ (|Mapping| |#2| |#2|) $) 135)) (|degree| (((|NonNegativeInteger|) $) NIL) (((|NonNegativeInteger|) $ (|SingletonAsOrderedSet|)) 16) (((|List| (|NonNegativeInteger|)) $ (|List| (|SingletonAsOrderedSet|))) 20)) (|content| ((|#2| $) NIL) (($ $ (|SingletonAsOrderedSet|)) 126)) (|composite| (((|Union| $ "failed") $ $) 162) (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) 158)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ |#2|) NIL) (($ (|SingletonAsOrderedSet|)) 50) (($ (|Fraction| (|Integer|))) NIL) (($ $) NIL))) 
(((|UnivariatePolynomialCategory&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |coerce| (|#1| |#1|)) (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |squareFree| ((|Factored| |#1|) |#1|)) (SIGNATURE |squareFreePart| (|#1| |#1|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |init| (|#1|)) (SIGNATURE |nextItem| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |elt| ((|Fraction| |#1|) |#1| (|Fraction| |#1|))) (SIGNATURE |euclideanSize| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |divide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |integrate| (|#1| |#1|)) (SIGNATURE |elt| (|#2| (|Fraction| |#1|) |#2|)) (SIGNATURE |separate| ((|Record| (|:| |primePart| |#1|) (|:| |commonPart| |#1|)) |#1| |#1|)) (SIGNATURE |pseudoDivide| ((|Record| (|:| |coef| |#2|) (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |pseudoQuotient| (|#1| |#1| |#1|)) (SIGNATURE |composite| ((|Union| (|Fraction| |#1|) "failed") (|Fraction| |#1|) |#1|)) (SIGNATURE |composite| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE |order| ((|NonNegativeInteger|) |#1| |#1|)) (SIGNATURE |elt| ((|Fraction| |#1|) (|Fraction| |#1|) (|Fraction| |#1|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |shiftLeft| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |shiftRight| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |karatsubaDivide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| (|NonNegativeInteger|))) (SIGNATURE |unmakeSUP| (|#1| (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |makeSUP| ((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |unvectorise| (|#1| (|Vector| |#2|))) (SIGNATURE |vectorise| ((|Vector| |#2|) |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |elt| (|#1| |#1| |#1|)) (SIGNATURE |elt| (|#2| |#1| |#2|)) (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) (SIGNATURE |squareFreePolynomial| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |factorPolynomial| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |factorSquareFreePolynomial| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |content| (|#1| |#1| (|SingletonAsOrderedSet|))) (SIGNATURE |variables| ((|List| (|SingletonAsOrderedSet|)) |#1|)) (SIGNATURE |totalDegree| ((|NonNegativeInteger|) |#1| (|List| (|SingletonAsOrderedSet|)))) (SIGNATURE |totalDegree| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |monomial| (|#1| |#1| (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |monomial| (|#1| |#1| (|SingletonAsOrderedSet|) (|NonNegativeInteger|))) (SIGNATURE |minimumDegree| ((|List| (|NonNegativeInteger|)) |#1| (|List| (|SingletonAsOrderedSet|)))) (SIGNATURE |minimumDegree| ((|NonNegativeInteger|) |#1| (|SingletonAsOrderedSet|))) (SIGNATURE |mainVariable| ((|Union| (|SingletonAsOrderedSet|) "failed") |#1|)) (SIGNATURE |degree| ((|List| (|NonNegativeInteger|)) |#1| (|List| (|SingletonAsOrderedSet|)))) (SIGNATURE |degree| ((|NonNegativeInteger|) |#1| (|SingletonAsOrderedSet|))) (SIGNATURE |retract| ((|SingletonAsOrderedSet|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|SingletonAsOrderedSet|) "failed") |#1|)) (SIGNATURE |coerce| (|#1| (|SingletonAsOrderedSet|))) (SIGNATURE |eval| (|#1| |#1| (|List| (|SingletonAsOrderedSet|)) (|List| |#1|))) (SIGNATURE |eval| (|#1| |#1| (|SingletonAsOrderedSet|) |#1|)) (SIGNATURE |eval| (|#1| |#1| (|List| (|SingletonAsOrderedSet|)) (|List| |#2|))) (SIGNATURE |eval| (|#1| |#1| (|SingletonAsOrderedSet|) |#2|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#1|) (|List| |#1|))) (SIGNATURE |eval| (|#1| |#1| |#1| |#1|)) (SIGNATURE |eval| (|#1| |#1| (|Equation| |#1|))) (SIGNATURE |eval| (|#1| |#1| (|List| (|Equation| |#1|)))) (SIGNATURE |degree| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |monomial| (|#1| |#2| (|NonNegativeInteger|))) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |minimumDegree| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |content| (|#2| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |differentiate| (|#1| |#1| (|SingletonAsOrderedSet|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|SingletonAsOrderedSet|)))) (SIGNATURE |differentiate| (|#1| |#1| (|SingletonAsOrderedSet|))) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|UnivariatePolynomialCategory| |#2|) (|Ring|)) (T |UnivariatePolynomialCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |coerce| (|#1| |#1|)) (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |squareFree| ((|Factored| |#1|) |#1|)) (SIGNATURE |squareFreePart| (|#1| |#1|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |init| (|#1|)) (SIGNATURE |nextItem| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |elt| ((|Fraction| |#1|) |#1| (|Fraction| |#1|))) (SIGNATURE |euclideanSize| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |divide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |integrate| (|#1| |#1|)) (SIGNATURE |elt| (|#2| (|Fraction| |#1|) |#2|)) (SIGNATURE |separate| ((|Record| (|:| |primePart| |#1|) (|:| |commonPart| |#1|)) |#1| |#1|)) (SIGNATURE |pseudoDivide| ((|Record| (|:| |coef| |#2|) (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |pseudoQuotient| (|#1| |#1| |#1|)) (SIGNATURE |composite| ((|Union| (|Fraction| |#1|) "failed") (|Fraction| |#1|) |#1|)) (SIGNATURE |composite| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE |order| ((|NonNegativeInteger|) |#1| |#1|)) (SIGNATURE |elt| ((|Fraction| |#1|) (|Fraction| |#1|) (|Fraction| |#1|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |shiftLeft| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |shiftRight| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |karatsubaDivide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| (|NonNegativeInteger|))) (SIGNATURE |unmakeSUP| (|#1| (|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |makeSUP| ((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |unvectorise| (|#1| (|Vector| |#2|))) (SIGNATURE |vectorise| ((|Vector| |#2|) |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|))) (SIGNATURE |differentiate| (|#1| |#1| (|Mapping| |#2| |#2|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|Symbol|)))) (SIGNATURE |differentiate| (|#1| |#1| (|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |elt| (|#1| |#1| |#1|)) (SIGNATURE |elt| (|#2| |#1| |#2|)) (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) (SIGNATURE |squareFreePolynomial| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |factorPolynomial| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |factorSquareFreePolynomial| ((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |content| (|#1| |#1| (|SingletonAsOrderedSet|))) (SIGNATURE |variables| ((|List| (|SingletonAsOrderedSet|)) |#1|)) (SIGNATURE |totalDegree| ((|NonNegativeInteger|) |#1| (|List| (|SingletonAsOrderedSet|)))) (SIGNATURE |totalDegree| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |monomial| (|#1| |#1| (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |monomial| (|#1| |#1| (|SingletonAsOrderedSet|) (|NonNegativeInteger|))) (SIGNATURE |minimumDegree| ((|List| (|NonNegativeInteger|)) |#1| (|List| (|SingletonAsOrderedSet|)))) (SIGNATURE |minimumDegree| ((|NonNegativeInteger|) |#1| (|SingletonAsOrderedSet|))) (SIGNATURE |mainVariable| ((|Union| (|SingletonAsOrderedSet|) "failed") |#1|)) (SIGNATURE |degree| ((|List| (|NonNegativeInteger|)) |#1| (|List| (|SingletonAsOrderedSet|)))) (SIGNATURE |degree| ((|NonNegativeInteger|) |#1| (|SingletonAsOrderedSet|))) (SIGNATURE |retract| ((|SingletonAsOrderedSet|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|SingletonAsOrderedSet|) "failed") |#1|)) (SIGNATURE |coerce| (|#1| (|SingletonAsOrderedSet|))) (SIGNATURE |eval| (|#1| |#1| (|List| (|SingletonAsOrderedSet|)) (|List| |#1|))) (SIGNATURE |eval| (|#1| |#1| (|SingletonAsOrderedSet|) |#1|)) (SIGNATURE |eval| (|#1| |#1| (|List| (|SingletonAsOrderedSet|)) (|List| |#2|))) (SIGNATURE |eval| (|#1| |#1| (|SingletonAsOrderedSet|) |#2|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#1|) (|List| |#1|))) (SIGNATURE |eval| (|#1| |#1| |#1| |#1|)) (SIGNATURE |eval| (|#1| |#1| (|Equation| |#1|))) (SIGNATURE |eval| (|#1| |#1| (|List| (|Equation| |#1|)))) (SIGNATURE |degree| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |monomial| (|#1| |#2| (|NonNegativeInteger|))) (SIGNATURE |retract| ((|Integer|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Integer|) "failed") |#1|)) (SIGNATURE |retract| ((|Fraction| (|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |minimumDegree| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |content| (|#2| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |differentiate| (|#1| |#1| (|SingletonAsOrderedSet|) (|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| (|List| (|SingletonAsOrderedSet|)))) (SIGNATURE |differentiate| (|#1| |#1| (|SingletonAsOrderedSet|))) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) 219)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) 109)) (|unvectorise| (($ (|Vector| |#1|)) 218)) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) 216)) (|univariate| (((|SparseUnivariatePolynomial| $) $ (|SingletonAsOrderedSet|)) 124) (((|SparseUnivariatePolynomial| |#1|) $) 123)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 85 (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) 86 (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) 88 (|has| |#1| (|IntegralDomain|)))) (|totalDegree| (((|NonNegativeInteger|) $) 111) (((|NonNegativeInteger|) $ (|List| (|SingletonAsOrderedSet|))) 110)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|subResultantGcd| (($ $ $) 203 (|has| |#1| (|IntegralDomain|)))) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 99 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(|retract| ((|#1| $) 164) (((|Fraction| (|Integer|)) $) 160 (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|Integer|) $) 158 (|has| |#1| (|RetractableTo| (|Integer|)))) (((|SingletonAsOrderedSet|) $) 134)) (|resultant| (($ $ $ (|SingletonAsOrderedSet|)) 107 (|has| |#1| (|CommutativeRing|))) ((|#1| $ $) 206 (|has| |#1| (|CommutativeRing|)))) (|rem| (($ $ $) 192 (|has| |#1| (|Field|)))) (|reductum| (($ $) 153)) (|reducedSystem| (((|Matrix| (|Integer|)) (|Matrix| $)) 133 (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| (|Integer|))) (|:| |vec| (|Vector| (|Integer|)))) (|Matrix| $) (|Vector| $)) 132 (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|)))) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) 131) (((|Matrix| |#1|) (|Matrix| $)) 130)) (|recip| (((|Union| $ "failed") $) 33)) (|quo| (($ $ $) 191 (|has| |#1| (|Field|)))) (|pseudoRemainder| (($ $ $) 209)) (|pseudoQuotient| (($ $ $) 200 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|#1| (|PatternMatchable| (|Integer|)))))) (|order| (((|NonNegativeInteger|) $ $) 204 (|has| |#1| (|IntegralDomain|)))) (|one?| (((|Boolean|) $) 30)) (|numberOfMonomials| (((|NonNegativeInteger|) $) 168)) (|nextItem| (((|Union| $ "failed") $) 184 (|has| |#1| (|StepThrough|)))) (|multivariate| (($ (|SparseUnivariatePolynomial| |#1|) (|SingletonAsOrderedSet|)) 116) (($ (|SparseUnivariatePolynomial| $) (|SingletonAsOrderedSet|)) 115)) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) 215)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 195 (|has| |#1| (|Field|)))) (|monomials| (((|List| $) $) 125)) (|monomial?| (((|Boolean|) $) 151)) (|monomial| (($ |#1| (|NonNegativeInteger|)) 152) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) 118) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) 117)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ (|SingletonAsOrderedSet|)) 119) (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 213)) (|minimumDegree| (((|NonNegativeInteger|) $) 169) (((|NonNegativeInteger|) $ (|SingletonAsOrderedSet|)) 121) (((|List| (|NonNegativeInteger|)) $ (|List| (|SingletonAsOrderedSet|))) 120)) (|min| (($ $ $) 77 (|has| |#1| (|OrderedSet|)))) (|max| (($ $ $) 76 (|has| |#1| (|OrderedSet|)))) (|mapExponents| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) 170)) (|map| (($ (|Mapping| |#1| |#1|) $) 150)) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) 217)) (|mainVariable| (((|Union| (|SingletonAsOrderedSet|) "failed") $) 122)) (|leadingMonomial| (($ $) 148)) (|leadingCoefficient| ((|#1| $) 147)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 89 (|has| |#1| (|GcdDomain|)))) (|lcm| (($ (|List| $)) 93 (|has| |#1| (|GcdDomain|))) (($ $ $) 92 (|has| |#1| (|GcdDomain|)))) (|latex| (((|String|) $) 9)) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) 212)) (|isTimes| (((|Union| (|List| $) "failed") $) 113)) (|isPlus| (((|Union| (|List| $) "failed") $) 114)) (|isExpt| (((|Union| (|Record| (|:| |var| (|SingletonAsOrderedSet|)) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) 112)) (|integrate| (($ $) 196 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|init| (($) 183 (|has| |#1| (|StepThrough|)) CONST)) (|hash| (((|SingleInteger|) $) 10)) (|ground?| (((|Boolean|) $) 165)) (|ground| ((|#1| $) 166)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 94 (|has| |#1| (|GcdDomain|)))) (|gcd| (($ (|List| $)) 91 (|has| |#1| (|GcdDomain|))) (($ $ $) 90 (|has| |#1| (|GcdDomain|)))) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 101 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 100 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|factor| (((|Factored| $) $) 98 (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 194 (|has| |#1| (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 193 (|has| |#1| (|Field|)))) (|exquo| (((|Union| $ "failed") $ |#1|) 173 (|has| |#1| (|IntegralDomain|))) (((|Union| $ "failed") $ $) 84 (|has| |#1| (|IntegralDomain|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 187 (|has| |#1| (|Field|)))) (|eval| (($ $ (|List| (|Equation| $))) 144) (($ $ (|Equation| $)) 143) (($ $ $ $) 142) (($ $ (|List| $) (|List| $)) 141) (($ $ (|SingletonAsOrderedSet|) |#1|) 140) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| |#1|)) 139) (($ $ (|SingletonAsOrderedSet|) $) 138) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| $)) 137)) (|euclideanSize| (((|NonNegativeInteger|) $) 189 (|has| |#1| (|Field|)))) (|elt| ((|#1| $ |#1|) 237) (($ $ $) 236) (((|Fraction| $) (|Fraction| $) (|Fraction| $)) 205 (|has| |#1| (|IntegralDomain|))) ((|#1| (|Fraction| $) |#1|) 197 (|has| |#1| (|Field|))) (((|Fraction| $) $ (|Fraction| $)) 185 (|has| |#1| (|IntegralDomain|)))) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) 214)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 190 (|has| |#1| (|Field|)))) (|discriminant| (($ $ (|SingletonAsOrderedSet|)) 106 (|has| |#1| (|CommutativeRing|))) ((|#1| $) 207 (|has| |#1| (|CommutativeRing|)))) (|differentiate| (($ $ (|SingletonAsOrderedSet|)) 41) (($ $ (|List| (|SingletonAsOrderedSet|))) 40) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) 39) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) 38) (($ $ (|NonNegativeInteger|)) 234) (($ $) 232) (($ $ (|Symbol|)) 231 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) 230 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 229 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 228 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) 221) (($ $ (|Mapping| |#1| |#1|)) 220) (($ $ (|Mapping| |#1| |#1|) $) 208)) (|degree| (((|NonNegativeInteger|) $) 149) (((|NonNegativeInteger|) $ (|SingletonAsOrderedSet|)) 129) (((|List| (|NonNegativeInteger|)) $ (|List| (|SingletonAsOrderedSet|))) 128)) (|convert| (((|Pattern| (|Float|)) $) 80 (AND (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))))) (((|Pattern| (|Integer|)) $) 79 (AND (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))))) (((|InputForm|) $) 78 (AND (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|InputForm|))) (|has| |#1| (|ConvertibleTo| (|InputForm|)))))) (|content| ((|#1| $) 174 (|has| |#1| (|GcdDomain|))) (($ $ (|SingletonAsOrderedSet|)) 105 (|has| |#1| (|GcdDomain|)))) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 103 (|and| (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))))) (|composite| (((|Union| $ "failed") $ $) 202 (|has| |#1| (|IntegralDomain|))) (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) 201 (|has| |#1| (|IntegralDomain|)))) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ |#1|) 162) (($ (|SingletonAsOrderedSet|)) 136) (($ (|Fraction| (|Integer|))) 70 (OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (($ $) 83 (|has| |#1| (|IntegralDomain|)))) (|coefficients| (((|List| |#1|) $) 167)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) 154) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) 127) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) 126)) (|charthRoot| (((|Union| $ "failed") $) 71 (OR (|and| (|has| $ (|CharacteristicNonZero|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|CharacteristicNonZero|))))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) 172 (|has| |#1| (|CommutativeRing|)))) (|associates?| (((|Boolean|) $ $) 87 (|has| |#1| (|IntegralDomain|)))) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $ (|SingletonAsOrderedSet|)) 37) (($ $ (|List| (|SingletonAsOrderedSet|))) 36) (($ $ (|SingletonAsOrderedSet|) (|NonNegativeInteger|)) 35) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|NonNegativeInteger|))) 34) (($ $ (|NonNegativeInteger|)) 235) (($ $) 233) (($ $ (|Symbol|)) 227 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|))) 226 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 225 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 224 (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) 223) (($ $ (|Mapping| |#1| |#1|)) 222)) (>= (((|Boolean|) $ $) 74 (|has| |#1| (|OrderedSet|)))) (> (((|Boolean|) $ $) 73 (|has| |#1| (|OrderedSet|)))) (= (((|Boolean|) $ $) 6)) (<= (((|Boolean|) $ $) 75 (|has| |#1| (|OrderedSet|)))) (< (((|Boolean|) $ $) 72 (|has| |#1| (|OrderedSet|)))) (/ (($ $ |#1|) 155 (|has| |#1| (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ (|Fraction| (|Integer|))) 157 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ (|Fraction| (|Integer|)) $) 156 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ |#1| $) 146) (($ $ |#1|) 145))) 
(((|UnivariatePolynomialCategory| |#1|) (|Category|) (|Ring|)) (T |UnivariatePolynomialCategory|)) 
((|vectorise| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Vector| *4)))) (|unvectorise| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|UnivariatePolynomialCategory| *3)))) (|makeSUP| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|unmakeSUP| (*1 *1 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|UnivariatePolynomialCategory| *3)))) (|multiplyExponents| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|divideExponents| (*1 *1 *1 *2) (|partial| AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|monicDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|UnivariatePolynomialCategory| *3)))) (|karatsubaDivide| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|UnivariatePolynomialCategory| *4)))) (|shiftRight| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|shiftLeft| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|pseudoRemainder| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|differentiate| (*1 *1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|discriminant| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|CommutativeRing|)))) (|resultant| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|CommutativeRing|)))) (|elt| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Fraction| *1)) (|ofCategory| *1 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|IntegralDomain|)))) (|order| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|subResultantGcd| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|IntegralDomain|)))) (|composite| (*1 *1 *1 *1) (|partial| AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|IntegralDomain|)))) (|composite| (*1 *2 *2 *1) (|partial| AND (|isDomain| *2 (|Fraction| *1)) (|ofCategory| *1 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|IntegralDomain|)))) (|pseudoQuotient| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|IntegralDomain|)))) (|pseudoDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |coef| *3) (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|UnivariatePolynomialCategory| *3)))) (|separate| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |primePart| *1) (|:| |commonPart| *1))) (|ofCategory| *1 (|UnivariatePolynomialCategory| *3)))) (|elt| (*1 *2 *3 *2) (AND (|isDomain| *3 (|Fraction| *1)) (|ofCategory| *1 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|integrate| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))))) 
(|Join| (|PolynomialCategory| |t#1| (|NonNegativeInteger|) (|SingletonAsOrderedSet|)) (|Eltable| |t#1| |t#1|) (|Eltable| $ $) (|DifferentialRing|) (|DifferentialExtension| |t#1|) (CATEGORY |domain| (SIGNATURE |vectorise| ((|Vector| |t#1|) $ (|NonNegativeInteger|))) (SIGNATURE |unvectorise| ($ (|Vector| |t#1|))) (SIGNATURE |makeSUP| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |unmakeSUP| ($ (|SparseUnivariatePolynomial| |t#1|))) (SIGNATURE |multiplyExponents| ($ $ (|NonNegativeInteger|))) (SIGNATURE |divideExponents| ((|Union| $ "failed") $ (|NonNegativeInteger|))) (SIGNATURE |monicDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |karatsubaDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|))) (SIGNATURE |shiftRight| ($ $ (|NonNegativeInteger|))) (SIGNATURE |shiftLeft| ($ $ (|NonNegativeInteger|))) (SIGNATURE |pseudoRemainder| ($ $ $)) (SIGNATURE |differentiate| ($ $ (|Mapping| |t#1| |t#1|) $)) (IF (|has| |t#1| (|StepThrough|)) (ATTRIBUTE (|StepThrough|)) |noBranch|) (IF (|has| |t#1| (|CommutativeRing|)) (PROGN (SIGNATURE |discriminant| (|t#1| $)) (SIGNATURE |resultant| (|t#1| $ $))) |noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (ATTRIBUTE (|Eltable| (|Fraction| $) (|Fraction| $))) (SIGNATURE |elt| ((|Fraction| $) (|Fraction| $) (|Fraction| $))) (SIGNATURE |order| ((|NonNegativeInteger|) $ $)) (SIGNATURE |subResultantGcd| ($ $ $)) (SIGNATURE |composite| ((|Union| $ "failed") $ $)) (SIGNATURE |composite| ((|Union| (|Fraction| $) "failed") (|Fraction| $) $)) (SIGNATURE |pseudoQuotient| ($ $ $)) (SIGNATURE |pseudoDivide| ((|Record| (|:| |coef| |t#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $))) |noBranch|) (IF (|has| |t#1| (|GcdDomain|)) (SIGNATURE |separate| ((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $)) |noBranch|) (IF (|has| |t#1| (|Field|)) (PROGN (ATTRIBUTE (|EuclideanDomain|)) (ATTRIBUTE |additiveValuation|) (SIGNATURE |elt| (|t#1| (|Fraction| $) |t#1|))) |noBranch|) (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $)) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| (|NonNegativeInteger|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|))) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|ConvertibleTo| (|InputForm|)) AND (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|InputForm|))) (|has| |#1| (|ConvertibleTo| (|InputForm|)))) ((|ConvertibleTo| (|Pattern| (|Float|))) AND (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|))))) ((|ConvertibleTo| (|Pattern| (|Integer|))) AND (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|))))) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) . T) ((|Eltable| (|Fraction| $) (|Fraction| $)) |has| |#1| (|IntegralDomain|)) ((|Eltable| |#1| |#1|) . T) ((|Eltable| $ $) . T) ((|EntireRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|))) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Evalable| $) . T) ((|FiniteAbelianMonoidRing| |#1| (|NonNegativeInteger|)) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|GcdDomain|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|))) ((|InnerEvalable| (|SingletonAsOrderedSet|) |#1|) . T) ((|InnerEvalable| (|SingletonAsOrderedSet|) $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|))) ((|LeftModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|))) ((|LinearlyExplicitRingOver| (|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|PartialDifferentialRing| (|SingletonAsOrderedSet|)) . T) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PatternMatchable| (|Float|)) AND (|has| (|SingletonAsOrderedSet|) (|PatternMatchable| (|Float|))) (|has| |#1| (|PatternMatchable| (|Float|)))) ((|PatternMatchable| (|Integer|)) AND (|has| (|SingletonAsOrderedSet|) (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Integer|)))) ((|PolynomialCategory| |#1| (|NonNegativeInteger|) (|SingletonAsOrderedSet|)) . T) ((|PolynomialFactorizationExplicit|) |has| |#1| (|PolynomialFactorizationExplicit|)) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| (|SingletonAsOrderedSet|)) . T) ((|RetractableTo| |#1|) . T) ((|RightModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|StepThrough|)) ((|UniqueFactorizationDomain|) |has| |#1| (|PolynomialFactorizationExplicit|))) 
((|variables| (((|List| (|SingletonAsOrderedSet|)) $) 28)) (|reductum| (($ $) 25)) (|monomial| (($ |#2| |#3|) NIL) (($ $ (|SingletonAsOrderedSet|) |#3|) 22) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| |#3|)) 20)) (|leadingMonomial| (($ $) 14)) (|leadingCoefficient| ((|#2| $) 12)) (|degree| ((|#3| $) 10))) 
(((|UnivariatePowerSeriesCategory&| |#1| |#2| |#3|) (CATEGORY |domain| (SIGNATURE |variables| ((|List| (|SingletonAsOrderedSet|)) |#1|)) (SIGNATURE |monomial| (|#1| |#1| (|List| (|SingletonAsOrderedSet|)) (|List| |#3|))) (SIGNATURE |monomial| (|#1| |#1| (|SingletonAsOrderedSet|) |#3|)) (SIGNATURE |reductum| (|#1| |#1|)) (SIGNATURE |monomial| (|#1| |#2| |#3|)) (SIGNATURE |degree| (|#3| |#1|)) (SIGNATURE |leadingMonomial| (|#1| |#1|)) (SIGNATURE |leadingCoefficient| (|#2| |#1|))) (|UnivariatePowerSeriesCategory| |#2| |#3|) (|Ring|) (|OrderedAbelianMonoid|)) (T |UnivariatePowerSeriesCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |variables| ((|List| (|SingletonAsOrderedSet|)) |#1|)) (SIGNATURE |monomial| (|#1| |#1| (|List| (|SingletonAsOrderedSet|)) (|List| |#3|))) (SIGNATURE |monomial| (|#1| |#1| (|SingletonAsOrderedSet|) |#3|)) (SIGNATURE |reductum| (|#1| |#1|)) (SIGNATURE |monomial| (|#1| |#2| |#3|)) (SIGNATURE |degree| (|#3| |#1|)) (SIGNATURE |leadingMonomial| (|#1| |#1|)) (SIGNATURE |leadingCoefficient| (|#2| |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) 70)) (|variable| (((|Symbol|) $) 98)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 50 (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) 51 (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) 53 (|has| |#1| (|IntegralDomain|)))) (|truncate| (($ $ |#2|) 93) (($ $ |#2| |#2|) 92)) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) 100)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|reductum| (($ $) 59)) (|recip| (((|Union| $ "failed") $) 33)) (|pole?| (((|Boolean|) $) 69)) (|order| ((|#2| $) 95) ((|#2| $ |#2|) 94)) (|one?| (((|Boolean|) $) 30)) (|multiplyExponents| (($ $ (|PositiveInteger|)) 96)) (|monomial?| (((|Boolean|) $) 61)) (|monomial| (($ |#1| |#2|) 60) (($ $ (|SingletonAsOrderedSet|) |#2|) 72) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| |#2|)) 71)) (|map| (($ (|Mapping| |#1| |#1|) $) 62)) (|leadingMonomial| (($ $) 64)) (|leadingCoefficient| ((|#1| $) 65)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|extend| (($ $ |#2|) 90)) (|exquo| (((|Union| $ "failed") $ $) 49 (|has| |#1| (|IntegralDomain|)))) (|eval| (((|Stream| |#1|) $ |#1|) 89 (|has| |#1| (SIGNATURE ** (|#1| |#1| |#2|))))) (|elt| ((|#1| $ |#2|) 99) (($ $ $) 76 (|has| |#2| (|SemiGroup|)))) (|differentiate| (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 84 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 83 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))))) (($ $ (|List| (|Symbol|))) 82 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))))) (($ $ (|Symbol|)) 81 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))))) (($ $ (|NonNegativeInteger|)) 79 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) (($ $) 77 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))))) (|degree| ((|#2| $) 63)) (|complete| (($ $) 68)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ (|Fraction| (|Integer|))) 56 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $) 48 (|has| |#1| (|IntegralDomain|))) (($ |#1|) 46 (|has| |#1| (|CommutativeRing|)))) (|coefficient| ((|#1| $ |#2|) 58)) (|charthRoot| (((|Union| $ "failed") $) 47 (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|center| ((|#1| $) 97)) (|associates?| (((|Boolean|) $ $) 52 (|has| |#1| (|IntegralDomain|)))) (|approximate| ((|#1| $ |#2|) 91 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| |#2|))) (|has| |#1| (SIGNATURE |coerce| (|#1| (|Symbol|))))))) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 88 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 87 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))))) (($ $ (|List| (|Symbol|))) 86 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))))) (($ $ (|Symbol|)) 85 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))))) (($ $ (|NonNegativeInteger|)) 80 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) (($ $) 78 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))))) (= (((|Boolean|) $ $) 6)) (/ (($ $ |#1|) 57 (|has| |#1| (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 67) (($ |#1| $) 66) (($ (|Fraction| (|Integer|)) $) 55 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) 54 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) 
(((|UnivariatePowerSeriesCategory| |#1| |#2|) (|Category|) (|Ring|) (|OrderedAbelianMonoid|)) (T |UnivariatePowerSeriesCategory|)) 
((|terms| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|Stream| (|Record| (|:| |k| *4) (|:| |c| *3)))))) (|elt| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *2 *3)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Ring|)))) (|variable| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|Symbol|)))) (|center| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *2 *3)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Ring|)))) (|multiplyExponents| (*1 *1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)))) (|order| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|order| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|truncate| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|truncate| (*1 *1 *1 *2 *2) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|approximate| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *2 *3)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|has| *2 (SIGNATURE ** (*2 *2 *3))) (|has| *2 (SIGNATURE |coerce| (*2 (|Symbol|)))) (|ofCategory| *2 (|Ring|)))) (|extend| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|eval| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|has| *3 (SIGNATURE ** (*3 *3 *4))) (|isDomain| *2 (|Stream| *3))))) 
(|Join| (|PowerSeriesCategory| |t#1| |t#2| (|SingletonAsOrderedSet|)) (CATEGORY |domain| (SIGNATURE |terms| ((|Stream| (|Record| (|:| |k| |t#2|) (|:| |c| |t#1|))) $)) (SIGNATURE |elt| (|t#1| $ |t#2|)) (SIGNATURE |variable| ((|Symbol|) $)) (SIGNATURE |center| (|t#1| $)) (SIGNATURE |multiplyExponents| ($ $ (|PositiveInteger|))) (SIGNATURE |order| (|t#2| $)) (SIGNATURE |order| (|t#2| $ |t#2|)) (SIGNATURE |truncate| ($ $ |t#2|)) (SIGNATURE |truncate| ($ $ |t#2| |t#2|)) (IF (|has| |t#1| (SIGNATURE |coerce| (|t#1| (|Symbol|)))) (IF (|has| |t#1| (SIGNATURE ** (|t#1| |t#1| |t#2|))) (SIGNATURE |approximate| (|t#1| $ |t#2|)) |noBranch|) |noBranch|) (SIGNATURE |extend| ($ $ |t#2|)) (IF (|has| |t#2| (|SemiGroup|)) (ATTRIBUTE (|Eltable| $ $)) |noBranch|) (IF (|has| |t#1| (SIGNATURE * (|t#1| |t#2| |t#1|))) (PROGN (ATTRIBUTE (|DifferentialRing|)) (IF (|has| |t#1| (|PartialDifferentialRing| (|Symbol|))) (ATTRIBUTE (|PartialDifferentialRing| (|Symbol|))) |noBranch|)) |noBranch|) (IF (|has| |t#1| (SIGNATURE ** (|t#1| |t#1| |t#2|))) (SIGNATURE |eval| ((|Stream| |t#1|) $ |t#1|)) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| |#2|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ((|Eltable| $ $) |has| |#2| (|SemiGroup|)) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|Module| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialRing| (|Symbol|)) AND (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PowerSeriesCategory| |#1| |#2| (|SingletonAsOrderedSet|)) . T) ((|RightModule| (|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((|squareFreePart| ((|#2| |#2|) 12)) (|squareFree| (((|Factored| |#2|) |#2|) 14)) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) 30))) 
(((|UnivariatePolynomialSquareFree| |#1| |#2|) (CATEGORY |package| (SIGNATURE |squareFree| ((|Factored| |#2|) |#2|)) (SIGNATURE |squareFreePart| (|#2| |#2|)) (SIGNATURE |BumInSepFFE| ((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))))) (|IntegralDomain|) (|Join| (|UnivariatePolynomialCategory| |#1|) (|IntegralDomain|) (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $))))) (T |UnivariatePolynomialSquareFree|)) 
((|BumInSepFFE| (*1 *2 *2) (AND (|isDomain| *2 (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) (|:| |xpnt| (|Integer|)))) (|ofCategory| *4 (|Join| (|UnivariatePolynomialCategory| *3) (|IntegralDomain|) (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $))))) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|UnivariatePolynomialSquareFree| *3 *4)))) (|squareFreePart| (*1 *2 *2) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *1 (|UnivariatePolynomialSquareFree| *3 *2)) (|ofCategory| *2 (|Join| (|UnivariatePolynomialCategory| *3) (|IntegralDomain|) (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $))))))) (|squareFree| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|UnivariatePolynomialSquareFree| *4 *3)) (|ofCategory| *3 (|Join| (|UnivariatePolynomialCategory| *4) (|IntegralDomain|) (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $)))))))) 
(CATEGORY |package| (SIGNATURE |squareFree| ((|Factored| |#2|) |#2|)) (SIGNATURE |squareFreePart| (|#2| |#2|)) (SIGNATURE |BumInSepFFE| ((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))))) 
((|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) 23))) 
(((|UnivariatePuiseuxSeriesFunctions2| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |map| ((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)))) (|Ring|) (|Ring|) (|Symbol|) (|Symbol|) |#1| |#2|) (T |UnivariatePuiseuxSeriesFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|UnivariatePuiseuxSeries| *5 *7 *9)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|Ring|)) (|ofType| *7 (|Symbol|)) (|ofType| *9 *5) (|ofType| *10 *6) (|isDomain| *2 (|UnivariatePuiseuxSeries| *6 *8 *10)) (|isDomain| *1 (|UnivariatePuiseuxSeriesFunctions2| *5 *6 *7 *8 *9 *10)) (|ofType| *8 (|Symbol|))))) 
(CATEGORY |package| (SIGNATURE |map| ((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) 70)) (|variable| (((|Symbol|) $) 98)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 50 (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) 51 (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) 53 (|has| |#1| (|IntegralDomain|)))) (|truncate| (($ $ (|Fraction| (|Integer|))) 93) (($ $ (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) 92)) (|terms| (((|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|))) $) 100)) (|tanh| (($ $) 127 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|tan| (($ $) 110 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 155 (|has| |#1| (|Field|)))) (|squareFree| (((|Factored| $) $) 156 (|has| |#1| (|Field|)))) (|sqrt| (($ $) 109 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sizeLess?| (((|Boolean|) $ $) 146 (|has| |#1| (|Field|)))) (|sinh| (($ $) 126 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sin| (($ $) 111 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) 165)) (|sech| (($ $) 125 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sec| (($ $) 112 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sample| (($) 16 T CONST)) (|rem| (($ $ $) 150 (|has| |#1| (|Field|)))) (|reductum| (($ $) 59)) (|recip| (((|Union| $ "failed") $) 33)) (|quo| (($ $ $) 149 (|has| |#1| (|Field|)))) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 144 (|has| |#1| (|Field|)))) (|prime?| (((|Boolean|) $) 157 (|has| |#1| (|Field|)))) (|pole?| (((|Boolean|) $) 69)) (|pi| (($) 137 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|order| (((|Fraction| (|Integer|)) $) 95) (((|Fraction| (|Integer|)) $ (|Fraction| (|Integer|))) 94)) (|one?| (((|Boolean|) $) 30)) (|nthRoot| (($ $ (|Integer|)) 108 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|multiplyExponents| (($ $ (|PositiveInteger|)) 96) (($ $ (|Fraction| (|Integer|))) 164)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 153 (|has| |#1| (|Field|)))) (|monomial?| (((|Boolean|) $) 61)) (|monomial| (($ |#1| (|Fraction| (|Integer|))) 60) (($ $ (|SingletonAsOrderedSet|) (|Fraction| (|Integer|))) 72) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|Fraction| (|Integer|)))) 71)) (|map| (($ (|Mapping| |#1| |#1|) $) 62)) (|log| (($ $) 134 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|leadingMonomial| (($ $) 64)) (|leadingCoefficient| ((|#1| $) 65)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 138 (|has| |#1| (|Field|)))) (|lcm| (($ (|List| $)) 142 (|has| |#1| (|Field|))) (($ $ $) 141 (|has| |#1| (|Field|)))) (|latex| (((|String|) $) 9)) (|inv| (($ $) 158 (|has| |#1| (|Field|)))) (|integrate| (($ $) 163 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Symbol|)) 162 (OR (AND (|has| |#1| (|AlgebraicallyClosedFunctionSpace| (|Integer|))) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (AND (|has| |#1| (SIGNATURE |variables| ((|List| (|Symbol|)) |#1|))) (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| (|Symbol|)))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))))) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 143 (|has| |#1| (|Field|)))) (|gcd| (($ (|List| $)) 140 (|has| |#1| (|Field|))) (($ $ $) 139 (|has| |#1| (|Field|)))) (|factor| (((|Factored| $) $) 154 (|has| |#1| (|Field|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 152 (|has| |#1| (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 151 (|has| |#1| (|Field|)))) (|extend| (($ $ (|Fraction| (|Integer|))) 90)) (|exquo| (((|Union| $ "failed") $ $) 49 (|has| |#1| (|IntegralDomain|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 145 (|has| |#1| (|Field|)))) (|exp| (($ $) 135 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|eval| (((|Stream| |#1|) $ |#1|) 89 (|has| |#1| (SIGNATURE ** (|#1| |#1| (|Fraction| (|Integer|))))))) (|euclideanSize| (((|NonNegativeInteger|) $) 147 (|has| |#1| (|Field|)))) (|elt| ((|#1| $ (|Fraction| (|Integer|))) 99) (($ $ $) 76 (|has| (|Fraction| (|Integer|)) (|SemiGroup|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 148 (|has| |#1| (|Field|)))) (|differentiate| (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 84 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 83 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))))) (($ $ (|List| (|Symbol|))) 82 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))))) (($ $ (|Symbol|)) 81 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))))) (($ $ (|NonNegativeInteger|)) 79 (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) (($ $) 77 (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))))) (|degree| (((|Fraction| (|Integer|)) $) 63)) (|csch| (($ $) 124 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|csc| (($ $) 113 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|coth| (($ $) 123 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cot| (($ $) 114 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cosh| (($ $) 122 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cos| (($ $) 115 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|complete| (($ $) 68)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ |#1|) 46 (|has| |#1| (|CommutativeRing|))) (($ (|Fraction| (|Integer|))) 56 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $) 48 (|has| |#1| (|IntegralDomain|)))) (|coefficient| ((|#1| $ (|Fraction| (|Integer|))) 58)) (|charthRoot| (((|Union| $ "failed") $) 47 (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|center| ((|#1| $) 97)) (|atanh| (($ $) 133 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|atan| (($ $) 121 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|associates?| (((|Boolean|) $ $) 52 (|has| |#1| (|IntegralDomain|)))) (|asinh| (($ $) 132 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asin| (($ $) 120 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asech| (($ $) 131 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asec| (($ $) 119 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|approximate| ((|#1| $ (|Fraction| (|Integer|))) 91 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| (|Fraction| (|Integer|))))) (|has| |#1| (SIGNATURE |coerce| (|#1| (|Symbol|))))))) (|acsch| (($ $) 130 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acsc| (($ $) 118 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acoth| (($ $) 129 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acot| (($ $) 117 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acosh| (($ $) 128 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acos| (($ $) 116 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 159 (|has| |#1| (|Field|)))) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (D (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 88 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 87 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))))) (($ $ (|List| (|Symbol|))) 86 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))))) (($ $ (|Symbol|)) 85 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))))) (($ $ (|NonNegativeInteger|)) 80 (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) (($ $) 78 (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))))) (= (((|Boolean|) $ $) 6)) (/ (($ $ |#1|) 57 (|has| |#1| (|Field|))) (($ $ $) 161 (|has| |#1| (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 160 (|has| |#1| (|Field|))) (($ $ $) 136 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) 107 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 67) (($ |#1| $) 66) (($ (|Fraction| (|Integer|)) $) 55 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) 54 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) 
(((|UnivariatePuiseuxSeriesCategory| |#1|) (|Category|) (|Ring|)) (T |UnivariatePuiseuxSeriesCategory|)) 
((|series| (*1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *3 (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| *4)))) (|ofCategory| *4 (|Ring|)) (|ofCategory| *1 (|UnivariatePuiseuxSeriesCategory| *4)))) (|multiplyExponents| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|ofCategory| *1 (|UnivariatePuiseuxSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|integrate| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))))) (|integrate| (*1 *1 *1 *2) (OR (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|UnivariatePuiseuxSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)) (AND (|ofCategory| *3 (|AlgebraicallyClosedFunctionSpace| (|Integer|))) (|ofCategory| *3 (|PrimitiveFunctionCategory|)) (|ofCategory| *3 (|TranscendentalFunctionCategory|)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))))) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|UnivariatePuiseuxSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)) (AND (|has| *3 (SIGNATURE |variables| ((|List| *2) *3))) (|has| *3 (SIGNATURE |integrate| (*3 *3 *2))) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))))))) 
(|Join| (|UnivariatePowerSeriesCategory| |t#1| (|Fraction| (|Integer|))) (CATEGORY |domain| (SIGNATURE |series| ($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |t#1|))))) (SIGNATURE |multiplyExponents| ($ $ (|Fraction| (|Integer|)))) (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |integrate| ($ $)) (IF (|has| |t#1| (SIGNATURE |integrate| (|t#1| |t#1| (|Symbol|)))) (IF (|has| |t#1| (SIGNATURE |variables| ((|List| (|Symbol|)) |t#1|))) (SIGNATURE |integrate| ($ $ (|Symbol|))) |noBranch|) |noBranch|) (IF (|has| |t#1| (|TranscendentalFunctionCategory|)) (IF (|has| |t#1| (|PrimitiveFunctionCategory|)) (IF (|has| |t#1| (|AlgebraicallyClosedFunctionSpace| (|Integer|))) (SIGNATURE |integrate| ($ $ (|Symbol|))) |noBranch|) |noBranch|) |noBranch|) (ATTRIBUTE (|RadicalCategory|)) (ATTRIBUTE (|TranscendentalFunctionCategory|))) |noBranch|) (IF (|has| |t#1| (|Field|)) (ATTRIBUTE (|Field|)) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| (|Fraction| (|Integer|))) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| $ $) |has| (|Fraction| (|Integer|)) (|SemiGroup|)) ((|EntireRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Field|) |has| |#1| (|Field|)) ((|GcdDomain|) |has| |#1| (|Field|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|IntegralDomain|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|LeftModule| (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) |has| |#1| (|Field|)) ((|Module| (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|PartialDifferentialRing| (|Symbol|)) AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PowerSeriesCategory| |#1| (|Fraction| (|Integer|)) (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariatePowerSeriesCategory| |#1| (|Fraction| (|Integer|))) . T)) 
((|zero?| (((|Boolean|) $) 12)) (|retractIfCan| (((|Union| |#3| "failed") $) 17)) (|retract| ((|#3| $) 14))) 
(((|UnivariatePuiseuxSeriesConstructorCategory&| |#1| |#2| |#3|) (CATEGORY |domain| (SIGNATURE |retract| (|#3| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#3| "failed") |#1|)) (SIGNATURE |zero?| ((|Boolean|) |#1|))) (|UnivariatePuiseuxSeriesConstructorCategory| |#2| |#3|) (|Ring|) (|UnivariateLaurentSeriesCategory| |#2|)) (T |UnivariatePuiseuxSeriesConstructorCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |retract| (|#3| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#3| "failed") |#1|)) (SIGNATURE |zero?| ((|Boolean|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) 70)) (|variable| (((|Symbol|) $) 98)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 50 (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) 51 (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) 53 (|has| |#1| (|IntegralDomain|)))) (|truncate| (($ $ (|Fraction| (|Integer|))) 93) (($ $ (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) 92)) (|terms| (((|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|))) $) 100)) (|tanh| (($ $) 127 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|tan| (($ $) 110 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 155 (|has| |#1| (|Field|)))) (|squareFree| (((|Factored| $) $) 156 (|has| |#1| (|Field|)))) (|sqrt| (($ $) 109 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sizeLess?| (((|Boolean|) $ $) 146 (|has| |#1| (|Field|)))) (|sinh| (($ $) 126 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sin| (($ $) 111 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) 165)) (|sech| (($ $) 125 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sec| (($ $) 112 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) 173)) (|retract| ((|#2| $) 172)) (|rem| (($ $ $) 150 (|has| |#1| (|Field|)))) (|reductum| (($ $) 59)) (|recip| (((|Union| $ "failed") $) 33)) (|rationalPower| (((|Fraction| (|Integer|)) $) 170)) (|quo| (($ $ $) 149 (|has| |#1| (|Field|)))) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) 171)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 144 (|has| |#1| (|Field|)))) (|prime?| (((|Boolean|) $) 157 (|has| |#1| (|Field|)))) (|pole?| (((|Boolean|) $) 69)) (|pi| (($) 137 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|order| (((|Fraction| (|Integer|)) $) 95) (((|Fraction| (|Integer|)) $ (|Fraction| (|Integer|))) 94)) (|one?| (((|Boolean|) $) 30)) (|nthRoot| (($ $ (|Integer|)) 108 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|multiplyExponents| (($ $ (|PositiveInteger|)) 96) (($ $ (|Fraction| (|Integer|))) 164)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 153 (|has| |#1| (|Field|)))) (|monomial?| (((|Boolean|) $) 61)) (|monomial| (($ |#1| (|Fraction| (|Integer|))) 60) (($ $ (|SingletonAsOrderedSet|) (|Fraction| (|Integer|))) 72) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|Fraction| (|Integer|)))) 71)) (|map| (($ (|Mapping| |#1| |#1|) $) 62)) (|log| (($ $) 134 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|leadingMonomial| (($ $) 64)) (|leadingCoefficient| ((|#1| $) 65)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 138 (|has| |#1| (|Field|)))) (|lcm| (($ (|List| $)) 142 (|has| |#1| (|Field|))) (($ $ $) 141 (|has| |#1| (|Field|)))) (|laurentRep| ((|#2| $) 169)) (|laurentIfCan| (((|Union| |#2| "failed") $) 167)) (|laurent| ((|#2| $) 168)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 158 (|has| |#1| (|Field|)))) (|integrate| (($ $) 163 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Symbol|)) 162 (OR (AND (|has| |#1| (|AlgebraicallyClosedFunctionSpace| (|Integer|))) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (AND (|has| |#1| (SIGNATURE |variables| ((|List| (|Symbol|)) |#1|))) (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| (|Symbol|)))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))))) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 143 (|has| |#1| (|Field|)))) (|gcd| (($ (|List| $)) 140 (|has| |#1| (|Field|))) (($ $ $) 139 (|has| |#1| (|Field|)))) (|factor| (((|Factored| $) $) 154 (|has| |#1| (|Field|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 152 (|has| |#1| (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 151 (|has| |#1| (|Field|)))) (|extend| (($ $ (|Fraction| (|Integer|))) 90)) (|exquo| (((|Union| $ "failed") $ $) 49 (|has| |#1| (|IntegralDomain|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 145 (|has| |#1| (|Field|)))) (|exp| (($ $) 135 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|eval| (((|Stream| |#1|) $ |#1|) 89 (|has| |#1| (SIGNATURE ** (|#1| |#1| (|Fraction| (|Integer|))))))) (|euclideanSize| (((|NonNegativeInteger|) $) 147 (|has| |#1| (|Field|)))) (|elt| ((|#1| $ (|Fraction| (|Integer|))) 99) (($ $ $) 76 (|has| (|Fraction| (|Integer|)) (|SemiGroup|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 148 (|has| |#1| (|Field|)))) 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(|has| |#1| (|Field|)))) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 160 (|has| |#1| (|Field|))) (($ $ $) 136 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) 107 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 67) (($ |#1| $) 66) (($ (|Fraction| (|Integer|)) $) 55 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) 54 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) 
(((|UnivariatePuiseuxSeriesConstructorCategory| |#1| |#2|) (|Category|) (|Ring|) (|UnivariateLaurentSeriesCategory| |t#1|)) (T |UnivariatePuiseuxSeriesConstructorCategory|)) 
((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|coerce| (*1 *1 *2) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)))) (|puiseux| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|ofCategory| *4 (|Ring|)) (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *4 *3)) (|ofCategory| *3 (|UnivariateLaurentSeriesCategory| *4)))) (|rationalPower| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|laurentRep| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)))) (|laurent| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)))) (|laurentIfCan| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3))))) 
(|Join| (|UnivariatePuiseuxSeriesCategory| |t#1|) (|RetractableTo| |t#2|) (CATEGORY |domain| (SIGNATURE |puiseux| ($ (|Fraction| (|Integer|)) |t#2|)) (SIGNATURE |rationalPower| ((|Fraction| (|Integer|)) $)) (SIGNATURE |laurentRep| (|t#2| $)) (SIGNATURE |degree| ((|Fraction| (|Integer|)) $)) (SIGNATURE |coerce| ($ |t#2|)) (SIGNATURE |laurent| (|t#2| $)) (SIGNATURE |laurentIfCan| ((|Union| |t#2| "failed") $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| (|Fraction| (|Integer|))) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| $ $) |has| (|Fraction| (|Integer|)) (|SemiGroup|)) ((|EntireRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Field|) |has| |#1| (|Field|)) ((|GcdDomain|) |has| |#1| (|Field|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|IntegralDomain|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|LeftModule| (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) |has| |#1| (|Field|)) ((|Module| (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|PartialDifferentialRing| (|Symbol|)) AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PowerSeriesCategory| |#1| (|Fraction| (|Integer|)) (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RetractableTo| |#2|) . T) ((|RightModule| (|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariatePowerSeriesCategory| |#1| (|Fraction| (|Integer|))) . T) ((|UnivariatePuiseuxSeriesCategory| |#1|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) NIL)) (|variable| (((|Symbol|) $) 96)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|truncate| (($ $ (|Fraction| (|Integer|))) 106) (($ $ (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) 108)) (|terms| (((|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|))) $) 51)) (|tanh| (($ $) 179 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|tan| (($ $) 155 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL (|has| |#1| (|Field|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#1| (|Field|)))) (|sqrt| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sizeLess?| 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|#1| (|Field|)))) (|lcm| (($ (|List| $)) NIL (|has| |#1| (|Field|))) (($ $ $) NIL (|has| |#1| (|Field|)))) (|laurentRep| ((|#2| $) 11)) (|laurentIfCan| (((|Union| |#2| "failed") $) 41)) (|laurent| ((|#2| $) 42)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) 93 (|has| |#1| (|Field|)))) (|integrate| (($ $) 135 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Symbol|)) 140 (OR (AND (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| (|Symbol|)))) (|has| |#1| (SIGNATURE |variables| ((|List| (|Symbol|)) |#1|))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (AND (|has| |#1| (|AlgebraicallyClosedFunctionSpace| (|Integer|))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|)))))) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|Field|)))) (|gcd| (($ (|List| $)) NIL (|has| |#1| (|Field|))) (($ $ $) NIL (|has| |#1| (|Field|)))) (|factor| (((|Factored| $) $) NIL (|has| |#1| (|Field|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL (|has| |#1| (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|extend| (($ $ (|Fraction| (|Integer|))) 112)) (|exquo| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) (|exp| (($ $) 147 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|eval| (((|Stream| |#1|) $ |#1|) 90 (|has| |#1| (SIGNATURE ** (|#1| |#1| (|Fraction| (|Integer|))))))) (|euclideanSize| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|Field|)))) (|elt| ((|#1| $ (|Fraction| (|Integer|))) 100) (($ $ $) 86 (|has| (|Fraction| (|Integer|)) (|SemiGroup|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|Field|)))) (|differentiate| (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|)) 127 (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) (($ $) 124 (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))))) (|degree| (((|Fraction| (|Integer|)) $) 16)) (|csch| (($ $) 185 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|csc| (($ $) 161 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|coth| (($ $) 181 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cot| (($ $) 157 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cosh| (($ $) 177 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cos| (($ $) 153 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|complete| (($ $) 110)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) 35) (($ |#1|) 27 (|has| |#1| (|CommutativeRing|))) (($ |#2|) 32) (($ (|Fraction| (|Integer|))) 128 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|coefficient| ((|#1| $ (|Fraction| (|Integer|))) 99)) (|charthRoot| (((|Union| $ "failed") $) NIL (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) 117)) (|center| ((|#1| $) 98)) (|atanh| (($ $) 191 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|atan| (($ $) 167 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|associates?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|asinh| (($ $) 187 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asin| (($ $) 163 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asech| (($ $) 195 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asec| (($ $) 171 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|approximate| ((|#1| $ (|Fraction| (|Integer|))) NIL (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| (|Fraction| (|Integer|))))) (|has| |#1| (SIGNATURE |coerce| (|#1| (|Symbol|))))))) (|acsch| (($ $) 197 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acsc| (($ $) 173 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acoth| (($ $) 193 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acot| (($ $) 169 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acosh| (($ $) 189 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acos| (($ $) 165 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| |#1| (|Field|)))) (|Zero| (($) 21 T CONST)) (|One| (($) 17 T CONST)) (D (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) (($ $) NIL (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))))) (= (((|Boolean|) $ $) 66)) (/ (($ $ |#1|) NIL (|has| |#1| (|Field|))) (($ $ $) 92 (|has| |#1| (|Field|)))) (- (($ $) 131) (($ $ $) 72)) (+ (($ $ $) 70)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 76) (($ $ (|Integer|)) 144 (|has| |#1| (|Field|))) (($ $ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) 145 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 74) (($ $ |#1|) NIL) (($ |#1| $) 126) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) 
(((|UnivariatePuiseuxSeriesConstructor| |#1| |#2|) (|UnivariatePuiseuxSeriesConstructorCategory| |#1| |#2|) (|Ring|) (|UnivariateLaurentSeriesCategory| |#1|)) (T |UnivariatePuiseuxSeriesConstructor|)) 
NIL 
(|UnivariatePuiseuxSeriesConstructorCategory| |#1| |#2|) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) NIL)) (|variable| (((|Symbol|) $) 11)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|truncate| (($ $ (|Fraction| (|Integer|))) NIL) (($ $ (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) NIL)) (|terms| (((|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|))) $) NIL)) (|tanh| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|tan| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|squareFreePart| (($ $) NIL (|has| |#1| (|Field|)))) (|squareFree| (((|Factored| $) $) NIL (|has| |#1| (|Field|)))) (|sqrt| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sizeLess?| (((|Boolean|) $ $) NIL (|has| |#1| (|Field|)))) (|sinh| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sin| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) NIL)) (|sech| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sec| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| (|UnivariateLaurentSeries| |#1| |#2| |#3|) "failed") $) 19) (((|Union| (|UnivariateTaylorSeries| |#1| |#2| |#3|) "failed") $) 22)) (|retract| (((|UnivariateLaurentSeries| |#1| |#2| |#3|) $) NIL) (((|UnivariateTaylorSeries| |#1| |#2| |#3|) $) NIL)) (|rem| (($ $ $) NIL (|has| |#1| (|Field|)))) (|reductum| (($ $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|rationalPower| (((|Fraction| (|Integer|)) $) 57)) (|quo| (($ $ $) NIL (|has| |#1| (|Field|)))) (|puiseux| (($ (|Fraction| (|Integer|)) (|UnivariateLaurentSeries| |#1| |#2| |#3|)) NIL)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) NIL (|has| |#1| (|Field|)))) (|prime?| (((|Boolean|) $) NIL (|has| |#1| (|Field|)))) (|pole?| (((|Boolean|) $) NIL)) (|pi| (($) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|order| (((|Fraction| (|Integer|)) $) NIL) (((|Fraction| (|Integer|)) $ (|Fraction| (|Integer|))) NIL)) (|one?| (((|Boolean|) $) NIL)) (|nthRoot| (($ $ (|Integer|)) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|multiplyExponents| (($ $ (|PositiveInteger|)) NIL) (($ $ (|Fraction| (|Integer|))) NIL)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) (|monomial?| (((|Boolean|) $) NIL)) (|monomial| (($ |#1| (|Fraction| (|Integer|))) 29) (($ $ (|SingletonAsOrderedSet|) (|Fraction| (|Integer|))) NIL) (($ $ (|List| (|SingletonAsOrderedSet|)) (|List| (|Fraction| (|Integer|)))) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|log| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|leadingMonomial| (($ $) NIL)) (|leadingCoefficient| ((|#1| $) NIL)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) NIL (|has| |#1| (|Field|)))) (|lcm| (($ (|List| $)) NIL (|has| |#1| (|Field|))) (($ $ $) NIL (|has| |#1| (|Field|)))) (|laurentRep| (((|UnivariateLaurentSeries| |#1| |#2| |#3|) $) 60)) (|laurentIfCan| (((|Union| (|UnivariateLaurentSeries| |#1| |#2| |#3|) "failed") $) NIL)) (|laurent| (((|UnivariateLaurentSeries| |#1| |#2| |#3|) $) NIL)) (|latex| (((|String|) $) NIL)) (|inv| (($ $) NIL (|has| |#1| (|Field|)))) (|integrate| (($ $) 38 (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Symbol|)) NIL (OR (AND (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| (|Symbol|)))) (|has| |#1| (SIGNATURE |variables| ((|List| (|Symbol|)) |#1|))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (AND (|has| |#1| (|AlgebraicallyClosedFunctionSpace| (|Integer|))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))))) (($ $ (|Variable| |#2|)) 39 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|hash| (((|SingleInteger|) $) NIL)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) NIL (|has| |#1| (|Field|)))) (|gcd| (($ (|List| $)) NIL (|has| |#1| (|Field|))) (($ $ $) NIL (|has| |#1| (|Field|)))) (|factor| (((|Factored| $) $) NIL (|has| |#1| (|Field|)))) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) NIL (|has| |#1| (|Field|))) (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL (|has| |#1| (|Field|)))) (|extend| (($ $ (|Fraction| (|Integer|))) NIL)) (|exquo| (((|Union| $ "failed") $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) NIL (|has| |#1| (|Field|)))) (|exp| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|eval| (((|Stream| |#1|) $ |#1|) NIL (|has| |#1| (SIGNATURE ** (|#1| |#1| (|Fraction| (|Integer|))))))) (|euclideanSize| (((|NonNegativeInteger|) $) NIL (|has| |#1| (|Field|)))) (|elt| ((|#1| $ (|Fraction| (|Integer|))) NIL) (($ $ $) NIL (|has| (|Fraction| (|Integer|)) (|SemiGroup|)))) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL (|has| |#1| (|Field|)))) (|differentiate| (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) (($ $) 36 (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) (($ $ (|Variable| |#2|)) 37)) (|degree| (((|Fraction| (|Integer|)) $) NIL)) (|csch| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|csc| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|coth| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cot| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cosh| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|cos| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|complete| (($ $) NIL)) (|coerce| (((|OutputForm|) $) 87) (($ (|Integer|)) NIL) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|))) (($ (|UnivariateLaurentSeries| |#1| |#2| |#3|)) 16) (($ (|UnivariateTaylorSeries| |#1| |#2| |#3|)) 17) (($ (|Variable| |#2|)) 35) (($ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $) NIL (|has| |#1| (|IntegralDomain|)))) (|coefficient| ((|#1| $ (|Fraction| (|Integer|))) NIL)) (|charthRoot| (((|Union| $ "failed") $) NIL (|has| |#1| (|CharacteristicNonZero|)))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|center| ((|#1| $) 12)) (|atanh| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|atan| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|associates?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|asinh| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asin| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asech| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|asec| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|approximate| ((|#1| $ (|Fraction| (|Integer|))) 62 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| (|Fraction| (|Integer|))))) (|has| |#1| (SIGNATURE |coerce| (|#1| (|Symbol|))))))) (|acsch| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acsc| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acoth| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acot| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acosh| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|acos| (($ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| |#1| (|Field|)))) (|Zero| (($) 31 T CONST)) (|One| (($) 26 T CONST)) (D (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) (($ $) NIL (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))))) (= (((|Boolean|) $ $) NIL)) (/ (($ $ |#1|) NIL (|has| |#1| (|Field|))) (($ $ $) NIL (|has| |#1| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) 33)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|Integer|)) NIL (|has| |#1| (|Field|))) (($ $ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ |#1|) NIL) (($ |#1| $) NIL) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) 
(((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) (|Join| (|UnivariatePuiseuxSeriesConstructorCategory| |#1| (|UnivariateLaurentSeries| |#1| |#2| |#3|)) (|RetractableTo| (|UnivariateTaylorSeries| |#1| |#2| |#3|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Variable| |#2|))) (SIGNATURE |differentiate| ($ $ (|Variable| |#2|))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ (|Variable| |#2|))) |noBranch|))) (|Ring|) (|Symbol|) |#1|) (T |UnivariatePuiseuxSeries|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|)) (|isDomain| *1 (|UnivariatePuiseuxSeries| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3))) (|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|)) (|isDomain| *1 (|UnivariatePuiseuxSeries| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3))) (|integrate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|)) (|isDomain| *1 (|UnivariatePuiseuxSeries| *3 *4 *5)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))) 
(|Join| (|UnivariatePuiseuxSeriesConstructorCategory| |#1| (|UnivariateLaurentSeries| |#1| |#2| |#3|)) (|RetractableTo| (|UnivariateTaylorSeries| |#1| |#2| |#3|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Variable| |#2|))) (SIGNATURE |differentiate| ($ $ (|Variable| |#2|))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ (|Variable| |#2|))) |noBranch|))) 
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(((|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (|Join| (|FiniteAbelianMonoidRing| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|) (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|IntegralDomain|) (CATEGORY |domain| (SIGNATURE |limitPlus| ((|Union| (|OrderedCompletion| |#2|) "failed") $)) (SIGNATURE |dominantTerm| ((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $)))) (|Join| (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|GcdDomain|)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|)) (|Symbol|) |#2|) (T |UnivariatePuiseuxSeriesWithExponentialSingularity|)) 
((|limitPlus| (*1 *2 *1) (|partial| AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|GcdDomain|))) (|isDomain| *2 (|OrderedCompletion| *4)) (|isDomain| *1 (|UnivariatePuiseuxSeriesWithExponentialSingularity| *3 *4 *5 *6)) (|ofCategory| *4 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *3))) (|ofType| *5 (|Symbol|)) (|ofType| *6 *4))) (|dominantTerm| (*1 *2 *1) (|partial| AND (|ofCategory| *3 (|Join| (|OrderedSet|) (|RetractableTo| (|Integer|)) (|LinearlyExplicitRingOver| (|Integer|)) (|GcdDomain|))) (|isDomain| *2 (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| *4 *5 *6)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| *4 *5 *6)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| *4)))))) (|:| |%type| (|String|)))) (|isDomain| *1 (|UnivariatePuiseuxSeriesWithExponentialSingularity| *3 *4 *5 *6)) (|ofCategory| *4 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *3))) (|ofType| *5 (|Symbol|)) (|ofType| *6 *4)))) 
(|Join| (|FiniteAbelianMonoidRing| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|) (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|IntegralDomain|) (CATEGORY |domain| (SIGNATURE |limitPlus| ((|Union| (|OrderedCompletion| |#2|) "failed") $)) (SIGNATURE |dominantTerm| ((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $)))) 
((|value| ((|#2| $) 28)) (|third| ((|#2| $) 18)) (|tail| (($ $) 35)) (|split!| (($ $ (|Integer|)) 63)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 32)) (|setvalue!| ((|#2| $ |#2|) 60)) (|setlast!| ((|#2| $ |#2|) 58)) (|setelt| ((|#2| $ "value" |#2|) NIL) ((|#2| $ "first" |#2|) 51) (($ $ "rest" $) 55) ((|#2| $ "last" |#2|) 53)) (|setchildren!| (($ $ (|List| $)) 59)) (|second| ((|#2| $) 17)) (|rest| (($ $) NIL) (($ $ (|NonNegativeInteger|)) 41)) (|nodes| (((|List| $) $) 25)) (|node?| (((|Boolean|) $ $) 49)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 31)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 30)) (|leaf?| (((|Boolean|) $) 27)) (|last| ((|#2| $) 23) (($ $ (|NonNegativeInteger|)) 45)) (|elt| ((|#2| $ "value") NIL) ((|#2| $ "first") 10) (($ $ "rest") 16) ((|#2| $ "last") 13)) (|cyclic?| (((|Boolean|) $) 21)) (|cycleTail| (($ $) 38)) (|cycleSplit!| (($ $) 64)) (|cycleLength| (((|NonNegativeInteger|) $) 40)) (|cycleEntry| (($ $) 39)) (|concat| (($ $ $) 57) (($ |#2| $) NIL)) (|children| (((|List| $) $) 26)) (= (((|Boolean|) $ $) 47)) (|#| (((|NonNegativeInteger|) $) 34))) 
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NIL 
(CATEGORY |domain| (SIGNATURE |split!| (|#1| |#1| (|Integer|))) (SIGNATURE |setelt| (|#2| |#1| "last" |#2|)) (SIGNATURE |setlast!| (|#2| |#1| |#2|)) (SIGNATURE |setelt| (|#1| |#1| "rest" |#1|)) (SIGNATURE |setelt| (|#2| |#1| "first" |#2|)) (SIGNATURE |cycleSplit!| (|#1| |#1|)) (SIGNATURE |cycleTail| (|#1| |#1|)) (SIGNATURE |cycleLength| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |cycleEntry| (|#1| |#1|)) (SIGNATURE |third| (|#2| |#1|)) (SIGNATURE |second| (|#2| |#1|)) (SIGNATURE |tail| (|#1| |#1|)) (SIGNATURE |last| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |elt| (|#2| |#1| "last")) (SIGNATURE |last| (|#2| |#1|)) (SIGNATURE |rest| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |elt| (|#1| |#1| "rest")) (SIGNATURE |rest| (|#1| |#1|)) (SIGNATURE |elt| (|#2| |#1| "first")) (SIGNATURE |concat| (|#1| |#2| |#1|)) (SIGNATURE |concat| (|#1| |#1| |#1|)) (SIGNATURE |setvalue!| (|#2| |#1| |#2|)) (SIGNATURE |setelt| (|#2| |#1| "value" |#2|)) (SIGNATURE |setchildren!| (|#1| |#1| (|List| |#1|))) (SIGNATURE |node?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |cyclic?| ((|Boolean|) |#1|)) (SIGNATURE |elt| (|#2| |#1| "value")) (SIGNATURE |value| (|#2| |#1|)) (SIGNATURE |leaf?| ((|Boolean|) |#1|)) (SIGNATURE |nodes| ((|List| |#1|) |#1|)) (SIGNATURE |children| ((|List| |#1|) |#1|)) (SIGNATURE = ((|Boolean|) |#1| |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |size?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) |#1| (|NonNegativeInteger|))) (SIGNATURE |less?| ((|Boolean|) |#1| (|NonNegativeInteger|)))) 
((~= (((|Boolean|) $ $) 18 (|has| |#1| (|SetCategory|)))) (|value| ((|#1| $) 45)) (|third| ((|#1| $) 62)) (|tail| (($ $) 64)) (|split!| (($ $ (|Integer|)) 49 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 8)) (|setvalue!| ((|#1| $ |#1|) 36 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setrest!| (($ $ $) 53 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setlast!| ((|#1| $ |#1|) 51 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setfirst!| ((|#1| $ |#1|) 55 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setelt| ((|#1| $ "value" |#1|) 37 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ "first" |#1|) 54 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ "rest" $) 52 (|has| $ (ATTRIBUTE |shallowlyMutable|))) ((|#1| $ "last" |#1|) 50 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|setchildren!| (($ $ (|List| $)) 38 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|second| ((|#1| $) 63)) (|sample| (($) 7 T CONST)) (|rest| (($ $) 70) (($ $ (|NonNegativeInteger|)) 68)) (|parts| (((|List| |#1|) $) 30 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|nodes| (((|List| $) $) 47)) (|node?| (((|Boolean|) $ $) 39 (|has| |#1| (|SetCategory|)))) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 9)) (|members| (((|List| |#1|) $) 29 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#1| $) 27 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|map!| (($ (|Mapping| |#1| |#1|) $) 34 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#1| |#1|) $) 35)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 10)) (|leaves| (((|List| |#1|) $) 42)) (|leaf?| (((|Boolean|) $) 46)) (|latex| (((|String|) $) 22 (|has| |#1| (|SetCategory|)))) (|last| ((|#1| $) 67) (($ $ (|NonNegativeInteger|)) 65)) (|hash| (((|SingleInteger|) $) 21 (|has| |#1| (|SetCategory|)))) (|first| ((|#1| $) 73) (($ $ (|NonNegativeInteger|)) 71)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 32 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| (|Equation| |#1|))) 26 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|Equation| |#1|)) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ |#1| |#1|) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|)))) (($ $ (|List| |#1|) (|List| |#1|)) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) 14)) (|empty?| (((|Boolean|) $) 11)) (|empty| (($) 12)) (|elt| ((|#1| $ "value") 44) ((|#1| $ "first") 72) (($ $ "rest") 69) ((|#1| $ "last") 66)) (|distance| (((|Integer|) $ $) 41)) (|cyclic?| (((|Boolean|) $) 43)) (|cycleTail| (($ $) 59)) (|cycleSplit!| (($ $) 56 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|cycleLength| (((|NonNegativeInteger|) $) 60)) (|cycleEntry| (($ $) 61)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 31 (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|NonNegativeInteger|) |#1| $) 28 (AND (|has| |#1| (|SetCategory|)) (|has| $ (ATTRIBUTE |finiteAggregate|))))) (|copy| (($ $) 13)) (|concat!| (($ $ $) 58 (|has| $ (ATTRIBUTE |shallowlyMutable|))) (($ $ |#1|) 57 (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|concat| (($ $ $) 75) (($ |#1| $) 74)) (|coerce| (((|OutputForm|) $) 20 (|has| |#1| (|SetCategory|)))) (|children| (((|List| $) $) 48)) (|child?| (((|Boolean|) $ $) 40 (|has| |#1| (|SetCategory|)))) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 33 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (= (((|Boolean|) $ $) 19 (|has| |#1| (|SetCategory|)))) (|#| (((|NonNegativeInteger|) $) 6 (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|UnaryRecursiveAggregate| |#1|) (|Category|) (|Type|)) (T |UnaryRecursiveAggregate|)) 
((|concat| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|concat| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|first| (*1 *2 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 "first") (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|first| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|rest| (*1 *1 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|elt| (*1 *1 *1 *2) (AND (|isDomain| *2 "rest") (|ofCategory| *1 (|UnaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|rest| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|last| (*1 *2 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 "last") (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|last| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|tail| (*1 *1 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|second| (*1 *2 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|third| (*1 *2 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|cycleEntry| (*1 *1 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|cycleLength| (*1 *2 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|cycleTail| (*1 *1 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|concat!| (*1 *1 *1 *1) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|concat!| (*1 *1 *1 *2) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|cycleSplit!| (*1 *1 *1) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setfirst!| (*1 *2 *1 *2) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setelt| (*1 *2 *1 *3 *2) (AND (|isDomain| *3 "first") (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setrest!| (*1 *1 *1 *1) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setelt| (*1 *1 *1 *2 *1) (AND (|isDomain| *2 "rest") (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|setlast!| (*1 *2 *1 *2) (AND (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setelt| (*1 *2 *1 *3 *2) (AND (|isDomain| *3 "last") (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|split!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|has| *1 (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|))))) 
(|Join| (|RecursiveAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |concat| ($ $ $)) (SIGNATURE |concat| ($ |t#1| $)) (SIGNATURE |first| (|t#1| $)) (SIGNATURE |elt| (|t#1| $ "first")) (SIGNATURE |first| ($ $ (|NonNegativeInteger|))) (SIGNATURE |rest| ($ $)) (SIGNATURE |elt| ($ $ "rest")) (SIGNATURE |rest| ($ $ (|NonNegativeInteger|))) (SIGNATURE |last| (|t#1| $)) (SIGNATURE |elt| (|t#1| $ "last")) (SIGNATURE |last| ($ $ (|NonNegativeInteger|))) (SIGNATURE |tail| ($ $)) (SIGNATURE |second| (|t#1| $)) (SIGNATURE |third| (|t#1| $)) (SIGNATURE |cycleEntry| ($ $)) (SIGNATURE |cycleLength| ((|NonNegativeInteger|) $)) (SIGNATURE |cycleTail| ($ $)) (IF (|has| $ (ATTRIBUTE |shallowlyMutable|)) (PROGN (SIGNATURE |concat!| ($ $ $)) (SIGNATURE |concat!| ($ $ |t#1|)) (SIGNATURE |cycleSplit!| ($ $)) (SIGNATURE |setfirst!| (|t#1| $ |t#1|)) (SIGNATURE |setelt| (|t#1| $ "first" |t#1|)) (SIGNATURE |setrest!| ($ $ $)) (SIGNATURE |setelt| ($ $ "rest" $)) (SIGNATURE |setlast!| (|t#1| $ |t#1|)) (SIGNATURE |setelt| (|t#1| $ "last" |t#1|)) (SIGNATURE |split!| ($ $ (|Integer|)))) |noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|SetCategory|)) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) 17))) 
(((|UnivariateTaylorSeriesFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#2| |#1|) |#3|))) (|Ring|) (|Ring|) (|UnivariateTaylorSeriesCategory| |#1|) (|UnivariateTaylorSeriesCategory| |#2|)) (T |UnivariateTaylorSeriesFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *6)) (|isDomain| *1 (|UnivariateTaylorSeriesFunctions2| *5 *6 *4 *2)) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *5))))) 
(CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#2| |#1|) |#3|))) 
((|zero?| (((|Boolean|) $) 15)) (|tanh| (($ $) 90)) (|tan| (($ $) 66)) (|sinh| (($ $) 86)) (|sin| (($ $) 62)) (|sech| (($ $) 94)) (|sec| (($ $) 70)) (|log| (($ $) 60)) (|exp| (($ $) 58)) (|csch| (($ $) 96)) (|csc| (($ $) 72)) (|coth| (($ $) 92)) (|cot| (($ $) 68)) (|cosh| (($ $) 88)) (|cos| (($ $) 64)) (|coerce| (((|OutputForm|) $) 46) (($ (|Integer|)) NIL) (($ (|Fraction| (|Integer|))) NIL) (($ $) NIL) (($ |#2|) NIL)) (|atanh| (($ $) 102)) (|atan| (($ $) 78)) (|asinh| (($ $) 98)) (|asin| (($ $) 74)) (|asech| (($ $) 106)) (|asec| (($ $) 82)) (|acsch| (($ $) 108)) (|acsc| (($ $) 84)) (|acoth| (($ $) 104)) (|acot| (($ $) 80)) (|acosh| (($ $) 100)) (|acos| (($ $) 76)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ |#2|) 50) (($ $ $) 53) (($ $ (|Fraction| (|Integer|))) 56))) 
(((|UnivariateTaylorSeriesCategory&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE ** (|#1| |#1| (|Fraction| (|Integer|)))) (SIGNATURE |tan| (|#1| |#1|)) (SIGNATURE |sin| (|#1| |#1|)) (SIGNATURE |sec| (|#1| |#1|)) (SIGNATURE |csc| (|#1| |#1|)) (SIGNATURE |cot| (|#1| |#1|)) (SIGNATURE |cos| (|#1| |#1|)) (SIGNATURE |acos| (|#1| |#1|)) (SIGNATURE |acot| (|#1| |#1|)) (SIGNATURE |acsc| (|#1| |#1|)) (SIGNATURE |asec| (|#1| |#1|)) (SIGNATURE |asin| (|#1| |#1|)) (SIGNATURE |atan| (|#1| |#1|)) (SIGNATURE |cosh| (|#1| |#1|)) (SIGNATURE |coth| (|#1| |#1|)) (SIGNATURE |csch| (|#1| |#1|)) (SIGNATURE |sech| (|#1| |#1|)) (SIGNATURE |sinh| (|#1| |#1|)) (SIGNATURE |tanh| (|#1| |#1|)) (SIGNATURE |acosh| (|#1| |#1|)) (SIGNATURE |acoth| (|#1| |#1|)) (SIGNATURE |acsch| (|#1| |#1|)) (SIGNATURE |asech| (|#1| |#1|)) (SIGNATURE |asinh| (|#1| |#1|)) (SIGNATURE |atanh| (|#1| |#1|)) (SIGNATURE |log| (|#1| |#1|)) (SIGNATURE |exp| (|#1| |#1|)) (SIGNATURE ** (|#1| |#1| |#1|)) (SIGNATURE ** (|#1| |#1| |#2|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| |#1|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |zero?| ((|Boolean|) |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|UnivariateTaylorSeriesCategory| |#2|) (|Ring|)) (T |UnivariateTaylorSeriesCategory&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE ** (|#1| |#1| (|Fraction| (|Integer|)))) (SIGNATURE |tan| (|#1| |#1|)) (SIGNATURE |sin| (|#1| |#1|)) (SIGNATURE |sec| (|#1| |#1|)) (SIGNATURE |csc| (|#1| |#1|)) (SIGNATURE |cot| (|#1| |#1|)) (SIGNATURE |cos| (|#1| |#1|)) (SIGNATURE |acos| (|#1| |#1|)) (SIGNATURE |acot| (|#1| |#1|)) (SIGNATURE |acsc| (|#1| |#1|)) (SIGNATURE |asec| (|#1| |#1|)) (SIGNATURE |asin| (|#1| |#1|)) (SIGNATURE |atan| (|#1| |#1|)) (SIGNATURE |cosh| (|#1| |#1|)) (SIGNATURE |coth| (|#1| |#1|)) (SIGNATURE |csch| (|#1| |#1|)) (SIGNATURE |sech| (|#1| |#1|)) (SIGNATURE |sinh| (|#1| |#1|)) (SIGNATURE |tanh| (|#1| |#1|)) (SIGNATURE |acosh| (|#1| |#1|)) (SIGNATURE |acoth| (|#1| |#1|)) (SIGNATURE |acsch| (|#1| |#1|)) (SIGNATURE |asech| (|#1| |#1|)) (SIGNATURE |asinh| (|#1| |#1|)) (SIGNATURE |atanh| (|#1| |#1|)) (SIGNATURE |log| (|#1| |#1|)) (SIGNATURE |exp| (|#1| |#1|)) (SIGNATURE ** (|#1| |#1| |#1|)) (SIGNATURE ** (|#1| |#1| |#2|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| |#1|)) (SIGNATURE |coerce| (|#1| (|Fraction| (|Integer|)))) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |zero?| ((|Boolean|) |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) 70)) (|variable| (((|Symbol|) $) 98)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 50 (|has| |#1| (|IntegralDomain|)))) (|unitCanonical| (($ $) 51 (|has| |#1| (|IntegralDomain|)))) (|unit?| (((|Boolean|) $) 53 (|has| |#1| (|IntegralDomain|)))) (|truncate| (($ $ (|NonNegativeInteger|)) 93) (($ $ (|NonNegativeInteger|) (|NonNegativeInteger|)) 92)) (|terms| (((|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|))) $) 100)) (|tanh| (($ $) 127 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|tan| (($ $) 110 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sqrt| (($ $) 109 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sinh| (($ $) 126 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sin| (($ $) 111 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|series| (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) 147) (($ (|Stream| |#1|)) 145)) (|sech| (($ $) 125 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sec| (($ $) 112 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|sample| (($) 16 T CONST)) (|reductum| (($ $) 59)) (|recip| (((|Union| $ "failed") $) 33)) (|quoByVar| (($ $) 144)) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) 142) (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) 141)) (|pole?| (((|Boolean|) $) 69)) (|pi| (($) 137 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|order| (((|NonNegativeInteger|) $) 95) (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) 94)) (|one?| (((|Boolean|) $) 30)) (|nthRoot| (($ $ (|Integer|)) 108 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|multiplyExponents| (($ $ (|PositiveInteger|)) 96)) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) 143)) (|monomial?| (((|Boolean|) $) 61)) (|monomial| (($ 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|#1| (|IntegralDomain|)))) (|exp| (($ $) 135 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (|eval| (((|Stream| |#1|) $ |#1|) 89 (|has| |#1| (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|)))))) (|elt| ((|#1| $ (|NonNegativeInteger|)) 99) (($ $ $) 76 (|has| (|NonNegativeInteger|) (|SemiGroup|)))) (|differentiate| (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|))) 84 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) 83 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))))) (($ $ (|List| (|Symbol|))) 82 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))))) (($ $ (|Symbol|)) 81 (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))))) (($ $ (|NonNegativeInteger|)) 79 (|has| 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NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|) (|NonNegativeInteger|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|List| (|Symbol|))) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|Symbol|)) NIL (AND (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)))) (($ $) NIL (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))))) (= (((|Boolean|) $ $) NIL)) (/ (($ $ |#1|) NIL (|has| |#1| (|Field|)))) (- (($ $) NIL) (($ $ $) 100)) (+ (($ $ $) 18)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL) (($ $ |#1|) 138 (|has| |#1| (|Field|))) (($ $ $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))))) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ $ |#1|) NIL) (($ |#1| $) 99) (($ (|Fraction| (|Integer|)) $) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (($ $ (|Fraction| (|Integer|))) NIL (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))))) 
(((|UnivariateTaylorSeries| |#1| |#2| |#3|) (|Join| (|UnivariateTaylorSeriesCategory| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|UnivariatePolynomial| |#2| |#1|))) (SIGNATURE |univariatePolynomial| ((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|))) (SIGNATURE |coerce| ($ (|Variable| |#2|))) (SIGNATURE |differentiate| ($ $ (|Variable| |#2|))) (SIGNATURE |lagrange| ($ $)) (SIGNATURE |lambert| ($ $)) (SIGNATURE |oddlambert| ($ $)) (SIGNATURE |evenlambert| ($ $)) (SIGNATURE |generalLambert| ($ $ (|Integer|) (|Integer|))) (SIGNATURE |revert| ($ $)) (SIGNATURE |multisect| ($ (|Integer|) (|Integer|) $)) (SIGNATURE |invmultisect| ($ (|Integer|) (|Integer|) $)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ (|Variable| |#2|))) |noBranch|))) (|Ring|) (|Symbol|) |#1|) (T |UnivariateTaylorSeries|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|UnivariatePolynomial| *4 *3)) (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3) (|isDomain| *1 (|UnivariateTaylorSeries| *3 *4 *5)))) (|univariatePolynomial| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|UnivariatePolynomial| *5 *4)) (|isDomain| *1 (|UnivariateTaylorSeries| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofType| *5 (|Symbol|)) (|ofType| *6 *4))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|)) (|isDomain| *1 (|UnivariateTaylorSeries| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3))) (|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|)) (|isDomain| *1 (|UnivariateTaylorSeries| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3))) (|lagrange| (*1 *1 *1) (AND (|isDomain| *1 (|UnivariateTaylorSeries| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofType| *3 (|Symbol|)) (|ofType| *4 *2))) (|lambert| (*1 *1 *1) (AND (|isDomain| *1 (|UnivariateTaylorSeries| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofType| *3 (|Symbol|)) (|ofType| *4 *2))) (|oddlambert| (*1 *1 *1) (AND (|isDomain| *1 (|UnivariateTaylorSeries| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofType| *3 (|Symbol|)) (|ofType| *4 *2))) (|evenlambert| (*1 *1 *1) (AND (|isDomain| *1 (|UnivariateTaylorSeries| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofType| *3 (|Symbol|)) (|ofType| *4 *2))) (|generalLambert| (*1 *1 *1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|UnivariateTaylorSeries| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3))) (|revert| (*1 *1 *1) (AND (|isDomain| *1 (|UnivariateTaylorSeries| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofType| *3 (|Symbol|)) (|ofType| *4 *2))) (|multisect| (*1 *1 *2 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|UnivariateTaylorSeries| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3))) (|invmultisect| (*1 *1 *2 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|UnivariateTaylorSeries| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3))) (|integrate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|)) (|isDomain| *1 (|UnivariateTaylorSeries| *3 *4 *5)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))) 
(|Join| (|UnivariateTaylorSeriesCategory| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|UnivariatePolynomial| |#2| |#1|))) (SIGNATURE |univariatePolynomial| ((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|))) (SIGNATURE |coerce| ($ (|Variable| |#2|))) (SIGNATURE |differentiate| ($ $ (|Variable| |#2|))) (SIGNATURE |lagrange| ($ $)) (SIGNATURE |lambert| ($ $)) (SIGNATURE |oddlambert| ($ $)) (SIGNATURE |evenlambert| ($ $)) (SIGNATURE |generalLambert| ($ $ (|Integer|) (|Integer|))) (SIGNATURE |revert| ($ $)) (SIGNATURE |multisect| ($ (|Integer|) (|Integer|) $)) (SIGNATURE |invmultisect| ($ (|Integer|) (|Integer|) $)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ (|Variable| |#2|))) |noBranch|))) 
((|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) 24)) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) 16)) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) 13)) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) 48)) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) 46)) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) 54)) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) 61)) (|fixedPointExquo| ((|#2| |#2| |#2|) 43))) 
(((|UnivariateTaylorSeriesODESolver| |#1| |#2|) (CATEGORY |package| (SIGNATURE |stFunc1| ((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|))) (SIGNATURE |stFunc2| ((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|))) (SIGNATURE |stFuncN| ((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|)))) (SIGNATURE |fixedPointExquo| (|#2| |#2| |#2|)) (SIGNATURE |ode1| (|#2| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |ode2| (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|)) (SIGNATURE |ode| (|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|))) (SIGNATURE |mpsode| ((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))))) (|Algebra| (|Fraction| (|Integer|))) (|UnivariateTaylorSeriesCategory| |#1|)) (T |UnivariateTaylorSeriesODESolver|)) 
((|mpsode| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|List| (|Mapping| *6 (|List| *6)))) (|ofCategory| *5 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *6 (|UnivariateTaylorSeriesCategory| *5)) (|isDomain| *2 (|List| *6)) (|isDomain| *1 (|UnivariateTaylorSeriesODESolver| *5 *6)))) (|ode| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *2 (|List| *2))) (|isDomain| *4 (|List| *5)) (|ofCategory| *5 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *5)) (|isDomain| *1 (|UnivariateTaylorSeriesODESolver| *5 *2)))) (|ode2| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|Mapping| *2 *2 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *4)) (|isDomain| *1 (|UnivariateTaylorSeriesODESolver| *4 *2)) (|ofCategory| *4 (|Algebra| (|Fraction| (|Integer|)))))) (|ode1| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *2 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *4)) (|isDomain| *1 (|UnivariateTaylorSeriesODESolver| *4 *2)) (|ofCategory| *4 (|Algebra| (|Fraction| (|Integer|)))))) (|fixedPointExquo| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|UnivariateTaylorSeriesODESolver| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|stFuncN| (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| *5 (|List| *5))) (|ofCategory| *5 (|UnivariateTaylorSeriesCategory| *4)) (|ofCategory| *4 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *2 (|Mapping| (|Stream| *4) (|List| (|Stream| *4)))) (|isDomain| *1 (|UnivariateTaylorSeriesODESolver| *4 *5)))) (|stFunc2| (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| *5 *5 *5)) (|ofCategory| *5 (|UnivariateTaylorSeriesCategory| *4)) (|ofCategory| *4 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *2 (|Mapping| (|Stream| *4) (|Stream| *4) (|Stream| *4))) (|isDomain| *1 (|UnivariateTaylorSeriesODESolver| *4 *5)))) (|stFunc1| (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| *5 *5)) (|ofCategory| *5 (|UnivariateTaylorSeriesCategory| *4)) (|ofCategory| *4 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *2 (|Mapping| (|Stream| *4) (|Stream| *4))) (|isDomain| *1 (|UnivariateTaylorSeriesODESolver| *4 *5))))) 
(CATEGORY |package| (SIGNATURE |stFunc1| ((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|))) (SIGNATURE |stFunc2| ((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|))) (SIGNATURE |stFuncN| ((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|)))) (SIGNATURE |fixedPointExquo| (|#2| |#2| |#2|)) (SIGNATURE |ode1| (|#2| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |ode2| (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|)) (SIGNATURE |ode| (|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|))) (SIGNATURE |mpsode| ((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))))) 
((UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) 30)) (UP2UTS ((|#4| |#2|) 25)) (RF2UTS ((|#4| (|Fraction| |#2|)) 51 (|has| |#1| (|IntegralDomain|)))) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) 45))) 
(((|UTSodetools| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE UP2UTS (|#4| |#2|)) (SIGNATURE UTS2UP (|#2| |#4| (|NonNegativeInteger|))) (SIGNATURE LODO2FUN ((|Mapping| |#4| (|List| |#4|)) |#3|)) (IF (|has| |#1| (|IntegralDomain|)) (SIGNATURE RF2UTS (|#4| (|Fraction| |#2|))) |noBranch|)) (|Ring|) (|UnivariatePolynomialCategory| |#1|) (|LinearOrdinaryDifferentialOperatorCategory| |#2|) (|UnivariateTaylorSeriesCategory| |#1|)) (T |UTSodetools|)) 
((RF2UTS (*1 *2 *3) (AND (|isDomain| *3 (|Fraction| *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *4)) (|isDomain| *1 (|UTSodetools| *4 *5 *6 *2)) (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *5)))) (LODO2FUN (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Mapping| *6 (|List| *6))) (|isDomain| *1 (|UTSodetools| *4 *5 *3 *6)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *5)) (|ofCategory| *6 (|UnivariateTaylorSeriesCategory| *4)))) (UTS2UP (*1 *2 *3 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *5)) (|isDomain| *1 (|UTSodetools| *5 *2 *6 *3)) (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *3 (|UnivariateTaylorSeriesCategory| *5)))) (UP2UTS (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *4)) (|isDomain| *1 (|UTSodetools| *4 *3 *5 *2)) (|ofCategory| *5 (|LinearOrdinaryDifferentialOperatorCategory| *3))))) 
(CATEGORY |package| (SIGNATURE UP2UTS (|#4| |#2|)) (SIGNATURE UTS2UP (|#2| |#4| (|NonNegativeInteger|))) (SIGNATURE LODO2FUN ((|Mapping| |#4| (|List| |#4|)) |#3|)) (IF (|has| |#1| (|IntegralDomain|)) (SIGNATURE RF2UTS (|#4| (|Fraction| |#2|))) |noBranch|)) 
((|seriesSolve| ((|#2| (|Mapping| |#3| |#3|) (|List| |#1|)) 67))) 
(((|TaylorSolve| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |seriesSolve| (|#2| (|Mapping| |#3| |#3|) (|List| |#1|)))) (|Field|) (|UnivariateTaylorSeriesCategory| |#1|) (|UnivariateTaylorSeriesCategory| (|SparseUnivariatePolynomialExpressions| |#1|))) (T |TaylorSolve|)) 
((|seriesSolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *6)) (|isDomain| *4 (|List| *5)) (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|UnivariateTaylorSeriesCategory| (|SparseUnivariatePolynomialExpressions| *5))) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *5)) (|isDomain| *1 (|TaylorSolve| *5 *2 *6))))) 
(CATEGORY |package| (SIGNATURE |seriesSolve| (|#2| (|Mapping| |#3| |#3|) (|List| |#1|)))) 
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(((|VectorCategory| |#1|) (|Category|) (|Type|)) (T |VectorCategory|)) 
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((|vector| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|Vector| *3))))) 
(|Join| (|VectorCategory| |#1|) (CATEGORY |domain| (SIGNATURE |vector| ($ (|List| |#1|))))) 
((~= (((|Boolean|) $ $) NIL)) (|write| (((|String|) $ (|String|)) 87) (((|String|) $ (|String|) (|String|)) 85) (((|String|) $ (|String|) (|List| (|String|))) 84)) (|viewport2D| (($) 56)) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) 42)) (|units| (((|Void|) $ (|PositiveInteger|) (|String|)) 70) (((|Void|) $ (|PositiveInteger|) (|Palette|)) 71)) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) 45)) (|title| (((|Void|) $ (|String|)) 66)) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) 75)) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) 46)) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) 43)) (|reset| (((|Void|) $) 67)) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) 74)) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) 30)) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) 73)) (|options| (((|List| (|DrawOption|)) $) 22) (($ $ (|List| (|DrawOption|))) 23)) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) 40)) (|makeViewport2D| (($ $) 57) (($ (|GraphImage|) (|List| (|DrawOption|))) 58)) (|latex| (((|String|) $) NIL)) (|key| (((|Integer|) $) 37)) (|hash| (((|SingleInteger|) $) NIL)) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) 36)) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) 35)) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) 65)) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) NIL)) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) 32)) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) 39)) (|controlPanel| (((|Void|) $ (|String|)) 76)) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) 72)) (|coerce| (((|OutputForm|) $) 82)) (|close| (((|Void|) $) 77)) (|axes| (((|Void|) $ (|PositiveInteger|) (|String|)) 68) (((|Void|) $ (|PositiveInteger|) (|Palette|)) 69)) (= (((|Boolean|) $ $) NIL))) 
(((|TwoDimensionalViewport|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |getPickedPoints| ((|List| (|Point| (|DoubleFloat|))) $)) (SIGNATURE |viewport2D| ($)) (SIGNATURE |makeViewport2D| ($ $)) (SIGNATURE |options| ((|List| (|DrawOption|)) $)) (SIGNATURE |options| ($ $ (|List| (|DrawOption|)))) (SIGNATURE |makeViewport2D| ($ (|GraphImage|) (|List| (|DrawOption|)))) (SIGNATURE |graphState| ((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|))) (SIGNATURE |graphStates| ((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $)) (SIGNATURE |graphs| ((|Vector| (|Union| (|GraphImage|) "undefined")) $)) (SIGNATURE |title| ((|Void|) $ (|String|))) (SIGNATURE |putGraph| ((|Void|) $ (|GraphImage|) (|PositiveInteger|))) (SIGNATURE |getGraph| ((|GraphImage|) $ (|PositiveInteger|))) (SIGNATURE |axes| ((|Void|) $ (|PositiveInteger|) (|String|))) (SIGNATURE |axes| ((|Void|) $ (|PositiveInteger|) (|Palette|))) (SIGNATURE |units| ((|Void|) $ (|PositiveInteger|) (|String|))) (SIGNATURE |units| ((|Void|) $ (|PositiveInteger|) (|Palette|))) (SIGNATURE |points| ((|Void|) $ (|PositiveInteger|) (|String|))) (SIGNATURE |region| ((|Void|) $ (|PositiveInteger|) (|String|))) (SIGNATURE |connect| ((|Void|) $ (|PositiveInteger|) (|String|))) (SIGNATURE |controlPanel| ((|Void|) $ (|String|))) (SIGNATURE |close| ((|Void|) $)) (SIGNATURE |dimensions| ((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |scale| ((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|))) (SIGNATURE |translate| ((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|))) (SIGNATURE |show| ((|Void|) $ (|PositiveInteger|) (|String|))) (SIGNATURE |move| ((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |update| ((|Void|) $ (|GraphImage|) (|PositiveInteger|))) (SIGNATURE |resize| ((|Void|) $ (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |write| ((|String|) $ (|String|))) (SIGNATURE |write| ((|String|) $ (|String|) (|String|))) (SIGNATURE |write| ((|String|) $ (|String|) (|List| (|String|)))) (SIGNATURE |reset| ((|Void|) $)) (SIGNATURE |key| ((|Integer|) $)) (SIGNATURE |coerce| ((|OutputForm|) $))))) (T |TwoDimensionalViewport|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|getPickedPoints| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Point| (|DoubleFloat|)))) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|viewport2D| (*1 *1) (|isDomain| *1 (|TwoDimensionalViewport|))) (|makeViewport2D| (*1 *1 *1) (|isDomain| *1 (|TwoDimensionalViewport|))) (|options| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|DrawOption|))) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|options| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|DrawOption|))) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|makeViewport2D| (*1 *1 *2 *3) (AND (|isDomain| *2 (|GraphImage|)) (|isDomain| *3 (|List| (|DrawOption|))) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|graphState| (*1 *2 *1 *3 *4 *4 *4 *4 *5 *5 *5 *5 *6 *5 *6 *5) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|DoubleFloat|)) (|isDomain| *5 (|Integer|)) (|isDomain| *6 (|Palette|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|graphStates| (*1 *2 *1) (AND (|isDomain| *2 (|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|))))) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|graphs| (*1 *2 *1) (AND (|isDomain| *2 (|Vector| (|Union| (|GraphImage|) "undefined"))) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|title| (*1 *2 *1 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|putGraph| (*1 *2 *1 *3 *4) (AND (|isDomain| *3 (|GraphImage|)) (|isDomain| *4 (|PositiveInteger|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|getGraph| (*1 *2 *1 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|GraphImage|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|axes| (*1 *2 *1 *3 *4) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|axes| (*1 *2 *1 *3 *4) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|Palette|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|units| (*1 *2 *1 *3 *4) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|units| (*1 *2 *1 *3 *4) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|Palette|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|points| (*1 *2 *1 *3 *4) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|region| (*1 *2 *1 *3 *4) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|connect| (*1 *2 *1 *3 *4) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|controlPanel| (*1 *2 *1 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|close| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|dimensions| (*1 *2 *1 *3 *3 *4 *4) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|PositiveInteger|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|scale| (*1 *2 *1 *3 *4 *4) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|Float|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|translate| (*1 *2 *1 *3 *4 *4) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|Float|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|show| (*1 *2 *1 *3 *4) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|move| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|update| (*1 *2 *1 *3 *4) (AND (|isDomain| *3 (|GraphImage|)) (|isDomain| *4 (|PositiveInteger|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|resize| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|write| (*1 *2 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|write| (*1 *2 *1 *2 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|write| (*1 *2 *1 *2 *3) (AND (|isDomain| *3 (|List| (|String|))) (|isDomain| *2 (|String|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|reset| (*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|)))) (|key| (*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|TwoDimensionalViewport|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |getPickedPoints| ((|List| (|Point| (|DoubleFloat|))) $)) (SIGNATURE |viewport2D| ($)) (SIGNATURE |makeViewport2D| ($ $)) (SIGNATURE |options| ((|List| (|DrawOption|)) $)) (SIGNATURE |options| ($ $ (|List| (|DrawOption|)))) (SIGNATURE |makeViewport2D| ($ (|GraphImage|) (|List| (|DrawOption|)))) (SIGNATURE |graphState| ((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|))) (SIGNATURE |graphStates| ((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $)) (SIGNATURE |graphs| ((|Vector| (|Union| (|GraphImage|) "undefined")) $)) (SIGNATURE |title| ((|Void|) $ (|String|))) (SIGNATURE |putGraph| ((|Void|) $ (|GraphImage|) (|PositiveInteger|))) (SIGNATURE |getGraph| ((|GraphImage|) $ (|PositiveInteger|))) (SIGNATURE |axes| ((|Void|) $ (|PositiveInteger|) (|String|))) (SIGNATURE |axes| ((|Void|) $ (|PositiveInteger|) (|Palette|))) (SIGNATURE |units| ((|Void|) $ (|PositiveInteger|) (|String|))) (SIGNATURE |units| ((|Void|) $ (|PositiveInteger|) (|Palette|))) (SIGNATURE |points| ((|Void|) $ (|PositiveInteger|) (|String|))) (SIGNATURE |region| ((|Void|) $ (|PositiveInteger|) (|String|))) (SIGNATURE |connect| ((|Void|) $ (|PositiveInteger|) (|String|))) (SIGNATURE |controlPanel| ((|Void|) $ (|String|))) (SIGNATURE |close| ((|Void|) $)) (SIGNATURE |dimensions| ((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |scale| ((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|))) (SIGNATURE |translate| ((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|))) (SIGNATURE |show| ((|Void|) $ (|PositiveInteger|) (|String|))) (SIGNATURE |move| ((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |update| ((|Void|) $ (|GraphImage|) (|PositiveInteger|))) (SIGNATURE |resize| ((|Void|) $ (|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |write| ((|String|) $ (|String|))) (SIGNATURE |write| ((|String|) $ (|String|) (|String|))) (SIGNATURE |write| ((|String|) $ (|String|) (|List| (|String|)))) (SIGNATURE |reset| ((|Void|) $)) (SIGNATURE |key| ((|Integer|) $)) (SIGNATURE |coerce| ((|OutputForm|) $)))) 
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(((|ViewDefaultsPackage|) (CATEGORY |package| (SIGNATURE |pointColorDefault| ((|Palette|))) (SIGNATURE |pointColorDefault| ((|Palette|) (|Palette|))) (SIGNATURE |lineColorDefault| ((|Palette|))) (SIGNATURE |lineColorDefault| ((|Palette|) (|Palette|))) (SIGNATURE |axesColorDefault| ((|Palette|))) (SIGNATURE |axesColorDefault| ((|Palette|) (|Palette|))) (SIGNATURE |unitsColorDefault| ((|Palette|))) (SIGNATURE |unitsColorDefault| ((|Palette|) (|Palette|))) (SIGNATURE |pointSizeDefault| ((|PositiveInteger|))) (SIGNATURE |pointSizeDefault| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |viewPosDefault| ((|List| (|NonNegativeInteger|)))) (SIGNATURE |viewPosDefault| ((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |viewSizeDefault| ((|List| (|PositiveInteger|)))) (SIGNATURE |viewSizeDefault| ((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|)))) (SIGNATURE |viewDefaults| ((|Void|))) (SIGNATURE |viewWriteDefault| ((|List| (|String|)))) (SIGNATURE |viewWriteDefault| ((|List| (|String|)) (|List| (|String|)))) (SIGNATURE |viewWriteAvailable| ((|List| (|String|)))) (SIGNATURE |var1StepsDefault| ((|PositiveInteger|))) (SIGNATURE |var2StepsDefault| ((|PositiveInteger|))) (SIGNATURE |var1StepsDefault| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |var2StepsDefault| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |tubePointsDefault| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |tubePointsDefault| ((|PositiveInteger|))) (SIGNATURE |tubeRadiusDefault| ((|DoubleFloat|) (|Float|))) (SIGNATURE |tubeRadiusDefault| ((|DoubleFloat|))))) (T |ViewDefaultsPackage|)) 
((|tubeRadiusDefault| (*1 *2) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|tubeRadiusDefault| (*1 *2 *3) (AND (|isDomain| *3 (|Float|)) (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|tubePointsDefault| (*1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|tubePointsDefault| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|var2StepsDefault| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|var1StepsDefault| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|var2StepsDefault| (*1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|var1StepsDefault| (*1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|viewWriteAvailable| (*1 *2) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|viewWriteDefault| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|viewWriteDefault| (*1 *2) (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|viewDefaults| (*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|viewSizeDefault| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|PositiveInteger|))) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|viewSizeDefault| (*1 *2) (AND (|isDomain| *2 (|List| (|PositiveInteger|))) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|viewPosDefault| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|NonNegativeInteger|))) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|viewPosDefault| (*1 *2) (AND (|isDomain| *2 (|List| (|NonNegativeInteger|))) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|pointSizeDefault| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|pointSizeDefault| (*1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|unitsColorDefault| (*1 *2 *2) (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|unitsColorDefault| (*1 *2) (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|axesColorDefault| (*1 *2 *2) (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|axesColorDefault| (*1 *2) (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|lineColorDefault| (*1 *2 *2) (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|lineColorDefault| (*1 *2) (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|pointColorDefault| (*1 *2 *2) (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|ViewDefaultsPackage|)))) (|pointColorDefault| (*1 *2) (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|ViewDefaultsPackage|))))) 
(CATEGORY |package| (SIGNATURE |pointColorDefault| ((|Palette|))) (SIGNATURE |pointColorDefault| ((|Palette|) (|Palette|))) (SIGNATURE |lineColorDefault| ((|Palette|))) (SIGNATURE |lineColorDefault| ((|Palette|) (|Palette|))) (SIGNATURE |axesColorDefault| ((|Palette|))) (SIGNATURE |axesColorDefault| ((|Palette|) (|Palette|))) (SIGNATURE |unitsColorDefault| ((|Palette|))) (SIGNATURE |unitsColorDefault| ((|Palette|) (|Palette|))) (SIGNATURE |pointSizeDefault| ((|PositiveInteger|))) (SIGNATURE |pointSizeDefault| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |viewPosDefault| ((|List| (|NonNegativeInteger|)))) (SIGNATURE |viewPosDefault| ((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|)))) (SIGNATURE |viewSizeDefault| ((|List| (|PositiveInteger|)))) (SIGNATURE |viewSizeDefault| ((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|)))) (SIGNATURE |viewDefaults| ((|Void|))) (SIGNATURE |viewWriteDefault| ((|List| (|String|)))) (SIGNATURE |viewWriteDefault| ((|List| (|String|)) (|List| (|String|)))) (SIGNATURE |viewWriteAvailable| ((|List| (|String|)))) (SIGNATURE |var1StepsDefault| ((|PositiveInteger|))) (SIGNATURE |var2StepsDefault| ((|PositiveInteger|))) (SIGNATURE |var1StepsDefault| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |var2StepsDefault| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |tubePointsDefault| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |tubePointsDefault| ((|PositiveInteger|))) (SIGNATURE |tubeRadiusDefault| ((|DoubleFloat|) (|Float|))) (SIGNATURE |tubeRadiusDefault| ((|DoubleFloat|)))) 
((|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) 17) (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) 16) (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) 15)) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) 23) (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) 22)) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) 34))) 
(((|ViewportPackage|) (CATEGORY |package| (SIGNATURE |graphCurves| ((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|)))) (SIGNATURE |graphCurves| ((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))))) (SIGNATURE |graphCurves| ((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|)))) (SIGNATURE |drawCurves| ((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|)))) (SIGNATURE |drawCurves| ((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|)))) (SIGNATURE |coerce| ((|TwoDimensionalViewport|) (|GraphImage|))))) (T |ViewportPackage|)) 
((|coerce| (*1 *2 *3) (AND (|isDomain| *3 (|GraphImage|)) (|isDomain| *2 (|TwoDimensionalViewport|)) (|isDomain| *1 (|ViewportPackage|)))) (|drawCurves| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|List| (|Point| (|DoubleFloat|))))) (|isDomain| *4 (|List| (|DrawOption|))) (|isDomain| *2 (|TwoDimensionalViewport|)) (|isDomain| *1 (|ViewportPackage|)))) (|drawCurves| (*1 *2 *3 *4 *4 *5 *6) (AND (|isDomain| *3 (|List| (|List| (|Point| (|DoubleFloat|))))) (|isDomain| *4 (|Palette|)) (|isDomain| *5 (|PositiveInteger|)) (|isDomain| *6 (|List| (|DrawOption|))) (|isDomain| *2 (|TwoDimensionalViewport|)) (|isDomain| *1 (|ViewportPackage|)))) (|graphCurves| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|List| (|Point| (|DoubleFloat|))))) (|isDomain| *4 (|List| (|DrawOption|))) (|isDomain| *2 (|GraphImage|)) (|isDomain| *1 (|ViewportPackage|)))) (|graphCurves| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|List| (|Point| (|DoubleFloat|))))) (|isDomain| *2 (|GraphImage|)) (|isDomain| *1 (|ViewportPackage|)))) (|graphCurves| (*1 *2 *3 *4 *4 *5 *6) (AND (|isDomain| *3 (|List| (|List| (|Point| (|DoubleFloat|))))) (|isDomain| *4 (|Palette|)) (|isDomain| *5 (|PositiveInteger|)) (|isDomain| *6 (|List| (|DrawOption|))) (|isDomain| *2 (|GraphImage|)) (|isDomain| *1 (|ViewportPackage|))))) 
(CATEGORY |package| (SIGNATURE |graphCurves| ((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|)))) (SIGNATURE |graphCurves| ((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))))) (SIGNATURE |graphCurves| ((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|)))) (SIGNATURE |drawCurves| ((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|)))) (SIGNATURE |drawCurves| ((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|)))) (SIGNATURE |coerce| ((|TwoDimensionalViewport|) (|GraphImage|)))) 
((|void| (($) 7)) (|coerce| (((|OutputForm|) $) 10))) 
(((|Void|) (CATEGORY |domain| (SIGNATURE |void| ($)) (SIGNATURE |coerce| ((|OutputForm|) $)))) (T |Void|)) 
((|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|Void|)))) (|void| (*1 *1) (|isDomain| *1 (|Void|)))) 
(CATEGORY |domain| (SIGNATURE |void| ($)) (SIGNATURE |coerce| ((|OutputForm|) $))) 
((/ (($ $ |#2|) 10))) 
(((|VectorSpace&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE / (|#1| |#1| |#2|))) (|VectorSpace| |#2|) (|Field|)) (T |VectorSpace&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE / (|#1| |#1| |#2|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|dimension| (((|CardinalNumber|)) 25)) (|coerce| (((|OutputForm|) $) 11)) (|Zero| (($) 17 T CONST)) (= (((|Boolean|) $ $) 6)) (/ (($ $ |#1|) 26)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ |#1| $) 22) (($ $ |#1|) 24))) 
(((|VectorSpace| |#1|) (|Category|) (|Field|)) (T |VectorSpace|)) 
((/ (*1 *1 *1 *2) (AND (|ofCategory| *1 (|VectorSpace| *2)) (|ofCategory| *2 (|Field|)))) (|dimension| (*1 *2) (AND (|ofCategory| *1 (|VectorSpace| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|CardinalNumber|))))) 
(|Join| (|Module| |t#1|) (CATEGORY |domain| (SIGNATURE / ($ $ |t#1|)) (SIGNATURE |dimension| ((|CardinalNumber|))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| |#1|) . T) ((|Module| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T)) 
((|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) 78)) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) 57)) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) 68)) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) 59)) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) 27)) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) 58))) 
(((|WeierstrassPreparation| |#1|) (CATEGORY |package| (SIGNATURE |crest| ((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|))) (SIGNATURE |cfirst| ((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|))) (SIGNATURE |sts2stst| ((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|)))) (SIGNATURE |clikeUniv| ((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |weierstrass| ((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|))) (SIGNATURE |qqq| ((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))))) (|Field|)) (T |WeierstrassPreparation|)) 
((|qqq| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *6 (|Field|)) (|isDomain| *4 (|TaylorSeries| *6)) (|isDomain| *2 (|Mapping| (|Stream| *4) (|Stream| *4))) (|isDomain| *1 (|WeierstrassPreparation| *6)) (|isDomain| *5 (|Stream| *4)))) (|weierstrass| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|List| (|TaylorSeries| *5))) (|isDomain| *1 (|WeierstrassPreparation| *5)) (|isDomain| *4 (|TaylorSeries| *5)))) (|clikeUniv| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| *4)) (|Polynomial| *4))) (|isDomain| *1 (|WeierstrassPreparation| *4)) (|ofCategory| *4 (|Field|)))) (|sts2stst| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Stream| (|Stream| (|Polynomial| *5)))) (|isDomain| *1 (|WeierstrassPreparation| *5)) (|isDomain| *4 (|Stream| (|Polynomial| *5))))) (|cfirst| (*1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Mapping| (|Stream| (|Polynomial| *4)) (|Stream| (|Polynomial| *4)))) (|isDomain| *1 (|WeierstrassPreparation| *4)) (|ofCategory| *4 (|Field|)))) (|crest| (*1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Mapping| (|Stream| (|Polynomial| *4)) (|Stream| (|Polynomial| *4)))) (|isDomain| *1 (|WeierstrassPreparation| *4)) (|ofCategory| *4 (|Field|))))) 
(CATEGORY |package| (SIGNATURE |crest| ((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|))) (SIGNATURE |cfirst| ((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|))) (SIGNATURE |sts2stst| ((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|)))) (SIGNATURE |clikeUniv| ((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|))) (SIGNATURE |weierstrass| ((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|))) (SIGNATURE |qqq| ((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))))) 
((|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) 74)) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) 73))) 
(((|WildFunctionFieldIntegralBasis| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |integralBasis| ((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))))) (SIGNATURE |localIntegralBasis| ((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|))) (|FiniteFieldCategory|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| |#2|) (|FramedAlgebra| |#2| |#3|)) (T |WildFunctionFieldIntegralBasis|)) 
((|localIntegralBasis| (*1 *2 *3) (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Record| (|:| |basis| (|Matrix| *3)) (|:| |basisDen| *3) (|:| |basisInv| (|Matrix| *3)))) (|isDomain| *1 (|WildFunctionFieldIntegralBasis| *4 *3 *5 *6)) (|ofCategory| *6 (|FramedAlgebra| *3 *5)))) (|integralBasis| (*1 *2) (AND (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Record| (|:| |basis| (|Matrix| *4)) (|:| |basisDen| *4) (|:| |basisInv| (|Matrix| *4)))) (|isDomain| *1 (|WildFunctionFieldIntegralBasis| *3 *4 *5 *6)) (|ofCategory| *6 (|FramedAlgebra| *4 *5))))) 
(CATEGORY |package| (SIGNATURE |integralBasis| ((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))))) (SIGNATURE |localIntegralBasis| ((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 41)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|coerce| (((|OutputForm|) $) 62) (($ (|Integer|)) NIL) ((|#4| $) 52) (($ |#4|) 47) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)))) (|characteristic| (((|NonNegativeInteger|)) NIL)) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) 16)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 26 T CONST)) (|One| (($) 65 T CONST)) (= (((|Boolean|) $ $) 67)) (/ (((|Union| $ "failed") $ $) NIL (|has| |#1| (|Field|)))) (- (($ $) 69) (($ $ $) NIL)) (+ (($ $ $) 45)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 71) (($ |#1| $) NIL (|has| |#1| (|CommutativeRing|))) (($ $ |#1|) NIL (|has| |#1| (|CommutativeRing|))))) 
(((|WeightedPolynomials| |#1| |#2| |#3| |#4| |#5| |#6| |#7|) (|Join| (|Ring|) (CATEGORY |domain| (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |#1|)) |noBranch|) (SIGNATURE |coerce| (|#4| $)) (IF (|has| |#1| (|Field|)) (SIGNATURE / ((|Union| $ "failed") $ $)) |noBranch|) (SIGNATURE |coerce| ($ |#4|)) (SIGNATURE |changeWeightLevel| ((|Void|) (|NonNegativeInteger|))))) (|Ring|) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|PolynomialCategory| |#1| |#3| |#2|) (|List| |#2|) (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) (T |WeightedPolynomials|)) 
((|coerce| (*1 *2 *1) (AND (|ofCategory| *2 (|PolynomialCategory| *3 *5 *4)) (|isDomain| *1 (|WeightedPolynomials| *3 *4 *5 *2 *6 *7 *8)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofType| *6 (|List| *4)) (|ofType| *7 (|List| (|NonNegativeInteger|))) (|ofType| *8 (|NonNegativeInteger|)))) (/ (*1 *1 *1 *1) (|partial| AND (|ofCategory| *2 (|Field|)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofType| *6 (|List| *3)) (|isDomain| *1 (|WeightedPolynomials| *2 *3 *4 *5 *6 *7 *8)) (|ofCategory| *5 (|PolynomialCategory| *2 *4 *3)) (|ofType| *7 (|List| (|NonNegativeInteger|))) (|ofType| *8 (|NonNegativeInteger|)))) (|coerce| (*1 *1 *2) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofType| *6 (|List| *4)) (|isDomain| *1 (|WeightedPolynomials| *3 *4 *5 *2 *6 *7 *8)) (|ofCategory| *2 (|PolynomialCategory| *3 *5 *4)) (|ofType| *7 (|List| (|NonNegativeInteger|))) (|ofType| *8 (|NonNegativeInteger|)))) (|changeWeightLevel| (*1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofType| *8 (|List| *5)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|WeightedPolynomials| *4 *5 *6 *7 *8 *9 *10)) (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5)) (|ofType| *9 (|List| *3)) (|ofType| *10 *3)))) 
(|Join| (|Ring|) (CATEGORY |domain| (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |#1|)) |noBranch|) (SIGNATURE |coerce| (|#4| $)) (IF (|has| |#1| (|Field|)) (SIGNATURE / ((|Union| $ "failed") $ $)) |noBranch|) (SIGNATURE |coerce| ($ |#4|)) (SIGNATURE |changeWeightLevel| ((|Void|) (|NonNegativeInteger|))))) 
((~= (((|Boolean|) $ $) NIL)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) NIL)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 87)) (|variables| (((|List| |#3|) $) NIL)) (|trivialIdeal?| (((|Boolean|) $) NIL)) (|triangular?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|stronglyReduced?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|stronglyReduce| ((|#4| |#4| $) NIL)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) NIL)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|select| (($ (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) (((|Union| |#4| "failed") $ |#3|) NIL)) (|sample| (($) NIL T CONST)) (|roughUnitIdeal?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|roughSubIdeal?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|roughEqualIdeals?| (((|Boolean|) $ $) NIL (|has| |#1| (|IntegralDomain|)))) (|roughBase?| (((|Boolean|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 27)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) 24 (|has| |#1| (|IntegralDomain|)))) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) NIL)) (|retract| (($ (|List| |#4|)) NIL)) (|rest| (((|Union| $ "failed") $) 69)) (|removeZero| ((|#4| |#4| $) 74)) (|removeDuplicates| (($ $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|))))) (|remove| (($ |#4| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|)))) (($ (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) NIL (|has| |#1| (|IntegralDomain|)))) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) NIL)) (|reduceByQuasiMonic| ((|#4| |#4| $) NIL)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|)))) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| (|Mapping| |#4| |#4| |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) NIL)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) NIL)) (|parts| (((|List| |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|normalized?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|mvar| ((|#3| $) 75)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|members| (((|List| |#4|) $) 28 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|member?| (((|Boolean|) |#4| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|))))) (|medialSet| (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) 31) (((|Union| $ "failed") (|List| |#4|)) 34)) (|map!| (($ (|Mapping| |#4| |#4|) $) NIL (|has| $ (ATTRIBUTE |shallowlyMutable|)))) (|map| (($ (|Mapping| |#4| |#4|) $) NIL)) (|mainVariables| (((|List| |#3|) $) NIL)) (|mainVariable?| (((|Boolean|) |#3| $) NIL)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) NIL)) (|latex| (((|String|) $) NIL)) (|last| (((|Union| |#4| "failed") $) NIL)) (|initials| (((|List| |#4|) $) 49)) (|initiallyReduced?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|initiallyReduce| ((|#4| |#4| $) 73)) (|infRittWu?| (((|Boolean|) $ $) 84)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) NIL (|has| |#1| (|IntegralDomain|)))) (|headReduced?| (((|Boolean|) |#4| $) NIL) (((|Boolean|) $) NIL)) (|headReduce| ((|#4| |#4| $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|first| (((|Union| |#4| "failed") $) 68)) (|find| (((|Union| |#4| "failed") (|Mapping| (|Boolean|) |#4|) $) NIL)) (|extendIfCan| (((|Union| $ "failed") $ |#4|) NIL)) (|extend| (($ $ |#4|) NIL)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ |#4| |#4|) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|Equation| |#4|)) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|)))) (($ $ (|List| (|Equation| |#4|))) NIL (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))))) (|eq?| (((|Boolean|) $ $) NIL)) (|empty?| (((|Boolean|) $) 66)) (|empty| (($) 41)) (|degree| (((|NonNegativeInteger|) $) NIL)) (|count| (((|NonNegativeInteger|) |#4| $) NIL (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|has| |#4| (|SetCategory|)))) (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|copy| (($ $) NIL)) (|convert| (((|InputForm|) $) NIL (|has| |#4| (|ConvertibleTo| (|InputForm|))))) (|construct| (($ (|List| |#4|)) NIL)) (|collectUpper| (($ $ |#3|) NIL)) (|collectUnder| (($ $ |#3|) NIL)) (|collectQuasiMonic| (($ $) NIL)) (|collect| (($ $ |#3|) NIL)) (|coerce| (((|OutputForm|) $) NIL) (((|List| |#4|) $) 56)) (|coHeight| (((|NonNegativeInteger|) $) NIL (|has| |#3| (|Finite|)))) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) 39) (((|Union| $ "failed") (|List| |#4|)) 40)) (|characteristicSerie| (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) 64) (((|List| $) (|List| |#4|)) 65)) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 23) (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) NIL)) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) NIL)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|algebraicVariables| (((|List| |#3|) $) NIL)) (|algebraic?| (((|Boolean|) |#3| $) NIL)) (= (((|Boolean|) $ $) NIL)) (|#| (((|NonNegativeInteger|) $) NIL (|has| $ (ATTRIBUTE |finiteAggregate|))))) 
(((|WuWenTsunTriangularSet| |#1| |#2| |#3| |#4|) (|Join| (|TriangularSetCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |medialSet| ((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|))) (SIGNATURE |medialSet| ((|Union| $ "failed") (|List| |#4|))) (SIGNATURE |characteristicSet| ((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|))) (SIGNATURE |characteristicSet| ((|Union| $ "failed") (|List| |#4|))) (SIGNATURE |characteristicSerie| ((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|))) (SIGNATURE |characteristicSerie| ((|List| $) (|List| |#4|))))) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|)) (T |WuWenTsunTriangularSet|)) 
((|medialSet| (*1 *1 *2 *3 *4) (|partial| AND (|isDomain| *2 (|List| *8)) (|isDomain| *3 (|Mapping| (|Boolean|) *8 *8)) (|isDomain| *4 (|Mapping| *8 *8 *8)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *1 (|WuWenTsunTriangularSet| *5 *6 *7 *8)))) (|medialSet| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|WuWenTsunTriangularSet| *3 *4 *5 *6)))) (|characteristicSet| (*1 *1 *2 *3 *4) (|partial| AND (|isDomain| *2 (|List| *8)) (|isDomain| *3 (|Mapping| (|Boolean|) *8 *8)) (|isDomain| *4 (|Mapping| *8 *8 *8)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *1 (|WuWenTsunTriangularSet| *5 *6 *7 *8)))) (|characteristicSet| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|WuWenTsunTriangularSet| *3 *4 *5 *6)))) (|characteristicSerie| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| *9)) (|isDomain| *4 (|Mapping| (|Boolean|) *9 *9)) (|isDomain| *5 (|Mapping| *9 *9 *9)) (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8)) (|ofCategory| *6 (|IntegralDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|isDomain| *2 (|List| (|WuWenTsunTriangularSet| *6 *7 *8 *9))) (|isDomain| *1 (|WuWenTsunTriangularSet| *6 *7 *8 *9)))) (|characteristicSerie| (*1 *2 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| (|WuWenTsunTriangularSet| *4 *5 *6 *7))) (|isDomain| *1 (|WuWenTsunTriangularSet| *4 *5 *6 *7))))) 
(|Join| (|TriangularSetCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |medialSet| ((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|))) (SIGNATURE |medialSet| ((|Union| $ "failed") (|List| |#4|))) (SIGNATURE |characteristicSet| ((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|))) (SIGNATURE |characteristicSet| ((|Union| $ "failed") (|List| |#4|))) (SIGNATURE |characteristicSerie| ((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|))) (SIGNATURE |characteristicSerie| ((|List| $) (|List| |#4|))))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sample| (($) 16 T CONST)) (|recip| (((|Union| $ "failed") $) 33)) (|one?| (((|Boolean|) $) 30)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ |#1|) 37)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ |#1|) 39) (($ |#1| $) 38))) 
(((|XAlgebra| |#1|) (|Category|) (|Ring|)) (T |XAlgebra|)) 
((|coerce| (*1 *1 *2) (AND (|ofCategory| *1 (|XAlgebra| *2)) (|ofCategory| *2 (|Ring|))))) 
(|Join| (|Ring|) (|BiModule| |t#1| |t#1|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |t#1|)) (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |t#1|)) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|varList| (((|List| |#1|) $) 45)) (|trunc| (($ $ (|NonNegativeInteger|)) 39)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sh| (($ $ (|NonNegativeInteger|)) 17 (|has| |#2| (|CommutativeRing|))) (($ $ $) 18 (|has| |#2| (|CommutativeRing|)))) (|sample| (($) NIL T CONST)) (|rquo| (($ $ $) 61) (($ $ (|OrderedFreeMonoid| |#1|)) 48) (($ $ |#1|) 52)) (|retractIfCan| (((|Union| (|OrderedFreeMonoid| |#1|) "failed") $) NIL)) (|retract| (((|OrderedFreeMonoid| |#1|) $) NIL)) (|reductum| (($ $) 32)) (|recip| (((|Union| $ "failed") $) NIL)) (|quasiRegular?| (((|Boolean|) $) NIL)) (|quasiRegular| (($ $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|numberOfMonomials| (((|NonNegativeInteger|) $) NIL)) (|monomials| (((|List| $) $) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) 31)) (|mirror| (($ $) 33)) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) 11)) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) NIL)) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) 34)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL)) (|lquo| (($ $ $) 60) (($ $ (|OrderedFreeMonoid| |#1|)) 50) (($ $ |#1|) 54)) (|listOfTerms| (((|List| (|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|))) $) NIL)) (|leadingTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) NIL)) (|leadingMonomial| (((|OrderedFreeMonoid| |#1|) $) 28)) (|leadingCoefficient| ((|#2| $) 30)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|degree| (((|NonNegativeInteger|) $) 36)) (|constant?| (((|Boolean|) $) 40)) (|constant| ((|#2| $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ (|OrderedFreeMonoid| |#1|)) 24) (($ |#1|) 25) (($ |#2|) NIL) (($ (|Integer|)) NIL)) (|coefficients| (((|List| |#2|) $) NIL)) (|coefficient| ((|#2| $ (|OrderedFreeMonoid| |#1|)) NIL)) (|coef| ((|#2| $ $) 63) ((|#2| $ (|OrderedFreeMonoid| |#1|)) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (^ (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|PositiveInteger|)) NIL)) (|Zero| (($) 12 T CONST)) (|One| (($) 14 T CONST)) (= (((|Boolean|) $ $) 38)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) 21)) (** (($ $ (|NonNegativeInteger|)) NIL) (($ $ (|PositiveInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ |#2| $) 20) (($ $ |#2|) 59) (($ |#2| (|OrderedFreeMonoid| |#1|)) NIL) (($ |#1| $) 27) (($ $ $) NIL))) 
(((|XDistributedPolynomial| |#1| |#2|) (|Join| (|FreeModuleCat| |#2| (|OrderedFreeMonoid| |#1|)) (|XPolynomialsCat| |#1| |#2|)) (|OrderedSet|) (|Ring|)) (T |XDistributedPolynomial|)) 
NIL 
(|Join| (|FreeModuleCat| |#2| (|OrderedFreeMonoid| |#1|)) (|XPolynomialsCat| |#1| |#2|)) 
((|log| ((|#3| |#3| (|NonNegativeInteger|)) 23)) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) 28)) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) 29))) 
(((|XExponentialPackage| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |exp| (|#3| |#3| (|NonNegativeInteger|))) (SIGNATURE |log| (|#3| |#3| (|NonNegativeInteger|))) (SIGNATURE |Hausdorff| (|#3| |#3| |#3| (|NonNegativeInteger|)))) (|Join| (|Ring|) (|Module| (|Fraction| (|Integer|)))) (|OrderedSet|) (|XPolynomialsCat| |#2| |#1|)) (T |XExponentialPackage|)) 
((|Hausdorff| (*1 *2 *2 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Join| (|Ring|) (|Module| (|Fraction| (|Integer|))))) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|XExponentialPackage| *4 *5 *2)) (|ofCategory| *2 (|XPolynomialsCat| *5 *4)))) (|log| (*1 *2 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Join| (|Ring|) (|Module| (|Fraction| (|Integer|))))) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|XExponentialPackage| *4 *5 *2)) (|ofCategory| *2 (|XPolynomialsCat| *5 *4)))) (|exp| (*1 *2 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Join| (|Ring|) (|Module| (|Fraction| (|Integer|))))) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 (|XExponentialPackage| *4 *5 *2)) (|ofCategory| *2 (|XPolynomialsCat| *5 *4))))) 
(CATEGORY |package| (SIGNATURE |exp| (|#3| |#3| (|NonNegativeInteger|))) (SIGNATURE |log| (|#3| |#3| (|NonNegativeInteger|))) (SIGNATURE |Hausdorff| (|#3| |#3| |#3| (|NonNegativeInteger|)))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|varList| (((|List| |#1|) $) 39)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sh| (($ $ $) 42 (|has| |#2| (|CommutativeRing|))) (($ $ (|NonNegativeInteger|)) 41 (|has| |#2| (|CommutativeRing|)))) (|sample| (($) 16 T CONST)) (|rquo| (($ $ |#1|) 53) (($ $ (|OrderedFreeMonoid| |#1|)) 52) (($ $ $) 51)) (|retractIfCan| (((|Union| (|OrderedFreeMonoid| |#1|) "failed") $) 63)) (|retract| (((|OrderedFreeMonoid| |#1|) $) 62)) (|recip| (((|Union| $ "failed") $) 33)) (|quasiRegular?| (((|Boolean|) $) 44)) (|quasiRegular| (($ $) 43)) (|one?| (((|Boolean|) $) 30)) (|monomial?| (((|Boolean|) $) 49)) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) 50)) (|mirror| (($ $) 48)) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) 59)) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) 60)) (|map| (($ (|Mapping| |#2| |#2|) $) 40)) (|lquo| (($ $ |#1|) 56) (($ $ (|OrderedFreeMonoid| |#1|)) 55) (($ $ $) 54)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|constant?| (((|Boolean|) $) 46)) (|constant| ((|#2| $) 45)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ |#2|) 67) (($ (|OrderedFreeMonoid| |#1|)) 64) (($ |#1|) 47)) (|coef| ((|#2| $ (|OrderedFreeMonoid| |#1|)) 58) ((|#2| $ $) 57)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ |#2| $) 66) (($ $ |#2|) 65) (($ |#1| $) 61))) 
(((|XFreeAlgebra| |#1| |#2|) (|Category|) (|OrderedSet|) (|Ring|)) (T |XFreeAlgebra|)) 
((* (*1 *1 *1 *2) (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *2)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *2 (|Ring|)))) (* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|)))) (|mindeg| (*1 *2 *1) (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|OrderedFreeMonoid| *3)))) (|mindegTerm| (*1 *2 *1) (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Record| (|:| |k| (|OrderedFreeMonoid| *3)) (|:| |c| *4))))) (|coef| (*1 *2 *1 *3) (AND (|isDomain| *3 (|OrderedFreeMonoid| *4)) (|ofCategory| *1 (|XFreeAlgebra| *4 *2)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|Ring|)))) (|coef| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *2)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *2 (|Ring|)))) (|lquo| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|)))) (|lquo| (*1 *1 *1 *2) (AND (|isDomain| *2 (|OrderedFreeMonoid| *3)) (|ofCategory| *1 (|XFreeAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)))) (|lquo| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|)))) (|rquo| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|)))) (|rquo| (*1 *1 *1 *2) (AND (|isDomain| *2 (|OrderedFreeMonoid| *3)) (|ofCategory| *1 (|XFreeAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)))) (|rquo| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|)))) (|monom| (*1 *1 *2 *3) (AND (|isDomain| *2 (|OrderedFreeMonoid| *4)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *1 (|XFreeAlgebra| *4 *3)) (|ofCategory| *3 (|Ring|)))) (|monomial?| (*1 *2 *1) (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Boolean|)))) (|mirror| (*1 *1 *1) (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|)))) (|coerce| (*1 *1 *2) (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|)))) (|constant?| (*1 *2 *1) (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Boolean|)))) (|constant| (*1 *2 *1) (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *2)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *2 (|Ring|)))) (|quasiRegular?| (*1 *2 *1) (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Boolean|)))) (|quasiRegular| (*1 *1 *1) (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|)))) (|sh| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|CommutativeRing|)))) (|sh| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|XFreeAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *4 (|CommutativeRing|)))) (|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|ofCategory| *1 (|XFreeAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)))) (|varList| (*1 *2 *1) (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|List| *3))))) 
(|Join| (|Ring|) (|XAlgebra| |t#2|) (|RetractableTo| (|OrderedFreeMonoid| |t#1|)) (CATEGORY |domain| (SIGNATURE * ($ |t#1| $)) (SIGNATURE * ($ $ |t#2|)) (SIGNATURE |mindeg| ((|OrderedFreeMonoid| |t#1|) $)) (SIGNATURE |mindegTerm| ((|Record| (|:| |k| (|OrderedFreeMonoid| |t#1|)) (|:| |c| |t#2|)) $)) (SIGNATURE |coef| (|t#2| $ (|OrderedFreeMonoid| |t#1|))) (SIGNATURE |coef| (|t#2| $ $)) (SIGNATURE |lquo| ($ $ |t#1|)) (SIGNATURE |lquo| ($ $ (|OrderedFreeMonoid| |t#1|))) (SIGNATURE |lquo| ($ $ $)) (SIGNATURE |rquo| ($ $ |t#1|)) (SIGNATURE |rquo| ($ $ (|OrderedFreeMonoid| |t#1|))) (SIGNATURE |rquo| ($ $ $)) (SIGNATURE |monom| ($ (|OrderedFreeMonoid| |t#1|) |t#2|)) (SIGNATURE |monomial?| ((|Boolean|) $)) (SIGNATURE |mirror| ($ $)) (SIGNATURE |coerce| ($ |t#1|)) (SIGNATURE |constant?| ((|Boolean|) $)) (SIGNATURE |constant| (|t#2| $)) (SIGNATURE |quasiRegular?| ((|Boolean|) $)) (SIGNATURE |quasiRegular| ($ $)) (IF (|has| |t#2| (|CommutativeRing|)) (PROGN (SIGNATURE |sh| ($ $ $)) (SIGNATURE |sh| ($ $ (|NonNegativeInteger|)))) |noBranch|) (SIGNATURE |map| ($ (|Mapping| |t#2| |t#2|) $)) (SIGNATURE |varList| ((|List| |t#1|) $)) (IF (|has| |t#2| (ATTRIBUTE |noZeroDivisors|)) (ATTRIBUTE |noZeroDivisors|) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#2|) |has| |#2| (|CommutativeRing|)) ((|BasicType|) . T) ((|BiModule| |#2| |#2|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| |#2|) . T) ((|LeftModule| $) . T) ((|Module| |#2|) |has| |#2| (|CommutativeRing|)) ((|Monoid|) . T) ((|RetractableTo| (|OrderedFreeMonoid| |#1|)) . T) ((|RightModule| |#2|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|XAlgebra| |#2|) . T)) 
((|transcendent?| (((|Boolean|) $) 13)) (|algebraic?| (((|Boolean|) $) 12)) (|Frobenius| (($ $) 17) (($ $ (|NonNegativeInteger|)) 18))) 
(((|ExtensionField&| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |Frobenius| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |Frobenius| (|#1| |#1|)) (SIGNATURE |transcendent?| ((|Boolean|) |#1|)) (SIGNATURE |algebraic?| ((|Boolean|) |#1|))) (|ExtensionField| |#2|) (|Field|)) (T |ExtensionField&|)) 
NIL 
(CATEGORY |domain| (SIGNATURE |Frobenius| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |Frobenius| (|#1| |#1|)) (SIGNATURE |transcendent?| ((|Boolean|) |#1|)) (SIGNATURE |algebraic?| ((|Boolean|) |#1|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 40)) (|unitCanonical| (($ $) 39)) (|unit?| (((|Boolean|) $) 37)) (|transcendent?| (((|Boolean|) $) 92)) (|transcendenceDegree| (((|NonNegativeInteger|)) 88)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|squareFreePart| (($ $) 73)) (|squareFree| (((|Factored| $) $) 72)) (|sizeLess?| (((|Boolean|) $ $) 58)) (|sample| (($) 16 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 99)) (|retract| ((|#1| $) 98)) (|rem| (($ $ $) 54)) (|recip| (((|Union| $ "failed") $) 33)) (|quo| (($ $ $) 55)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 50)) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) 85 (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|)))) (($ $) 84 (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|prime?| (((|Boolean|) $) 71)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 82 (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|one?| (((|Boolean|) $) 30)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 51)) (|lcmCoef| (((|Record| (|:| |llcmres| $) (|:| |coeff1| $) (|:| |coeff2| $)) $ $) 48)) (|lcm| (($ $ $) 45) (($ (|List| $)) 44)) (|latex| (((|String|) $) 9)) (|inv| (($ $) 70)) (|inGroundField?| (((|Boolean|) $) 91)) (|hash| (((|SingleInteger|) $) 10)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 43)) (|gcd| (($ $ $) 47) (($ (|List| $)) 46)) (|factor| (((|Factored| $) $) 74)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) 89)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 53) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 52)) (|exquo| (((|Union| $ "failed") $ $) 41)) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) 49)) (|euclideanSize| (((|NonNegativeInteger|) $) 57)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 56)) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) 83 (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|dimension| (((|CardinalNumber|)) 97)) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) 90)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ $) 42) (($ (|Fraction| (|Integer|))) 65) (($ |#1|) 100)) (|charthRoot| (((|Union| $ "failed") $) 81 (OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))))) (|characteristic| (((|NonNegativeInteger|)) 28)) (|associates?| (((|Boolean|) $ $) 38)) (|algebraic?| (((|Boolean|) $) 93)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32) (($ $ (|Integer|)) 69)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (|Frobenius| (($ $) 87 (|has| |#1| (|Finite|))) (($ $ (|NonNegativeInteger|)) 86 (|has| |#1| (|Finite|)))) (= (((|Boolean|) $ $) 6)) (/ (($ $ $) 64) (($ $ |#1|) 96)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31) (($ $ (|Integer|)) 68)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ $ (|Fraction| (|Integer|))) 67) (($ (|Fraction| (|Integer|)) $) 66) (($ $ |#1|) 95) (($ |#1| $) 94))) 
(((|ExtensionField| |#1|) (|Category|) (|Field|)) (T |ExtensionField|)) 
((|algebraic?| (*1 *2 *1) (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Boolean|)))) (|transcendent?| (*1 *2 *1) (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Boolean|)))) (|inGroundField?| (*1 *2 *1) (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Boolean|)))) (|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|OnePointCompletion| (|PositiveInteger|))))) (|extensionDegree| (*1 *2) (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|OnePointCompletion| (|PositiveInteger|))))) (|transcendenceDegree| (*1 *2) (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|Frobenius| (*1 *1 *1) (AND (|ofCategory| *1 (|ExtensionField| *2)) (|ofCategory| *2 (|Field|)) (|ofCategory| *2 (|Finite|)))) (|Frobenius| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|))))) 
(|Join| (|Field|) (|RetractableTo| |t#1|) (|VectorSpace| |t#1|) (CATEGORY |domain| (IF (|has| |t#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |noBranch|) (IF (|has| |t#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|FieldOfPrimeCharacteristic|)) |noBranch|) (SIGNATURE |algebraic?| ((|Boolean|) $)) (SIGNATURE |transcendent?| ((|Boolean|) $)) (SIGNATURE |inGroundField?| ((|Boolean|) $)) (SIGNATURE |degree| ((|OnePointCompletion| (|PositiveInteger|)) $)) (SIGNATURE |extensionDegree| ((|OnePointCompletion| (|PositiveInteger|)))) (SIGNATURE |transcendenceDegree| ((|NonNegativeInteger|))) (IF (|has| |t#1| (|Finite|)) (PROGN (ATTRIBUTE (|FieldOfPrimeCharacteristic|)) (SIGNATURE |Frobenius| ($ $)) (SIGNATURE |Frobenius| ($ $ (|NonNegativeInteger|)))) |noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| (|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) . T) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| |#1| (|Finite|)) (|has| |#1| (|CharacteristicNonZero|))) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|FieldOfPrimeCharacteristic|) OR (|has| |#1| (|Finite|)) (|has| |#1| (|CharacteristicNonZero|))) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftModule| (|Fraction| (|Integer|))) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LeftOreRing|) . T) ((|Module| (|Fraction| (|Integer|))) . T) ((|Module| |#1|) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RetractableTo| |#1|) . T) ((|RightModule| (|Fraction| (|Integer|))) . T) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|UniqueFactorizationDomain|) . T) ((|VectorSpace| |#1|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|varList| (((|List| |#1|) $) 84)) (|trunc| (($ $ (|NonNegativeInteger|)) 87)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sh| (($ $ $) NIL (|has| |#2| (|CommutativeRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#2| (|CommutativeRing|)))) (|sample| (($) NIL T CONST)) (|rquo| (($ $ |#1|) NIL) (($ $ (|OrderedFreeMonoid| |#1|)) NIL) (($ $ $) NIL)) (|retractIfCan| (((|Union| (|OrderedFreeMonoid| |#1|) "failed") $) NIL) (((|Union| (|PoincareBirkhoffWittLyndonBasis| |#1|) "failed") $) NIL)) (|retract| (((|OrderedFreeMonoid| |#1|) $) NIL) (((|PoincareBirkhoffWittLyndonBasis| |#1|) $) NIL)) (|reductum| (($ $) 86)) (|recip| (((|Union| $ "failed") $) NIL)) (|quasiRegular?| (((|Boolean|) $) 75)) (|quasiRegular| (($ $) 79)) (|product| (($ $ $ (|NonNegativeInteger|)) 88)) (|one?| (((|Boolean|) $) NIL)) (|numberOfMonomials| (((|NonNegativeInteger|) $) NIL)) (|monomials| (((|List| $) $) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) NIL) (($ (|PoincareBirkhoffWittLyndonBasis| |#1|) |#2|) 25)) (|mirror| (($ $) 101)) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) NIL)) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) NIL)) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) NIL)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL)) (|lquo| (($ $ |#1|) NIL) (($ $ (|OrderedFreeMonoid| |#1|)) NIL) (($ $ $) NIL)) (|log| (($ $ (|NonNegativeInteger|)) 95 (|has| |#2| (|Module| (|Fraction| (|Integer|)))))) (|listOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) NIL)) (|leadingTerm| (((|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|)) $) NIL)) (|leadingMonomial| (((|PoincareBirkhoffWittLyndonBasis| |#1|) $) 69)) (|leadingCoefficient| ((|#2| $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|exp| (($ $ (|NonNegativeInteger|)) 92 (|has| |#2| (|Module| (|Fraction| (|Integer|)))))) (|degree| (((|NonNegativeInteger|) $) 85)) (|constant?| (((|Boolean|) $) 70)) (|constant| ((|#2| $) 74)) (|coerce| (((|OutputForm|) $) 56) (($ (|Integer|)) NIL) (($ |#2|) 50) (($ (|OrderedFreeMonoid| |#1|)) NIL) (($ |#1|) 58) (($ (|PoincareBirkhoffWittLyndonBasis| |#1|)) NIL) (($ (|LiePolynomial| |#1| |#2|)) 42) (((|XDistributedPolynomial| |#1| |#2|) $) 63) (((|XRecursivePolynomial| |#1| |#2|) $) 68)) (|coefficients| (((|List| |#2|) $) NIL)) (|coefficient| ((|#2| $ (|PoincareBirkhoffWittLyndonBasis| |#1|)) NIL)) (|coef| ((|#2| $ (|OrderedFreeMonoid| |#1|)) NIL) ((|#2| $ $) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 21 T CONST)) (|One| (($) 24 T CONST)) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) 100)) (= (((|Boolean|) $ $) 64)) (- (($ $) 94) (($ $ $) 93)) (+ (($ $ $) 20)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 43) (($ |#2| $) 19) (($ $ |#2|) NIL) (($ |#1| $) NIL) (($ |#2| (|PoincareBirkhoffWittLyndonBasis| |#1|)) NIL))) 
(((|XPBWPolynomial| |#1| |#2|) (|Join| (|XPolynomialsCat| |#1| |#2|) (|FreeModuleCat| |#2| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|LiePolynomial| |#1| |#2|))) (SIGNATURE |coerce| ((|XDistributedPolynomial| |#1| |#2|) $)) (SIGNATURE |coerce| ((|XRecursivePolynomial| |#1| |#2|) $)) (SIGNATURE |LiePolyIfCan| ((|Union| (|LiePolynomial| |#1| |#2|) "failed") $)) (SIGNATURE |product| ($ $ $ (|NonNegativeInteger|))) (IF (|has| |#2| (|Module| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |exp| ($ $ (|NonNegativeInteger|))) (SIGNATURE |log| ($ $ (|NonNegativeInteger|)))) |noBranch|))) (|OrderedSet|) (|CommutativeRing|)) (T |XPBWPolynomial|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|LiePolynomial| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *1 (|XPBWPolynomial| *3 *4)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|XDistributedPolynomial| *3 *4)) (|isDomain| *1 (|XPBWPolynomial| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|XRecursivePolynomial| *3 *4)) (|isDomain| *1 (|XPBWPolynomial| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)))) (|LiePolyIfCan| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|LiePolynomial| *3 *4)) (|isDomain| *1 (|XPBWPolynomial| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)))) (|product| (*1 *1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|XPBWPolynomial| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)))) (|exp| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|XPBWPolynomial| *3 *4)) (|ofCategory| *4 (|Module| (|Fraction| (|Integer|)))) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)))) (|log| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|XPBWPolynomial| *3 *4)) (|ofCategory| *4 (|Module| (|Fraction| (|Integer|)))) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|))))) 
(|Join| (|XPolynomialsCat| |#1| |#2|) (|FreeModuleCat| |#2| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|LiePolynomial| |#1| |#2|))) (SIGNATURE |coerce| ((|XDistributedPolynomial| |#1| |#2|) $)) (SIGNATURE |coerce| ((|XRecursivePolynomial| |#1| |#2|) $)) (SIGNATURE |LiePolyIfCan| ((|Union| (|LiePolynomial| |#1| |#2|) "failed") $)) (SIGNATURE |product| ($ $ $ (|NonNegativeInteger|))) (IF (|has| |#2| (|Module| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |exp| ($ $ (|NonNegativeInteger|))) (SIGNATURE |log| ($ $ (|NonNegativeInteger|)))) |noBranch|))) 
((~= (((|Boolean|) $ $) 7)) (|zero?| (((|Boolean|) $) 15)) (|varList| (((|List| |#1|) $) 39)) (|trunc| (($ $ (|NonNegativeInteger|)) 68)) (|subtractIfCan| (((|Union| $ "failed") $ $) 18)) (|sh| (($ $ $) 42 (|has| |#2| (|CommutativeRing|))) (($ $ (|NonNegativeInteger|)) 41 (|has| |#2| (|CommutativeRing|)))) (|sample| (($) 16 T CONST)) (|rquo| (($ $ |#1|) 53) (($ $ (|OrderedFreeMonoid| |#1|)) 52) (($ $ $) 51)) (|retractIfCan| (((|Union| (|OrderedFreeMonoid| |#1|) "failed") $) 63)) (|retract| (((|OrderedFreeMonoid| |#1|) $) 62)) (|recip| (((|Union| $ "failed") $) 33)) (|quasiRegular?| (((|Boolean|) $) 44)) (|quasiRegular| (($ $) 43)) (|one?| (((|Boolean|) $) 30)) (|monomial?| (((|Boolean|) $) 49)) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) 50)) (|mirror| (($ $) 48)) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) 59)) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) 60)) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) 70)) (|map| (($ (|Mapping| |#2| |#2|) $) 40)) (|lquo| (($ $ |#1|) 56) (($ $ (|OrderedFreeMonoid| |#1|)) 55) (($ $ $) 54)) (|latex| (((|String|) $) 9)) (|hash| (((|SingleInteger|) $) 10)) (|degree| (((|NonNegativeInteger|) $) 69)) (|constant?| (((|Boolean|) $) 46)) (|constant| ((|#2| $) 45)) (|coerce| (((|OutputForm|) $) 11) (($ (|Integer|)) 27) (($ |#2|) 67) (($ (|OrderedFreeMonoid| |#1|)) 64) (($ |#1|) 47)) (|coef| ((|#2| $ (|OrderedFreeMonoid| |#1|)) 58) ((|#2| $ $) 57)) (|characteristic| (((|NonNegativeInteger|)) 28)) (^ (($ $ (|PositiveInteger|)) 25) (($ $ (|NonNegativeInteger|)) 32)) (|Zero| (($) 17 T CONST)) (|One| (($) 29 T CONST)) (= (((|Boolean|) $ $) 6)) (- (($ $) 21) (($ $ $) 20)) (+ (($ $ $) 13)) (** (($ $ (|PositiveInteger|)) 24) (($ $ (|NonNegativeInteger|)) 31)) (* (($ (|PositiveInteger|) $) 12) (($ (|NonNegativeInteger|) $) 14) (($ (|Integer|) $) 19) (($ $ $) 23) (($ |#2| $) 66) (($ $ |#2|) 65) (($ |#1| $) 61))) 
(((|XPolynomialsCat| |#1| |#2|) (|Category|) (|OrderedSet|) (|Ring|)) (T |XPolynomialsCat|)) 
((|maxdeg| (*1 *2 *1) (AND (|ofCategory| *1 (|XPolynomialsCat| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|OrderedFreeMonoid| *3)))) (|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|XPolynomialsCat| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|trunc| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|XPolynomialsCat| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))))) 
(|Join| (|XFreeAlgebra| |t#1| |t#2|) (CATEGORY |domain| (SIGNATURE |maxdeg| ((|OrderedFreeMonoid| |t#1|) $)) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |trunc| ($ $ (|NonNegativeInteger|))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#2|) |has| |#2| (|CommutativeRing|)) ((|BasicType|) . T) ((|BiModule| |#2| |#2|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftModule| |#2|) . T) ((|LeftModule| $) . T) ((|Module| |#2|) |has| |#2| (|CommutativeRing|)) ((|Monoid|) . T) ((|RetractableTo| (|OrderedFreeMonoid| |#1|)) . T) ((|RightModule| |#2|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|XAlgebra| |#2|) . T) ((|XFreeAlgebra| |#1| |#2|) . T)) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|varList| (((|List| (|Symbol|)) $) NIL)) (|unexpand| (($ (|XDistributedPolynomial| (|Symbol|) |#1|)) NIL)) (|trunc| (($ $ (|NonNegativeInteger|)) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sh| (($ $ $) NIL (|has| |#1| (|CommutativeRing|))) (($ $ (|NonNegativeInteger|)) NIL (|has| |#1| (|CommutativeRing|)))) (|sample| (($) NIL T CONST)) (|rquo| (($ $ (|Symbol|)) NIL) (($ $ (|OrderedFreeMonoid| (|Symbol|))) NIL) (($ $ $) NIL)) (|retractIfCan| (((|Union| (|OrderedFreeMonoid| (|Symbol|)) "failed") $) NIL)) (|retract| (((|OrderedFreeMonoid| (|Symbol|)) $) NIL)) (|recip| (((|Union| $ "failed") $) NIL)) (|quasiRegular?| (((|Boolean|) $) NIL)) (|quasiRegular| (($ $) NIL)) (|one?| (((|Boolean|) $) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monom| (($ (|OrderedFreeMonoid| (|Symbol|)) |#1|) NIL)) (|mirror| (($ $) NIL)) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| (|Symbol|))) (|:| |c| |#1|)) $) NIL)) (|mindeg| (((|OrderedFreeMonoid| (|Symbol|)) $) NIL)) (|maxdeg| (((|OrderedFreeMonoid| (|Symbol|)) $) NIL)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|lquo| (($ $ (|Symbol|)) NIL) (($ $ (|OrderedFreeMonoid| (|Symbol|))) NIL) (($ $ $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|expand| (((|XDistributedPolynomial| (|Symbol|) |#1|) $) NIL)) (|degree| (((|NonNegativeInteger|) $) NIL)) (|constant?| (((|Boolean|) $) NIL)) (|constant| ((|#1| $) NIL)) (|coerce| (((|OutputForm|) $) NIL) (($ (|Integer|)) NIL) (($ |#1|) NIL) (($ (|OrderedFreeMonoid| (|Symbol|))) NIL) (($ (|Symbol|)) NIL)) (|coef| ((|#1| $ (|OrderedFreeMonoid| (|Symbol|))) NIL) ((|#1| $ $) NIL)) (|characteristic| (((|NonNegativeInteger|)) NIL)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) NIL T CONST)) (|RemainderList| (((|List| (|Record| (|:| |k| (|Symbol|)) (|:| |c| $))) $) NIL)) (|One| (($) NIL T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) NIL) (($ |#1| $) NIL) (($ $ |#1|) NIL) (($ (|Symbol|) $) NIL))) 
(((|XPolynomial| |#1|) (|Join| (|XPolynomialsCat| (|Symbol|) |#1|) (CATEGORY |domain| (SIGNATURE |expand| ((|XDistributedPolynomial| (|Symbol|) |#1|) $)) (SIGNATURE |unexpand| ($ (|XDistributedPolynomial| (|Symbol|) |#1|))) (SIGNATURE |RemainderList| ((|List| (|Record| (|:| |k| (|Symbol|)) (|:| |c| $))) $)))) (|Ring|)) (T |XPolynomial|)) 
((|expand| (*1 *2 *1) (AND (|isDomain| *2 (|XDistributedPolynomial| (|Symbol|) *3)) (|isDomain| *1 (|XPolynomial| *3)) (|ofCategory| *3 (|Ring|)))) (|unexpand| (*1 *1 *2) (AND (|isDomain| *2 (|XDistributedPolynomial| (|Symbol|) *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|XPolynomial| *3)))) (|RemainderList| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |k| (|Symbol|)) (|:| |c| (|XPolynomial| *3))))) (|isDomain| *1 (|XPolynomial| *3)) (|ofCategory| *3 (|Ring|))))) 
(|Join| (|XPolynomialsCat| (|Symbol|) |#1|) (CATEGORY |domain| (SIGNATURE |expand| ((|XDistributedPolynomial| (|Symbol|) |#1|) $)) (SIGNATURE |unexpand| ($ (|XDistributedPolynomial| (|Symbol|) |#1|))) (SIGNATURE |RemainderList| ((|List| (|Record| (|:| |k| (|Symbol|)) (|:| |c| $))) $)))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sample| (($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) NIL)) (|retract| ((|#2| $) NIL)) (|reductum| (($ $) NIL)) (|recip| (((|Union| $ "failed") $) 34)) (|quasiRegular?| (((|Boolean|) $) 29)) (|quasiRegular| (($ $) 30)) (|one?| (((|Boolean|) $) NIL)) (|numberOfMonomials| (((|NonNegativeInteger|) $) NIL)) (|monomials| (((|List| $) $) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monom| (($ |#2| |#1|) NIL)) (|mindeg| ((|#2| $) 19)) (|maxdeg| ((|#2| $) 16)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL)) (|listOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) NIL)) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) NIL)) (|leadingMonomial| ((|#2| $) NIL)) (|leadingCoefficient| ((|#1| $) NIL)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|constant?| (((|Boolean|) $) 27)) (|constant| ((|#1| $) 28)) (|coerce| (((|OutputForm|) $) 53) (($ (|Integer|)) 38) (($ |#1|) 33) (($ |#2|) NIL)) (|coefficients| (((|List| |#1|) $) NIL)) (|coefficient| ((|#1| $ |#2|) NIL)) (|coef| ((|#1| $ |#2|) 24)) (|characteristic| (((|NonNegativeInteger|)) 14)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 25 T CONST)) (|One| (($) 11 T CONST)) (= (((|Boolean|) $ $) 26)) (/ (($ $ |#1|) 55 (|has| |#1| (|Field|)))) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) 42)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 44)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 43) (($ |#1| $) 39) (($ $ |#1|) NIL) (($ |#1| |#2|) NIL)) (|#| (((|NonNegativeInteger|) $) 15))) 
(((|XPolynomialRing| |#1| |#2|) (|Join| (|Ring|) (|XAlgebra| |#1|) (|FreeModuleCat| |#1| |#2|) (CATEGORY |domain| (SIGNATURE * ($ $ |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) $)) (SIGNATURE |coerce| ($ |#2|)) (SIGNATURE |maxdeg| (|#2| $)) (SIGNATURE |mindeg| (|#2| $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |coef| (|#1| $ |#2|)) (SIGNATURE |constant?| ((|Boolean|) $)) (SIGNATURE |constant| (|#1| $)) (SIGNATURE |quasiRegular?| ((|Boolean|) $)) (SIGNATURE |quasiRegular| ($ $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (IF (|has| |#1| (|Field|)) (SIGNATURE / ($ $ |#1|)) |noBranch|) (IF (|has| |#1| (ATTRIBUTE |noZeroDivisors|)) (ATTRIBUTE |noZeroDivisors|) |noBranch|) (IF (|has| |#1| (ATTRIBUTE |unitsKnown|)) (ATTRIBUTE |unitsKnown|) |noBranch|) (IF (|has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (ATTRIBUTE |canonicalUnitNormal|) |noBranch|))) (|Ring|) (|OrderedMonoid|)) (T |XPolynomialRing|)) 
((* (*1 *1 *1 *2) (AND (|isDomain| *1 (|XPolynomialRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedMonoid|)))) (|reductum| (*1 *1 *1) (AND (|isDomain| *1 (|XPolynomialRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedMonoid|)))) (|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|XPolynomialRing| *3 *4)) (|ofCategory| *4 (|OrderedMonoid|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *1 (|XPolynomialRing| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedMonoid|)))) (|#| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|XPolynomialRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedMonoid|)))) (|maxdeg| (*1 *2 *1) (AND (|ofCategory| *2 (|OrderedMonoid|)) (|isDomain| *1 (|XPolynomialRing| *3 *2)) (|ofCategory| *3 (|Ring|)))) (|mindeg| (*1 *2 *1) (AND (|ofCategory| *2 (|OrderedMonoid|)) (|isDomain| *1 (|XPolynomialRing| *3 *2)) (|ofCategory| *3 (|Ring|)))) (|coef| (*1 *2 *1 *3) (AND (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|XPolynomialRing| *2 *3)) (|ofCategory| *3 (|OrderedMonoid|)))) (|constant?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|XPolynomialRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedMonoid|)))) (|constant| (*1 *2 *1) (AND (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|XPolynomialRing| *2 *3)) (|ofCategory| *3 (|OrderedMonoid|)))) (|quasiRegular?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|XPolynomialRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedMonoid|)))) (|quasiRegular| (*1 *1 *1) (AND (|isDomain| *1 (|XPolynomialRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedMonoid|)))) (/ (*1 *1 *1 *2) (AND (|isDomain| *1 (|XPolynomialRing| *2 *3)) (|ofCategory| *2 (|Field|)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedMonoid|))))) 
(|Join| (|Ring|) (|XAlgebra| |#1|) (|FreeModuleCat| |#1| |#2|) (CATEGORY |domain| (SIGNATURE * ($ $ |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) $)) (SIGNATURE |coerce| ($ |#2|)) (SIGNATURE |maxdeg| (|#2| $)) (SIGNATURE |mindeg| (|#2| $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |coef| (|#1| $ |#2|)) (SIGNATURE |constant?| ((|Boolean|) $)) (SIGNATURE |constant| (|#1| $)) (SIGNATURE |quasiRegular?| ((|Boolean|) $)) (SIGNATURE |quasiRegular| ($ $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (IF (|has| |#1| (|Field|)) (SIGNATURE / ($ $ |#1|)) |noBranch|) (IF (|has| |#1| (ATTRIBUTE |noZeroDivisors|)) (ATTRIBUTE |noZeroDivisors|) |noBranch|) (IF (|has| |#1| (ATTRIBUTE |unitsKnown|)) (ATTRIBUTE |unitsKnown|) |noBranch|) (IF (|has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (ATTRIBUTE |canonicalUnitNormal|) |noBranch|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|varList| (((|List| |#1|) $) 119)) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) 43)) (|trunc| (($ $ (|NonNegativeInteger|)) 31)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|sh| (($ $ $) 47 (|has| |#2| (|CommutativeRing|))) (($ $ (|NonNegativeInteger|)) 45 (|has| |#2| (|CommutativeRing|)))) (|sample| (($) NIL T CONST)) (|rquo| (($ $ |#1|) 101) (($ $ (|OrderedFreeMonoid| |#1|)) 102) (($ $ $) 25)) (|retractIfCan| (((|Union| (|OrderedFreeMonoid| |#1|) "failed") $) NIL)) (|retract| (((|OrderedFreeMonoid| |#1|) $) NIL)) (|recip| (((|Union| $ "failed") $) 109)) (|quasiRegular?| (((|Boolean|) $) 104)) (|quasiRegular| (($ $) 105)) (|one?| (((|Boolean|) $) NIL)) (|monomial?| (((|Boolean|) $) NIL)) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) 19)) (|mirror| (($ $) NIL)) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) NIL)) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) 110)) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) 113)) (|map| (($ (|Mapping| |#2| |#2|) $) 118)) (|lquo| (($ $ |#1|) 99) (($ $ (|OrderedFreeMonoid| |#1|)) 100) (($ $ $) 55)) (|latex| (((|String|) $) NIL)) (|hash| (((|SingleInteger|) $) NIL)) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) 83)) (|degree| (((|NonNegativeInteger|) $) 116)) (|constant?| (((|Boolean|) $) 69)) (|constant| ((|#2| $) 27)) (|coerce| (((|OutputForm|) $) 62) (($ (|Integer|)) 76) (($ |#2|) 73) (($ (|OrderedFreeMonoid| |#1|)) 17) (($ |#1|) 72)) (|coef| ((|#2| $ (|OrderedFreeMonoid| |#1|)) 103) ((|#2| $ $) 26)) (|characteristic| (((|NonNegativeInteger|)) 107)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 14 T CONST)) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) 52)) (|One| (($) 28 T CONST)) (= (((|Boolean|) $ $) 13)) (- (($ $) 87) (($ $ $) 90)) (+ (($ $ $) 54)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 48)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) 46) (($ (|Integer|) $) 93) (($ $ $) 21) (($ |#2| $) 18) (($ $ |#2|) 20) (($ |#1| $) 81))) 
(((|XRecursivePolynomial| |#1| |#2|) (|Join| (|XPolynomialsCat| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |expand| ((|XDistributedPolynomial| |#1| |#2|) $)) (SIGNATURE |unexpand| ($ (|XDistributedPolynomial| |#1| |#2|))) (SIGNATURE |RemainderList| ((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $)))) (|OrderedSet|) (|Ring|)) (T |XRecursivePolynomial|)) 
((|expand| (*1 *2 *1) (AND (|isDomain| *2 (|XDistributedPolynomial| *3 *4)) (|isDomain| *1 (|XRecursivePolynomial| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)))) (|unexpand| (*1 *1 *2) (AND (|isDomain| *2 (|XDistributedPolynomial| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|XRecursivePolynomial| *3 *4)))) (|RemainderList| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Record| (|:| |k| *3) (|:| |c| (|XRecursivePolynomial| *3 *4))))) (|isDomain| *1 (|XRecursivePolynomial| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))))) 
(|Join| (|XPolynomialsCat| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |expand| ((|XDistributedPolynomial| |#1| |#2|) $)) (SIGNATURE |unexpand| ($ (|XDistributedPolynomial| |#1| |#2|))) (SIGNATURE |RemainderList| ((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $)))) 
((Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) 15) (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) 11))) 
(((|ParadoxicalCombinatorsForStreams| |#1|) (CATEGORY |package| (SIGNATURE Y ((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|)))) (SIGNATURE Y ((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)))) (|Type|)) (T |ParadoxicalCombinatorsForStreams|)) 
((Y (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| (|List| (|Stream| *5)) (|List| (|Stream| *5)))) (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|List| (|Stream| *5))) (|isDomain| *1 (|ParadoxicalCombinatorsForStreams| *5)) (|ofCategory| *5 (|Type|)))) (Y (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| (|Stream| *4) (|Stream| *4))) (|isDomain| *2 (|Stream| *4)) (|isDomain| *1 (|ParadoxicalCombinatorsForStreams| *4)) (|ofCategory| *4 (|Type|))))) 
(CATEGORY |package| (SIGNATURE Y ((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|)))) (SIGNATURE Y ((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)))) 
((|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) 145) (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) 144) (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) 143) (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) 142) (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) 127)) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) 70) (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) 69) (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) 68)) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) 59)) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) 112) (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) 111) (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) 110) (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) 109) (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) 104)) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) 117) (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) 116) (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) 115) (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) 114)) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) 96) (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) 87) (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) 94) (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) 92) (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) 32))) 
(((|ZeroDimensionalSolvePackage| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |triangSolve| ((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|))) (SIGNATURE |triangSolve| ((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|))) (SIGNATURE |triangSolve| ((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)))) (SIGNATURE |univariateSolve| ((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|))) (SIGNATURE |univariateSolve| ((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |univariateSolve| ((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|))) (SIGNATURE |univariateSolve| ((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|))) (SIGNATURE |univariateSolve| ((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)))) (SIGNATURE |realSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|))) (SIGNATURE |realSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |realSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|))) (SIGNATURE |realSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|))) (SIGNATURE |realSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)))) (SIGNATURE |positiveSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|))) (SIGNATURE |positiveSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|))) (SIGNATURE |positiveSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|))) (SIGNATURE |positiveSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)))) (SIGNATURE |squareFree| ((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|))) (SIGNATURE |convert| ((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (SIGNATURE |convert| ((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|))) (SIGNATURE |convert| ((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (SIGNATURE |convert| ((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |convert| ((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))))) (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|)) (|List| (|Symbol|)) (|List| (|Symbol|))) (T |ZeroDimensionalSolvePackage|)) 
((|convert| (*1 *2 *3) (AND (|isDomain| *3 (|SquareFreeRegularTriangularSet| *4 (|IndexedExponents| (|OrderedVariableList| *6)) (|OrderedVariableList| *6) (|NewSparseMultivariatePolynomial| *4 (|OrderedVariableList| *6)))) (|ofCategory| *4 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|ofType| *6 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|NewSparseMultivariatePolynomial| *4 (|OrderedVariableList| *6)))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6)) (|ofType| *5 (|List| (|Symbol|))))) (|convert| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *4)) (|ofCategory| *4 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|isDomain| *2 (|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| *4)))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6)) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|List| (|Symbol|))))) (|convert| (*1 *2 *3) (AND (|isDomain| *3 (|NewSparseMultivariatePolynomial| *4 (|OrderedVariableList| *6))) (|ofCategory| *4 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|ofType| *6 (|List| (|Symbol|))) (|isDomain| *2 (|Polynomial| (|RealClosure| (|Fraction| *4)))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6)) (|ofType| *5 (|List| (|Symbol|))))) (|convert| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| *4)) (|ofCategory| *4 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|isDomain| *2 (|Polynomial| (|RealClosure| (|Fraction| *4)))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6)) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|List| (|Symbol|))))) (|convert| (*1 *2 *3) (AND (|isDomain| *3 (|NewSparseMultivariatePolynomial| *4 (|OrderedVariableList| *5))) (|ofCategory| *4 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|ofType| *5 (|List| (|Symbol|))) (|isDomain| *2 (|NewSparseMultivariatePolynomial| *4 (|OrderedVariableList| *6))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6)) (|ofType| *6 (|List| (|Symbol|))))) (|squareFree| (*1 *2 *3) (AND (|isDomain| *3 (|RegularChain| *4 *5)) (|ofCategory| *4 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|ofType| *5 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|SquareFreeRegularTriangularSet| *4 (|IndexedExponents| (|OrderedVariableList| *6)) (|OrderedVariableList| *6) (|NewSparseMultivariatePolynomial| *4 (|OrderedVariableList| *6))))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6)) (|ofType| *6 (|List| (|Symbol|))))) (|positiveSolve| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Polynomial| *4))) (|ofCategory| *4 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *4))))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6)) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|List| (|Symbol|))))) (|positiveSolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *5))))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7)) (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|))))) (|positiveSolve| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *5))))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7)) (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|))))) (|positiveSolve| (*1 *2 *3) (AND (|isDomain| *3 (|RegularChain| *4 *5)) (|ofCategory| *4 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|ofType| *5 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *4))))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6)) (|ofType| *6 (|List| (|Symbol|))))) (|realSolve| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Polynomial| *4))) (|ofCategory| *4 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *4))))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6)) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|List| (|Symbol|))))) (|realSolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *5))))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7)) (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|))))) (|realSolve| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *5))))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7)) (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|))))) (|realSolve| (*1 *2 *3 *4 *4 *4) (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *5))))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7)) (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|))))) (|realSolve| (*1 *2 *3) (AND (|isDomain| *3 (|RegularChain| *4 *5)) (|ofCategory| *4 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|ofType| *5 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *4))))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6)) (|ofType| *6 (|List| (|Symbol|))))) (|univariateSolve| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|isDomain| *2 (|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *4)) (|:| |coordinates| (|List| (|Polynomial| *4)))))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6)) (|isDomain| *3 (|List| (|Polynomial| *4))) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|List| (|Symbol|))))) (|univariateSolve| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|isDomain| *2 (|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *5)) (|:| |coordinates| (|List| (|Polynomial| *5)))))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7)) (|isDomain| *3 (|List| (|Polynomial| *5))) (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|))))) (|univariateSolve| (*1 *2 *3 *4 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|isDomain| *2 (|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *5)) (|:| |coordinates| (|List| (|Polynomial| *5)))))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7)) (|isDomain| *3 (|List| (|Polynomial| *5))) (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|))))) (|univariateSolve| (*1 *2 *3 *4 *4 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|isDomain| *2 (|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *5)) (|:| |coordinates| (|List| (|Polynomial| *5)))))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7)) (|isDomain| *3 (|List| (|Polynomial| *5))) (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|))))) (|univariateSolve| (*1 *2 *3) (AND (|isDomain| *3 (|RegularChain| *4 *5)) (|ofCategory| *4 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|ofType| *5 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *4)) (|:| |coordinates| (|List| (|Polynomial| *4)))))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6)) (|ofType| *6 (|List| (|Symbol|))))) (|triangSolve| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Polynomial| *4))) (|ofCategory| *4 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|isDomain| *2 (|List| (|RegularChain| *4 *5))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6)) (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|List| (|Symbol|))))) (|triangSolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|isDomain| *2 (|List| (|RegularChain| *5 *6))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7)) (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|))))) (|triangSolve| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) (|isDomain| *2 (|List| (|RegularChain| *5 *6))) (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7)) (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|)))))) 
(CATEGORY |package| (SIGNATURE |triangSolve| ((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|))) (SIGNATURE |triangSolve| ((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|))) (SIGNATURE |triangSolve| ((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)))) (SIGNATURE |univariateSolve| ((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|))) (SIGNATURE |univariateSolve| ((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |univariateSolve| ((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|))) (SIGNATURE |univariateSolve| ((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|))) (SIGNATURE |univariateSolve| ((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)))) (SIGNATURE |realSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|))) (SIGNATURE |realSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|))) (SIGNATURE |realSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|))) (SIGNATURE |realSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|))) (SIGNATURE |realSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)))) (SIGNATURE |positiveSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|))) (SIGNATURE |positiveSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|))) (SIGNATURE |positiveSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|))) (SIGNATURE |positiveSolve| ((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)))) (SIGNATURE |squareFree| ((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|))) (SIGNATURE |convert| ((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (SIGNATURE |convert| ((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|))) (SIGNATURE |convert| ((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (SIGNATURE |convert| ((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |convert| ((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))))) 
((|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) 17)) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) 11)) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) 14))) 
(((|IntegerLinearDependence| |#1|) (CATEGORY |package| (SIGNATURE |linearlyDependentOverZ?| ((|Boolean|) (|Vector| |#1|))) (SIGNATURE |linearDependenceOverZ| ((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|))) (SIGNATURE |solveLinearlyOverQ| ((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|))) (|LinearlyExplicitRingOver| (|Integer|))) (T |IntegerLinearDependence|)) 
((|solveLinearlyOverQ| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Vector| *4)) (|ofCategory| *4 (|LinearlyExplicitRingOver| (|Integer|))) (|isDomain| *2 (|Vector| (|Fraction| (|Integer|)))) (|isDomain| *1 (|IntegerLinearDependence| *4)))) (|linearDependenceOverZ| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|Vector| *4)) (|ofCategory| *4 (|LinearlyExplicitRingOver| (|Integer|))) (|isDomain| *2 (|Vector| (|Integer|))) (|isDomain| *1 (|IntegerLinearDependence| *4)))) (|linearlyDependentOverZ?| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *4)) (|ofCategory| *4 (|LinearlyExplicitRingOver| (|Integer|))) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|IntegerLinearDependence| *4))))) 
(CATEGORY |package| (SIGNATURE |linearlyDependentOverZ?| ((|Boolean|) (|Vector| |#1|))) (SIGNATURE |linearDependenceOverZ| ((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|))) (SIGNATURE |solveLinearlyOverQ| ((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|))) 
((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 11)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|size| (((|NonNegativeInteger|)) 8)) (|sample| (($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) 43)) (|random| (($) 36)) (|one?| (((|Boolean|) $) NIL)) (|nextItem| (((|Union| $ "failed") $) 29)) (|lookup| (((|PositiveInteger|) $) 15)) (|latex| (((|String|) $) NIL)) (|init| (($) 25 T CONST)) (|index| (($ (|PositiveInteger|)) 37)) (|hash| (((|SingleInteger|) $) NIL)) (|enumerate| (((|List| $)) NIL)) (|convert| (((|Integer|) $) 13)) (|coerce| (((|OutputForm|) $) 22) (($ (|Integer|)) 19)) (|characteristic| (((|NonNegativeInteger|)) 9)) (^ (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) NIL)) (|Zero| (($) 23 T CONST)) (|One| (($) 24 T CONST)) (= (((|Boolean|) $ $) 27)) (- (($ $) 38) (($ $ $) 35)) (+ (($ $ $) 26)) (** (($ $ (|PositiveInteger|)) NIL) (($ $ (|NonNegativeInteger|)) 40)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) 32) (($ $ $) 31))) 
(((|IntegerMod| |#1|) (|Join| (|CommutativeRing|) (|Finite|) (|ConvertibleTo| (|Integer|)) (|StepThrough|)) (|PositiveInteger|)) (T |IntegerMod|)) 
NIL 
(|Join| (|CommutativeRing|) (|Finite|) (|ConvertibleTo| (|Integer|)) (|StepThrough|)) 
NIL 
NIL 
NIL 
NIL 
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258918 T ATRUNIT (NIL) |category| NIL NIL) (|ArcTrigonometricFunctionCategory| 257990 258109 258203 "ATRIG" 258656 T ATRIG (NIL) |category| NIL NIL) (|ArcTrigonometricFunctionCategory&| 257652 257695 257902 "ATRIG-" 257907 NIL ATRIG- (NIL T) |domain| NIL NIL) (|PartiallyOrderedSetAttribute| 257507 257512 257598 "ATPOSET" 257603 T ATPOSET (NIL) |category| NIL NIL) (|NoZeroDivisorsAttribute| 257372 257377 257453 "ATNZDIV" 257458 T ATNZDIV (NIL) |category| NIL NIL) (|NullSquareAttribute| 257245 257250 257318 "ATNULSQ" 257323 T ATNULSQ (NIL) |category| NIL NIL) (|NotherianAttribute| 257120 257125 257191 "ATNOTHR" 257196 T ATNOTHR (NIL) |category| NIL NIL) (|MultiplicativeValuationAttribute| 256967 256972 257066 "ATMULVA" 257071 T ATMULVA (NIL) |category| NIL NIL) (|LeftUnitaryAttribute| 256838 256843 256913 "ATLUNIT" 256918 T ATLUNIT (NIL) |category| NIL NIL) (|LazyRepresentationAttribute| 256695 256700 256784 "ATLR" 256789 T ATLR (NIL) |category| NIL NIL) (|JacobiIdentityAttribute| 256560 256565 256641 "ATJACID" 256646 T ATJACID (NIL) |category| NIL NIL) (|FiniteAggregateAttribute| 256423 256428 256506 "ATFINAG" 256511 T ATFINAG (NIL) |category| NIL NIL) (|CanonicalUnitNormalAttribute| 256278 256283 256369 "ATCUNOR" 256374 T ATCUNOR (NIL) |category| NIL NIL) (|CommutativeStarAttribute| 256141 256146 256224 "ATCS" 256229 T ATCS (NIL) |category| NIL NIL) (|CentralAttribute| 256020 256025 256087 "ATCENRL" 256092 T ATCENRL (NIL) |category| NIL NIL) (|CanonicalAttribute| 255895 255900 255966 "ATCANON" 255971 T ATCANON (NIL) |category| NIL NIL) (|CanonicalClosedAttribute| 255758 255763 255841 "ATCANCL" 255846 T ATCANCL (NIL) |category| NIL NIL) (|ArbitraryPrecisionAttribute| 255615 255620 255704 "ATARBPR" 255709 T ATARBPR (NIL) |category| NIL NIL) (|ArbitraryExponentAttribute| 255474 255479 255561 "ATARBEX" 255566 T ATARBEX (NIL) |category| NIL NIL) (|ApproximateAttribute| 255345 255350 255420 "ATAPPRO" 255425 T ATAPPRO (NIL) |category| NIL NIL) (|AdditiveValuationAttribute| 255204 255209 255291 "ATADDVA" 255296 T ATADDVA (NIL) |category| NIL NIL) (|ArrayStack| 245017 247184 248909 "ASTACK" 253536 NIL ASTACK (NIL T) |domain| NIL NIL) (|AssociatedEquations| 242420 242868 243501 "ASSOCEQ" 244519 NIL ASSOCEQ (NIL T T) |package| NIL NIL) (|Asp9| 240912 241853 242063 "ASP9" 242250 NIL ASP9 (NIL NIL) |domain| NIL NIL) (|Asp8| 240546 240813 240880 "ASP8" 240885 NIL ASP8 (NIL NIL) |domain| NIL NIL) (|Asp80| 238781 239886 240130 "ASP80" 240344 NIL ASP80 (NIL NIL) |domain| NIL NIL) (|Asp7| 237080 238169 238396 "ASP7" 238594 NIL ASP7 (NIL NIL) |domain| NIL NIL) (|Asp78| 235417 236495 236714 "ASP78" 236903 NIL ASP78 (NIL NIL) |domain| NIL NIL) (|Asp77| 233753 234832 235051 "ASP77" 235240 NIL ASP77 (NIL NIL) |domain| NIL NIL) (|Asp74| 232049 233138 233367 "ASP74" 233566 NIL ASP74 (NIL NIL) |domain| NIL NIL) (|Asp73| 230347 231434 231663 "ASP73" 231862 NIL ASP73 (NIL NIL) |domain| NIL NIL) (|Asp6| 228686 229765 229982 "ASP6" 230170 NIL ASP6 (NIL NIL) |domain| NIL NIL) (|Asp55| 227016 228101 228320 "ASP55" 228509 NIL ASP55 (NIL NIL) |domain| NIL NIL) (|Asp50| 225347 226428 226648 "ASP50" 226838 NIL ASP50 (NIL NIL) |domain| NIL NIL) (|Asp4| 223879 224810 225010 "ASP4" 225187 NIL ASP4 (NIL NIL) |domain| NIL NIL) (|Asp49| 222408 223339 223541 "ASP49" 223719 NIL ASP49 (NIL NIL) |domain| NIL NIL) (|Asp42| 220552 221663 221938 "ASP42" 222207 NIL ASP42 (NIL NIL NIL NIL) |domain| NIL NIL) (|Asp41| 218705 219813 220086 "ASP41" 220353 NIL ASP41 (NIL NIL NIL NIL) |domain| NIL NIL) (|Asp35| 217038 218120 218339 "ASP35" 218528 NIL ASP35 (NIL NIL) |domain| NIL NIL) (|Asp34| 216670 216937 217006 "ASP34" 217011 NIL ASP34 (NIL NIL) |domain| NIL NIL) (|Asp33| 216222 216314 216455 "ASP33" 216571 NIL ASP33 (NIL NIL) |domain| NIL NIL) (|Asp31| 214515 215607 215836 "ASP31" 216035 NIL ASP31 (NIL NIL) |domain| NIL NIL) (|Asp30| 214147 214414 214483 "ASP30" 214488 NIL ASP30 (NIL NIL) |domain| NIL NIL) (|Asp29| 213697 213791 213932 "ASP29" 214048 NIL ASP29 (NIL NIL) |domain| NIL NIL) (|Asp28| 213329 213596 213665 "ASP28" 213670 NIL ASP28 (NIL NIL) |domain| NIL NIL) (|Asp27| 212961 213228 213297 "ASP27" 213302 NIL ASP27 (NIL NIL) |domain| NIL NIL) (|Asp24| 211486 212418 212621 "ASP24" 212800 NIL ASP24 (NIL NIL) |domain| NIL NIL) (|Asp20| 209768 210862 211094 "ASP20" 211296 NIL ASP20 (NIL NIL) |domain| NIL NIL) (|Asp1| 208300 209231 209431 "ASP1" 209608 NIL ASP1 (NIL NIL) |domain| NIL NIL) (|Asp19| 206625 207712 207932 "ASP19" 208122 NIL ASP19 (NIL NIL) |domain| NIL NIL) (|Asp12| 206177 206269 206410 "ASP12" 206526 NIL ASP12 (NIL NIL) |domain| NIL NIL) (|Asp10| 204411 205514 205759 "ASP10" 205974 NIL ASP10 (NIL NIL) |domain| NIL NIL) (|TwoDimensionalArray| 201270 204024 204249 "ARRAY2" 204254 NIL ARRAY2 (NIL T) |domain| NIL NIL) (|OneDimensionalArray| 195159 200535 200789 "ARRAY1" 201084 NIL ARRAY1 (NIL T) |domain| NIL NIL) (|OneDimensionalArrayFunctions2| 193375 193663 194087 "ARRAY12" 194837 NIL ARRAY12 (NIL T T) |package| NIL NIL) (|TwoDimensionalArrayCategory| 183671 186279 186451 "ARR2CAT" 191766 NIL ARR2CAT (NIL T T T) |category| NIL 192975) (|TwoDimensionalArrayCategory&| 179838 180860 182368 "ARR2CAT-" 182373 NIL ARR2CAT- (NIL T T T T) |domain| NIL NIL) (|ApplyRules| 177722 177928 178437 "APPRULE" 179583 NIL APPRULE (NIL T T T) |package| NIL NIL) (|ApplyUnivariateSkewPolynomial| 177093 177150 177391 "APPLYORE" 177641 NIL APPLYORE (NIL T T T) |package| NIL NIL) (|ApplicationProgramInterface| 175651 175869 176201 "API" 176831 T API (NIL) |package| NIL NIL) (|Any| 174083 174471 174795 "ANY" 175349 T ANY (NIL) |domain| NIL NIL) (|AnyFunctions1| 172933 173099 173360 "ANY1" 173878 NIL ANY1 (NIL T) |package| NIL NIL) (|AntiSymm| 169143 170384 170948 "ANTISYM" 172440 NIL ANTISYM (NIL T NIL) |domain| NIL NIL) (|AnonymousFunction| 168892 169054 169121 "ANON" 169126 T ANON (NIL) |domain| NIL NIL) (|AlgebraicNumber| 159460 165887 166849 "AN" 167976 T AN (NIL) |domain| NIL NIL) (|AbelianMonoidRing| 153584 155485 155593 "AMR" 157017 NIL AMR (NIL T T) |category| NIL 157953) (|AbelianMonoidRing&| 152263 152558 153135 "AMR-" 153140 NIL AMR- (NIL T T T) |domain| NIL NIL) (|AssociationList| 131828 152090 152218 "ALIST" 152223 NIL ALIST (NIL T T) |domain| NIL NIL) (|AlgebraGivenByStructuralConstants| 127001 131087 131416 "ALGSC" 131678 NIL ALGSC (NIL T NIL NIL NIL) |domain| NIL NIL) (|AlgebraPackage| 120277 121187 122332 "ALGPKG" 125966 NIL ALGPKG (NIL T T) |package| NIL NIL) (|AlgebraicMultFact| 118768 118962 119357 "ALGMFACT" 120043 NIL ALGMFACT (NIL T T T) |package| NIL NIL) (|AlgebraicManipulations| 111091 112039 113114 "ALGMANIP" 118067 NIL ALGMANIP (NIL T T) |package| NIL NIL) (|AlgebraicFunctionField| 97882 110316 110634 "ALGFF" 110957 NIL ALGFF (NIL T T T NIL) |domain| NIL NIL) (|AlgFactor| 96410 96599 96930 "ALGFACT" 97643 NIL ALGFACT (NIL T) |package| NIL NIL) (|Algebra| 94976 95767 95836 "ALGEBRA" 95938 NIL ALGEBRA (NIL T) |category| NIL 96025) (|Algebra&| 94543 94618 94834 "ALGEBRA-" 94839 NIL ALGEBRA- (NIL T T) |domain| NIL NIL) (|AssociationListAggregate| 70289 91056 91176 "ALAGG" 91399 NIL ALAGG (NIL T T) |category| |AssociationList| 91625) (|ArcHyperbolicFunctionCategory| 69449 69574 69662 "AHYP" 70103 T AHYP (NIL) |category| NIL NIL) (|Aggregate| 67687 68056 68104 "AGG" 68958 T AGG (NIL) |category| NIL 69431) (|Aggregate&| 66746 66993 67365 "AGG-" 67370 NIL AGG- (NIL T) |domain| NIL NIL) (|AffineSpaceCategory| 62636 63427 63510 "AFSPCAT" 65807 NIL AFSPCAT (NIL T) |category| NIL 66632) (|AlgebraicFunction| 58425 59087 59831 "AF" 62018 NIL AF (NIL T T) |package| NIL NIL) (|AffineSpace| 57480 58279 58390 "AFFSP" 58395 NIL AFFSP (NIL NIL T) |domain| NIL NIL) (|AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| 56013 57190 57405 "AFFPLPS" 57410 NIL AFFPLPS (NIL T) |domain| NIL NIL) (|AffinePlane| 55078 55895 55978 "AFFPL" 55983 NIL AFFPL (NIL T) |domain| NIL NIL) (|AffineAlgebraicSetComputeWithResultant| 48512 49389 50647 "AFALGRES" 54122 NIL AFALGRES (NIL T NIL T T T) |package| NIL NIL) (|AffineAlgebraicSetComputeWithGroebnerBasis| 45978 46239 46844 "AFALGGRO" 48217 NIL AFALGGRO (NIL T NIL T T T) |package| NIL NIL) (|PlaneAlgebraicCurvePlot| 44687 45081 45400 "ACPLOT" 45721 T ACPLOT (NIL) |domain| NIL NIL) (|AlgebraicallyClosedFunctionSpace| 28628 39906 40048 "ACFS" 41463 NIL ACFS (NIL T) |category| |Expression| 41846) (|AlgebraicallyClosedFunctionSpace&| 25328 26092 27446 "ACFS-" 27451 NIL ACFS- (NIL T T) |domain| NIL NIL) (|AlgebraicallyClosedField| 18951 21835 21913 "ACF" 23646 T ACF (NIL) |category| NIL 24442) (|AlgebraicallyClosedField&| 16600 17188 18117 "ACF-" 18122 NIL ACF- (NIL T) |domain| NIL NIL) (|AbelianSemiGroup| 15981 16189 16251 "ABELSG" 16410 T ABELSG (NIL) |category| NIL 16518) (|AbelianSemiGroup&| 15728 15766 15909 "ABELSG-" 15914 NIL ABELSG- (NIL T) |domain| NIL NIL) (|AbelianMonoid| 14733 15060 15116 "ABELMON" 15417 T ABELMON (NIL) |category| NIL 15619) (|AbelianMonoid&| 14172 14295 14545 "ABELMON-" 14550 NIL ABELMON- (NIL T) |domain| NIL NIL) (|AbelianGroup| 13194 13622 13676 "ABELGRP" 13869 T ABELGRP (NIL) |category| NIL 14003) (|AbelianGroup&| 12401 12575 12914 "ABELGRP-" 12919 NIL ABELGRP- (NIL T) |domain| NIL NIL) (|OneDimensionalArrayAggregate| 6156 11366 11466 "A1AGG" 11471 NIL A1AGG (NIL T) |category| NIL 11565) (|OneDimensionalArrayAggregate&| 30 1630 3956 "A1AGG-" 3961 NIL A1AGG- (NIL T T) |domain| NIL NIL))